THE FORM AND SENSE OF VIDEO artscanada, 1973

Robert Arn

How then, if formal characteristics are so im- lessly walking, created Man With a Movie portant, are we to explain the assumption that Camera and revealed the new possibilities open television is like filrn~ Or the almost total ab- to man's cinextcnded perception . He called this sence, after more than 20 years, of formal des- mechanically extended perception "cinc eye." criptions of the television process ~ The answers Through his viewfinder Vertov saw space ex- are mostly to be found in economic and social pand and contract and perspective shift with rather than artistic history and need not concern lens change. He found that time was under his us here. The fact remains that to date, television control : crank the camera a little faster and it all both in production and viewing has been domi- slowed down. Film allowed man to experience nated by the conventions and assumptions of what was hitherto beyond his perception - the narrative film. It is criticized in terms ofcontent malleability ofspace and time. However, others ofthe crudest narrative or logical type. Which is realized the corollary: to say that filtn extends odd, since very few who regard television in this perception is the same, in one sense, as saying limited way would chance interpreting film that it distorts perception. Current followers of purely in terms of the narrative conventions of Vertov - sayJean-Luc Godard andJim McBride the novel. - maintain a reflexive commentary in their films From the first, film has been perceived on the distortions of reality introduced by the practically, critically, and theoretically by those filming process and our conditioned expecta- whose interest is primarily narrative or content- tions ofit. In fact, the illusion of reality is only related, or by those who see its process as open- achieved by relatively large distortions ofactual- ing new forms ofperception to the audience and ity. Vertov tells us what now seems obvious - thus new fields ofexpression to the artist . But of that the matter of film is the manipulation of course film did not safer from a flight of intel- time and space. lectuals at its birth. Born in the Constructivist Intuitively, one might expect the manipula- period oftechnological optimism, it was imme- tion of time to be the dominant formal charac- diately the focus ofintellectual attention, while teristic offilm - the illusion of movement after television even now faces a technological para- all is its primary difference from mere photo- noia which has blocked serious conceptual study graphy, and its primary use is in dramatic ofits formal characteristics and has thus enforced narrative which exists (barring several attempts an artistic triviality as profound as its social im- at Aristotelian temporal unity such as Agnes pact. However, even film criticism is shaky in Varda's Cleo de 5 a' 7) by tricking the time sense. some of its formal descriptions ; some miscon- Intuition is a bad guide in this case, however, ceptions about the filtnic treatment of time will since such a system of temporal illusion is the need to be righted before we can reach an ade- basis of all narrative art whatever . Much more quate formal description ofvideo (or television- to the point is the question of how film differs as-an-art-form). from other forms in its use oftime. Film's most In 1924 film was new and fascinated with characteristic means of temporal manipulation, itself. Dziga Vertov, out with his camera end- parallel editing (The Maiden on the Railway

183 EIGENWELT DER APPARATEWELT

Track Rescue at Hand, phenomenon ; or, Mean- vintage Eisensteinian montage. Most video ar- while Back at the Ranch) is not intrinsic to film tists who create such work support themselves at all but derived from the Dickensian novel by by producing documentary tapes for business Griffith and developed by Eisenstein. It, like and organizations who demand film-like prod- most other conventions of film editing, is neces- ucts; and I suspect film conventions inevitably sary to all flexible narrative forms and is found creep over into their other work. Now when I equally in most. The most purely filmic distor- see video oftraditional film editing style it seems tion of time - slow or fast motion - is seldom slightly out of place. The critics' dileinma : how used and relatively obtrusive, a "tic" of certain to avoid seeing "different" as "inferior." directors and penchant of the inexperienced. In film the impression ofmovement is derived The basic problem of film editing is easily from a succession of frozen moments. In con- stated - what shot to use next? Eisenstein saw trast, the video image, even if each fraine is that the decision was not a purely narrative or examined, is all motion. Even a still video iinagc temporal one - that certain shots "worked" and is in motion - a single rapidly moving and some did not and that this was determined not constantly clianging dot, one dot only, does all by narrative sequence but by the graphic, com- the work. The basic illusion of film is motiorr. positional relationships ofconsecutive shots: ed- The basic illusion of video is stillness. A detail of iting sequence follows spatial relationship . Thus, the video image may be located by pointing out though film does inevitably alter both time and where it is (as in film), but also by specifying space, it is primarily space art. A visual Marxist its distance in time from any other point of the like Eisenstein cut for graphic conflict while image. Any point on the image is both "where" most directors cut for graphic similarity to and "when" or "whercwhen" from any other achieve smooth continuity. But composition point. Video is quite literally a space/time rules the cut. Graphic space orders time. machine. In this context the lack of the simple Video art, in contrast to film (and also to tele- juxtaposition of shots characteristic of film vision which is mostly a feeble narrative reflec- editing is more comprehensible. Continuous tion of film), has suffered an arrested develop- motion or metamorphosis is the continuity line ment. After 25 years of television, video art is of most video art ; an art of becoming rather entering its adolescence - still looking for its than comparison, an art oftime. Dziga Vertov and vainly awaiting its Eisenstein. Before exploring in more detail the space/ Like film in its earliest period, video is in a phase time nature of video and its implications in the of self-examination or perhaps narcissism, ab- work of video artists, some of the ways video sorbed in its own processes. The difficulty for the resembles film in its processing o£ reality should viewer is the, fact that these processes - so super- be considered . Godard has said that film is the ficially like those offilm - are really quite differ- truth 24 times a second, which is to say that it is ent; and the responses we bring to film are in- a lie - unless truth really happens at that fre- adequate and deceptive in relation to video. For quency. Video, then, is a lie 30 frames per example, for a long time I thought that the ap- second, or rather 60 "fields" a second since each parently clumsy editing of video pieces was a frame consists of two alternate fields of scan mere function of the mechanical difficulties of lines.' The intermittent nature of both film and editing with existing equipment. The low-cost 1/2' and 1" tape recording equipment used by most artists does display its instability particu- larly in editing. But I now suspect that I have "The repetition rate of video is not determinedjust by been applying expectations derived from film, the persistence of vision but also by theline frequency where spatial graphic continuity determines ed- ofthe electrical power-lines. Hence in North America film on video runs six frames per second faster than in iting, to video whose space/time structure makes the theater- but in Europeit runs the same speed, such criteria meaningless. Classic editing tecluu- since the power-line frequency of 50 cycles per second dtte is to be found among video artists. Andy gives 25 fraines per second, which is equal to the established European tine-camera speed. Mann, for instance, produces tapes of almost

184 ROBERT ARN video gives rise to the stagecoach wheel plie- own problems seriously and actively after they nouicnon, or "strobing." Combine two periodic have been assured of their own reality by seeing motions and you get an apparent motion pro- themselves on television. Such image/reality portional to the difference in rates. We have inversions are not unique to video. What writer accepted this distortion in relation to rotary mo- has not felt his self-image enhanced by seeing tion, but cameramen arc careful with panning his work in print and tilting rates across vertically or horizontally The ability of video to overwhelm our other barred fields to avoid strobing effects that might reality indices is demonstrated by experiments destroy the illusion ofreality . that require subjects to perform simple tactile In both film and video, achieving realistic tasks while watching a slightly delayed recorded color requires some distortion of actuality and image of the action . Total confusion is the usual here we find a phenomenon of art that would result. Even when one can feel an object, the have delighted Yeats. Video has become so image of the object is convincing enough to widespread that public reality is modifying make us doubt our tactile sense. In the wider itself so as to look "real" on television. The context ofsocial response, few people who have announcer's blue shirt was just the beginning. seen a studio television production with live The decor of almost all public events is now audience have failed to notice the audience pre- chosen with an eye to the sensitivity of cathode ference for watching the action on the studio ray tubes. The line /scan of the video picture is monitors even though the original is immedi- also an important factor in this context. Hori- ately before them. Two notable pieces recently zontal stripes have almost disappeared from shown in Toronto demonstrate video artists' public life since they react with the scan lines or concern with the power of their medium to "raster" on television to produce a disturbing dominate reality ; both share a major metaphor more. A reality which cannot be comfortably indicating a basic distrust of such domination. facsimiled on television tends to drop out of Elsa Tambellini's piece Cats, shown at the inter- public life. nationalfestival ofwomen andfilm portrays caged The nexus ofimage/reality is the catalyst ofa tigers pacing nervously behind 300 bars. Live whole branch of video art that might mis- performers shooting each other with closed cir- leadingly be called documentary, but is, I cuit cameras and finally stringing rope bars be- Suspect closer to some sort of reality repair. tween the audience and its own picture on mon- Because of its low cost and immediate playback itors, imprison first actors then audience in the capabilities, video is becoming a major tool in medium [see p 38]. Juan Downey's piece at the psychotherapy and social action . Trapped as we Electric Gallery traces the image of imprison- seem to be in the clichc of alienation, we seek ment, or reality as medium, to its source in corroboration of our existence, and video is on Plato's Myth of the Cave . The image is somehow its way to being a mirror for masses. The dis- more actual than the action it emulates. Is it any placement of reality into the conventions of wonder that psychiatry and politics talk so much representation leads us to paraphrase Descartes - ofimage? Pygmalion and Dorian Grey admon- I appear on the screen, therefore I am. The key ish from the mythic wings. to therapeutic and activist use of video is found However, I doubt that we should regard con- in the ambiguity of the word "image". Thera- fusion ofimage and reality as pathological . That pists talk of the difficulty of their patients in confusion surrounds one of the most para- generating a body image ; activists have found doxical and contentious issues of art. What is that politics is the art ofthe body politic image. real in art? In film, graininess and greytone Glancing through the National Film Board's degradation- the side effects oflow lighting and Challenge for Change newsletter you catch a forced processing of newsreel footage - became double refrain. People become real to bureau- conventions ofa school of realism, the stamp of crats only when they can document themselves write on any film image. It is difficult to know within the conventions of television reality. to what extent Cinema Write looks like news- And, even more basically, people only take their reel footage because of similar technical con-

185 EIGENWELT DER APPARATEWELT straints, and to what extent it tries to produce a Yeats never guessed that crass conventional grainy and degraded image in the knowledge forms of representing reality would be wide- that the audience associates such an image with spread or powerful enough to create "reality." recordings of real events. In my experience the But further speculation on epistemological pro- two are inextricably tangled. Clearly the con- blems common to all arts will not bring us vention is totally conscious in Godard's Le closer to a description ofthose formal processes Petit Soldat, or Les Carabiniers, films which dwell and possibilities that are unique to video - and on our tendency to confuse conventional repre- just such a description is necessary before we can sentations with the "real thing" . The conquering understand the field of intent and judge the heroes of Les Carabiniers return with postcards execution of a piece ofvideo art. of conquered wonders as booty. They feel they It is difficult fully to comprehend that calling have plundered the things themselves . The video an art of time is not a metaphorical newsreel quality surface of the film presents us statement but a literal description ofthe process with the same dilemma as the heroes - is news- ofgenerating the video image, any video image. reel really real As I mentioned before, the image o£video is an Manipulation of the conventions of repre- illusion ; there is only one rapidly moving dot of sentation has by now become almost a cliche - varying intensity on the screen. In an ordinary the bread and circuses of intellectuals. Never- television picture the dot scans regularly theless, the relation of art, conventional repre- whether an image is present or not, generating sentation, and reality is perhaps the basic the set of525 lines called a raster. To produce an theoretical issue of modern art and has been so image, one introduces a patterned modulation since the late nineteenth century. Does art ofthe dot's intensity as it races across the screen. imitate reality? Or does it create our very con- The varying intensity of the beam is perceived ception of the ultimately unknowable "out- as a range of grey tones from white to black. there?" The issue is not substantially different in The critical point here is that the video image is poetry, fiction, graphic art, film, orvideo. Video sensitive. It is not fixed but responsive to outside just accelerates this eternal dialectic of art. So control and alteration at any point in its scan. Yeats argues: Thus the essential nature of the video artist is quite different from that of the film artist who seizes discrete frozen images. The video artist That girls at puberty might find controls or intervenes strategicallyin an ongoing Thatfirst Adam in their thought process. Clearly, the aesthetic and critical im- Shut the door ofthe Popes chapel, plications of this distinction, in relation to the Keep those children out. typical concerns ofmost video artists, are sweep- There on that scaffolding reclines ing. Michael Angelo Perhaps the simplest and most obvious con- With no more sound than the mice make cern ofvideo art is with the nature of "process" His hand moves to and fro itself, and with the paradoxes and illusions of Like a long legged fly upon the stream time on which the concept rests. Consider, for His mind moves upon silence. example, the multiple tape-delay environments which have fascinated so many, video artists. He refers of course to Michelangelo's The simplest form of tape-delay is familiar to masterpiece ofGod creating Adam- The Touch. broadcast television viewers ; the instant replay Yeats describes Michelangelo's painting hand has transformed sports viewing. But few sports in relation to the picture as the same as the enthusiasts realize how an extension of this relation of God's hand to Adam in the picture. technique can break down the conventions of Who then is the Prime Mover? Who created time, and cause and effect." Video, unlike film, Adam? And God? Substitute Chic Young for requires no processing ; it may record a live Michelangelo and a half-tone screen for the event on one machine and. play it back simul- brush, and Yeats gives birth to Andy Warhol . taneously with varying delays by passing the tape through playback decks at various distances

186 ROBERT ARN

from the recording machine. Moreover, while viewer's physiological process, and hence a dif- the tape by its nature must pass in progression ferent viewing style is required. The viewer from one machine to the next, the displays from must become part of the process of what he these playbacks may be arranged so that the views, and this requires a much longer attention viewer experiences them out of their normal span than the usual scan of graphic art, or the temporal order. Most tape-delay pieces multiply fitful attention of narrative film. Physiological these time-windows and often scramble their process video operates on a longer time scheme sequence so as to attack our conventional sense than most other experimental forms and seems of time. It requires very little in these environ- merely boring if not pursued to the point of ments for the viewer-actor to lose track of the object/observer fusion . (Luckily for artists present - even though the screens may be studying physiological process, videotape is portraying his own actions. Present, past and cheap - their work would be prohibitively ex- future become arbitrary, cause and effect absurd . pensive, even if possible, in film format .) Any- The environmental pieces ofWoody and Steina one experimenting with video in any form is Vasulka pursue the paradoxes of reality a step likely to chance on physiological interaction further. Again, multiple presentation ofimage is patterns incidentally. I have noticed that vivid used, but now the same image is displayed color hallucinations may be produced by pulsing moving uniformly across the screen so that it different parts of a video image at different appears to enter at one side and leave the other. rates. Many people will see such a black and Strings ofscreens placed next to each other give white picture in vivid (if unpredictable) color. the impression at first that the image is moving Interestingly, there seems to be some positive from one screen to the next, but soon the images correlation between intensity of color halluci- seem to stand still leaving the viewer with the nation and the incidence of night blindness. impression that the whole environment is Sadly, I don't hallucinate colors at all. accelerating across the field ofthe image like the sensation. of a train pulling out of a station : a Feedback concrete representation of the paradoxes of In imitation of physiological systems, an image Einsteinian physics - relativity art. (Michael that is responsive to control can become re- Hayden has remarked to me that he responded flexive - self-controlling or regulative. This to neon signs and theater marquees in this way possibility gives rise to perhaps the purest line of and I suspect we can anticipate relativity effects video art : feedback patterning. "Feedback" in in three dimensions in his projected Waves this usage is a technical term, designating the video /computer project.) procedure of connecting camera and display- Obviouslyin all such pieces the viewpoint and monitor in a loop, the camera photographing reactions of the viewer are an essential part of the display and feeding the result back into the the work itself - these trees make no sound as same display. If, for example, a camera is photo- they fall in an empty gallery. An interlocked graphing its monitor and projecting this image loop tends to form of the video process and the via its monitor, and the camera is then tilted, "Alength of film ortape represents a temporal the monitor will be receiving a tilted image of separation ofrecorded events. That is, since videotape itself - but this new image will contain the movesthroughthe playback deck at approximately upright image of the monitor that was already 71A inchesper second and 16 mm film through the projector at 40/24 feet per second, an event separated on the screen before tilting the camera: there is in time from anotherby one second is separated in no hiatus . The resulting image thus appears as a distance by 71h inches or 40/24 feet respectively. If we kind ofsuperimposition ; and with every subse- use several playbacks, displayed continuously and simultaneously, of the same tape or film, the distance quent alteration of the system the image will between the machines will determinethe temporal accumulate, generating an echo-corridor pattern separation between theimages. Anyimage appearing on one display will eventually appear on the next; which rapidly transforms itself into the mandala- the intervening time being determined by the dis- like imagery typical of much feedback work. It tance thatpoint on the tape or filmhas to travel to the is through step-by-step control of this cumula- next deckor projector. Filth, however, cannot be recorded and played back simultaneously. It must be tive property ofthe feedback system that feed- sent away for processing.

187 EIGENWELT DER APPARATEWELT back images are constructed . Images may be one simple form to control or alter an aspect of injected into the loop from other cameras or another simple form. Very complex patterns tape machines, or by placing objects between may be produced by elaborating the stages of the camera and the screen; but even without control and relationship . Anyone who has used external image intervention the system is itself a Spirograph knows how to operate an ana- a source of almost infinitely varying patterns, logue computer. merely echoing the shape of the screen and the A deepening fascination with the processes of texture ofthe scan raster. analogy is easy to detect in the background of most video artists. Some, of course, came to video from film or the graphic arts, but the majority had some involvement in the light- Synthesis show movement ofthe 60s, and moved through in feedback, we reach the limit oftalking about an interest in electronic music before working the video image as image. A feedback image is in video. The drive of lightshows was fairly not a picture ofanything finally ; it is a balance simple ; a quest to give a visual impression of of purely electronic forces below the threshold sound. The full significance of that drive, as an of perception . It is our entrance into that very exploration ofthe central mystery of metaphor specialized branch of video called image syn- and symbol, and hence of art, has only become thesis, in which the images are not records but clear in artists' successive absorption in electronic creations achieved by manipulating the basic music and video. electronic forces at work in video cameras and The lightshow is a single term analogy ; image displays . The term "synthesis" is familiar in the is controlled so as to be analogous to the music. context of electronic music and the Moo, syn- Eisenstein grapples with this concept in his thesizer - or even in relation to chemistry or theorizing on the use of sound in film. He tends physics. Before a pure synthesis of anything is to reject simple, positive one-to-one correspond- possible we must have a set ofbasic forms, forces, ence as too mechanical and prefers a negative or building blocks from which to start. We do counterpoint relationship, not noticing that a not synthesize a house from walls and roof but negative relationship is equally an analogy as is from board, brick and nails. Only when such a positive . It is not the valence of relationship basic units are established by analysis can we that matters, but its complexity; most meta- decide on a system of inter-relation which will phors are interlocking analogue systems of great lead us to the desired final product. Ifyou don't complexity. The search for methods and princi- analyse to small enough basic units you limit the ples ofrelationship seems to have intuitively at- variety of end products - witness the prefab tracted artists to electronic music and the Moo, house. synthesizer, which builds up complex sound pat- In electronic media the basic units are not terns out of the inter-action of simple electronic tangible shapes or forms but forces - electrical wavefortns ; and then finally to video synthesis energy : complex patterns ofenergy are built by where both image and sound may be analysed ac- inter-relating simple ones just as in more con- cording to basic waveforms which in interaction crete forms of synthesis. In this context, how- with one another may produce literally any ever, the methods ofinter-relating energy forms sound/image. Study of artists concerned with are of greater and more critical interest because the analogue process seems to have led an intui- they bear directly on the fundamental concepts tive critic like Gene Youngblood to create what of all art - analogy and metaphor. To control can be seen as an aesthetic of analogy : he calls one thing with another is the simplest case of most avant-garde video art "synaesthetic." Un- what we call analogy; a successful analogue fortunately, his aesthetic is partisan and value- relationship may result in a fusion which we based. and fails to reveal the connection between could call a metaphor. To create complex pat- the arts ofcomplex analogy and the more gen- terns of energy one simply uses one aspect of eral process ofmetaphor at work in all art. ROBERT ARN

Video synthesis proceeds along two lines - dace graphics for broadcast television. direct synthesis; which creates patterns by direct It is tempting to see the technical problems of manipulation of time without any external in- video synthesis as essentially solved. Combina- put; and indirect or image-buffered synthesis tions of the different synthesizer types give ana- which modulates input from an external source. logue control access to almost all dimensional Synthesizers developed by Eric Segal and Steven aspects of the video image. Work remains to be Beck work on the direct system ; machines de- done on electronic color, switching, keying and veloped by N:unJune Paik, Steve Rutt and Bill special effects - some ofwhich is going ahead in Etra work on indirect principles . For direct syn- Canada in my laboratory at Brock University, thesis, imagine the raster of scan lines of the St Catharines, Ontario.* Still, when all the tech- video image as a time track. Switching the beam nical work is done one has merely established a intensity in varying time intervals will result in certain possibility- the equivalent of a brush, a basic geometric patterns on the screen. These chisel, a musical instrument. It remains for simple patterns can be elaborated by feedback artists to create human and significant metaphors into ever more complex shapes . Steven Beck's with this analogue capability, and for critics to synthesizer starts from the very simple basis of find descriptive terms that illumine their con- generating two vertical and two horizontal lines, cerns. the positions of which may be changed by determine changing the time constants which * Anyone wishing a copy ofour first technical bulletin, a their positions; and simple logic circuits can 30 minute videotape outlining the state o£the art in cancel thelines, leaving only the dots where they helical scan video equipment, send 1/Z' or 1" videotape plus $S dubbing fee (if no tape is available, send $20) cross. A combination ofexternal control on line to: Video Support Project, 36 Decew Road, R.R. 1, position (each line may be made to move in St. Catharines, Ontario . (Specify English or French analogy to a separate outside control) and feed- version .) ing the image back on itself results in both deli- cacy ofcontrol and amazing complexity. The indirect method of synthesis stems from NamJune Paik's early experiments in magnetic distortion ofthe video image. Since the raster of scan lines of the video tubes is generated by magnetic deflection of a single beam of elec- trons, any outside magnetic field will distort the scan field and any image it carries. Paik started by using permanent magnets which introduced a stable distortion to all images displayed on the altered set, but finally tapped into the deflection coils of the set itself so that he could introduce special distortions by means ofan external con- trol system . Rutt and Etra's design extends Paik's design by incorporating a separate de- flection amplifier designed to permit modula- tion by outside control signals rather than by tapping into the somewhat crude deflection circuitry ofthe display monitor. The Rutt/Etra design gives analogue control over size and shape of picture, tonal structure of image, and spatial distortion on three axes. Its capabilities outrun those ofthe very expensive and inflexible digital computer systems currently in use to pro- IIGENWELT DER APPARATEWELT SPACE-TIME DYNAMICS IN VIDEO FEEDBACK Physica, 1984

James P . Crutchfield*

Video feedback provides a readily available experimental system to study complex spatial and temporal dynamics . This article outlines the use and modeling of video feedback systems. It includes a discussion of video physics and proposes two models for video feedback dynamics based on a discrete-time iterated functional equation and on a reaction-diffusion partial differential equation . Color photographs illustrate results from actual video experiments . Digital computer simulations of the models reproduce the basic spatio-temporal dynamics found in the experiments.

1. In the beginning there was feedback portant role in our current understanding of dy- namical behavior [3]. For example, electronic Video technology moves visual information analog computers in their heyday were used exten- from here to there, from camera to TV monitor. sively to simulate complex behavior that could not What happens, though, if a video camera looks at be readily calculated by hand. They consist of its monitor? The information no longer goes from function modules (integrators, adders, and multi- here to there, but rather round and round the pliers) patched together to form electronic feed- camera-monitor loop. That is video feedback . back networks. An analog computer is set up so From this dynamical flow of information some that the vdltages in different portions of its cir- truly startling and beautiful images emerge. cuitry evolve analogously to real physical variables. In a very real sense, a video feedback system is With them one can study the response and dynam- a space-time simulator. My intention here is to ics of a system without actually building or, per- discuss just what is simulated and I will be implic- haps, destroying it. Electronic analog computers itly arguing that video feedback is a space-time were the essential simulation machines, but they analog computer. To study the dynamics of this only allow for the simultaneous computation of a simulator is also to begin to understand a number relatively few system variables. In contrast, video of other problems in dynamical systems theory [1], feedback -processes entire images, and does so iterative image processing [2], cellular automata, rapidly. This would require an analog computer of and biological morphogenesis, for example. Its extremely large size. Video systems, however, are ready availability, relative low cost, and fast not as easily broken down into simple function space-time simulation, make video feedback an modules. But it is clear they do simulate some sort almost ideal test bed upon which to develop and of rich dynamical behavior. It now seems appropri- extend our appreciation of spatial complexity and ate that video feedback take its proper place in the dynamical behavior . larger endeavor of understanding complex spatial Simulation machines have played a very im- and temporal dynamics. Cellular automata are the simplest models avail- `Permanent address : Physics Department, University of able for this type of complexity. Their study, California, Berkeley, California 94720, USA. however, requires rapid simulation and the ability EIGENWELT DER APPARATEWELT

to alter their governing rules. Video feedback does, in fact, simulate some two-dimensional automata and rapidly, too. With a few additions to the basic system, it can easily simulate other rules. Thus video feedback has the potential to be a very fast and flexible two-dimensional automata simulator. The dynamics of cellular automata are governed by local rules, but video feedback also allows for the simulation of nonlocal automata. At the end, I will come back to these possibilities and describe how simulations of cellular automata, and their generalization to nonlinear lattice dynamical sys- tems, can be implemented with video feedback. This is largely an experimental report on the dynamics of a physical system, if you like, or a simulation machine, called video feedback. My intention is to make the reader aware of the fascinating behavior exhibited by this system. In however, 2 order to present the results, section Fig. 1 . Single video feedback . Information flows counter- includes the necessary background on the physics clockwise through the electronic and optical pathways . of video systems and a very straightforward de- scription of how to start experimenting. An im- portant theme here is that the dynamics can be on ad infinitum . The information thus flows in a described to a certain extent using dynamical sys- single direction around the feedback loop. In fig. 1 tems theory. Section 3 develops those ideas and the image information flows in a counterclockwise proposes both discrete and continuous models of loop. This information is successively encoded video feedback dynamics. The experimental re- electronically, then optically, as it circulates. sults, then, take the form in section 4 of an Each portion of the loop transforms the signal overview of a particular video feedback system's according to its characteristics. The camera, for behavior and several snapshots from a video tape example, breaks the continuous-time optical signal illustrate a little bit of the dynamical complexity. into a discrete set of rasters thirty times a second. (See fig. 2.) Within each raster it spatially dissects the incoming picture into a number of horizontal scan lines. It then superimposes synchronizing 2. Video hardware pulses to the electronic signal representing the intensity variation along each scan line. This com- In all feedback systems, video or other, some posite signal drives the monitor's electron beam to portion of the output signal is used as input. In the trace out in synchrony the raster on its phosphor simplest video system feedback is accomplished screen and so the image is recontructed. The lens optically by pointing the camera at the monitor, as controls the amount of light, degree of spatial shown in fig. 1 . The camera converts the optical magnification, and focus, of the image presented to image on the monitor into an electronic signal that the camera. is then converted by the monitor into an image on Although there are many possible variations, in its screen. This image is then electronically con- simple video feedback systems there are only a few verted and again displayed on the monitor, and so easily manipulated controls. (See table 1.)

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JAMES P. CRUTCHFIELD

monitor raster trols image sharpness by moving the focal plane in front or behind the camera tube's image target.

------The total amount of light admitted to the camera is set by the f/stop or iris control. When pointing the camera at the monitor the relative position, or ------translation, of the raster centers and the relative ------angle, or rotation, (fig. 2b) are important controls. Electronic transformation of the signal occurs in both the camera and the monitor. The sensitivity of the camera's tube is adjusted by a light level control. Some cameras also provide for luminance Fig. 2. Video raster with arrows indicating the direction of inversion that inverts the intensity of the color scanning . Solid lines correspond to when the electron beam is signals When switched on, this allows one, for on; the dashed lines when the beam is off during the retrace . time. (b) Since the raster defines the horizontal, in a feedback example, to view a color negative print with the system the relative orientation as shown of the camera and camera as it would appear in a positive print. The monitor is an important control parameter. image intensity can be adjusted again on the monitor with the brightness. The contrast controls the dynamic range of the AC portion of the The optical controls provide gross spatial trans- intensity signal. On color monitors the amount of formations ofthe image seen by the camera. Zoom, color in the image is set by the color control and available on most modern color cameras, con- the relative proportion of the primary colors veniently allows for spatial magnification or (red-green-blue) is governed by the hue. demagnification . The same effect can be produced While the effect of each individual adjustment using a camera without a zoom lens by moving it can be simply explained, taken together they closer to or further from the monitor. Focus con- present a formidable number of control variables

Table I Typical control parameters on color video feedback

Name Function

Optical zoom spatial magnification focus image clarity f/stop attenuates incident light level rotation relative angle of monitor and camera rasters translation relative position of monitor and camera raster centers

Electronic Camera light level adjust sensitivity of camera pickup tube luminance inversion inverts intensity signal for each color Monitor brightness varies overall intensity signal contrast amplifies dynamic range of intensity color attenuates color signals to black and white hue relative signal strength of colors

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EIGENWELT DER APPARATEWELT

that can interact nontrivially. These problems will on the monitor front, and zoom in enough so that be considered in greater detail in the ensuing the "first" image of the monitor front fills 90% of discussion of TV theory and possible mathematical the screen. models of feedback dynamics. This section now 8) Slowly tilt the camera trying to maintain the ends with a "cookbook" procedure for setting up camera point at the screen's center. On almost all a feedback system. tripods this will take some fiddling and read- Although the detailed and quantitative dynam- justment. Try zooming in at various rotation an- ics will vary with the specific equipment used, my gles between 20 and 60 degrees. experience indicates that almost all servicable cam- eras and monitors will give some interesting behav- Another important element in this is the am- ior. This may require some patience as there are a bient light level. Some behavior is quite sensitive number of controls to be properly set. But once to, or will not appear at all if, there is any external, "tuned up" a system will exhibit complex and source of light. Although, a flashlight, candle, or a striking imagery in a reasonably wide control quick flip of the light switch, can be good light range. For the movie [4] and pictures described sources to get the system oscillating again if the later the camera used was a Sony Trinicon HVC- screen goes dark. 2200 and a Sony Trinitron TV/Monitor KV-1913*. With this short description and a modicum of A typical start-up procedure might be as follows: patience the experimenter has a good chance of 1) Connect equipment as shown in fig. 1 . finding a wealth ofcomplex and fascinating spatial 2) Place camera five to six feet from monitor. and temporal dynamics. The distance will depend on the monitor screen size and is not that important if the camera has a zoom lens. 3. Toward a qualitative dynamics 3) Point camera at some object other than the monitor. Adjust camera and monitor controls to In the beginning, I argued that a video feedback give a good image on the monitor. Vary these system is a space-time simulator. But a simulator controls to get a feeling for their effect on the of what exactly? This section attempts to answer image. this question as concretely as possible at this time. 4) Now turn the camera to face the monitor. A very useful tool in this is the mathematical 5) Again adjust the camera controls, especially theory of dynamical systems . It provides a consis- the zoom and focus, noting their effect. A warning tent language for describing complex temporal is necessary at this point: it is not a good idea to behavior. Video feedback dynamics, though, is let the camera see any steady very bright image for interesting not only for the time-dependent behav- more than 10 to 20 seconds**. Bright, dynamic ior but also for its complex spatial patterns. In the moving images are generally OK. following section I will come back to the question 6) Adjust camera on its tripod so that it can be of whether current dynamical systems theory is tilted about its optical axis. adequate for the rich spatio-temporal behavior 7) Point the camera again at the monitor, focus found in video feedback. This section introduces the qualitative language of dynamical systems * The cost for this space-time simulator is a little over $1000, [5], and then develops a set approximately a cheap home computer. . of discrete-time models for video feedback based ** Some new cameras incorporate "burn proof" camera on the physics of video systems . At the section's tubes. They are much less susceptible than earliercameras to the end I propose a continuum model akin to the image "burn" that can permanently damage the tubes. Can - tion should still be exercised. Excessively bright images will reaction-diffusion equations used to model chem- shorten tube life . ical dynamics and biological morphogenesis.

194 JAMES P. CRUTCHFIELD

Dynamic, time-dependent behavior is best de- The behavior described by a fixed point or a scribed in a state space. A particular configuration, limit cycle is predictable: knowledge of the system's or state, of a system corresponds to a point in this state determines its future. The last type** of space. The system's temporal evolution then be- attractor, that is in fact a very broad and rich class, comes the motion of an orbit or trajectory through gives rise to unpredictable behavior. These are the a sequence of points in the state space. The dy- chaotic attractors. While globally stable, they con- namic is the collection of rules that specify the tain local instabilities that amplify noise, for exam- evolution from each point to the next in time. In ple. They also have extremely complex orbit struc- many cases these rules can be simply summarized ture composed of unstable periodic orbits and as transformations of the state space to itself by aperiodic orbits. iterated mappings or by differential equations. An important branch of dynamical systems the- As will be seen shortly, video feedback is a ory concerns how one attractor changes to an- dissipative dynamical system. This means that on other, or disappears altogether, with the variation the average "volumes" in the state space contract, ofsome control parameter. The motivation for this or in physical terms, that energy flows through the line ofinquiry is clearly to model experimentalists's system and is lost to microscopic degrees of free- control over their apparatus. A bifurcation occurs dom. This property limits the range of possible when an attractor changes qualitatively with the behavior. Starting from many different initial smooth variation of control parameter . Changing states, after a long time the system's evolution will controls corresponds to moving along a sequence occupy a relatively small region of the state space, of different dynamical systems . In the space of all this is the system's attractor*. An attractor is dynamical systems, the sequences appear as arcs globally stable in the sense that the system will punctuated by particular control settings at which return if perturbed off the attactor. Different initial bifurcations occur. It is now known that these conditions, even states very near each other, can punctuations can be quite complex: continuous end up on different attractors. The set of points, arcs themselves or even Cantor sets or fractals. The though, that go to a given attractor are in its basin physical interpretation of these possibilities is very of attraction. The picture for a particular dynam- complex sequences of bifurcations . Thus dynam- ical system is that its state space is partitioned into ical systems theory leads us to expect not only one or many basins of attraction, perhaps in- unpredictable behavior at fixed parameters, but timately intertwined, each with its own attractor. complex changes between those chaotic attractors. Very roughly there are three flavors of attractor. With modifications much of this qualitative pic- The simplest is the fixed point attractor. It is the ture can be carried over to the dynamics of video analog to the physicist's notion of equilibrium: feedback. It is especially useful for describing the starting at various initial states a system asymp- context in which the complex behavior arises. In totically approaches the same single state. .The next the following I also will point out possible inade- attractor in a hierarchy of complexity is the limit quacies of the naive application of dynamical cycle or stable oscillation . In the state space this is systems. a sequence of states that is visited periodically. A single state of a video feedback system corre- sponds to an entire image, on the monitor's screen, say. The state is specified not by a small set of numbers, but rather a function I(z); the intensity * Unbounded or divergent behavior can be interpreted as an at points z on the screen. The dynamics of video attractor at infinity. feedback transforms one image into another each ** For simplicity's sake, I have not included the predictable torus attractor. It is essentially the composition of periodic limit raster time. The domain of the intensity function cycle attractors. I(z) is the bounded plane, whereas the domain of

195

EIGENWELT DER APPARATEWELT

the dynamics is the space of functions or, simply, color systems the modeling is complicated by the the space of images. existence of three color signals and the particular This picture can be conveniently summarized by camera technology. Once the monochrome model introducing some notation. The monitor screen is is outlined, however, it is not difficult to make the the bounded plane Rz = [ - 1, 1] x [ - 1, 1] where step to color. the coordinates of a point x take values in the The construction of the monochrome model range [ - 1, 1]. With this convention the center of requires more detailed discussion of the electronic the screen is (0, 0). For the incoherent light ofvideo and optical transformations in the feedback loop. feedback, there is no phase information and so Fig. 3 presents the schematic upon which this intensity is all that is significant . The appropriate model is based. With the physics of these trans- mathematical description of an image's intensity formations as discussed in the appendix, a rela- distribution is the space of positive-valued func- tively complete model can be constructed . tions. We will denote the space of all possible The appendix reviews the operation of the com- images by J~' . The video feedback dynamic then is mon vidicon camera tube, how it (i) stores and a transformation T that takes elements I in 3~' to integrates images and (ii) introduces a diffusive other elements: T: .~->J : I F-+I' . coupling between picture elements. These attri- The task of modeling video feedback is now to butes impose upper temporal and spatial frequency write down the explicit form of T using ,our cutoffs, respectively. The focus turns out to be an knowledge of video system57 physics. To simplify easily manipulated control of the spatial diffusion matters, I will first develop models for mono- rate. The monitor's phosphor screen also stores an chrome (black and white) video feedback. With image but for a time negligible compared to that

Horizontal Sync

Vertical Sync

D D Optics A F

tae I Video Signal

Contrast Noise Source Brightness

Vidicon Display Tube

Fig. 3. Idealized monochrome video feedback . A: photoconductive image target ; B: pickup for video signal ; C: camera electron beam; D: scanning coils for electron beams; E: phosphor screen; F: beam intensity modulator; G: monitor electron beam .

JAMES P . CRUTCHFIELD

of the vidicon. The appendix indicates various corresponds to the f/stop. For a system with deviations from the ideal video feedback system of luminance inversion black regions become white fig. 3. and vice versa. -To take this into account the With the physics and electronics of video sys- parameter s is set to -1, rather than its normal tems in mind, the details of the transformation T value of unity. can be elucidated for the monochrome model. The Spatial diffusion due to the photoconductor, but first and perhaps most significant assumption, is largely controlled by focus, contributes to the that T be taken as a discrete-time transformation intensity at a point. It produces a spatial coupling of a spatially continuous function, the image In, to neighboring pixels that can be represenied con- tinuously by the following convolution integral :

(~ _xz Employing a "bias intensity", the intensity at a (In(x))x= dYln(Y)exp(-ly2(vf + av)z) point I(x) can be scaled to take values in the range R2J I [ - l, 1]; -1 being black and 1 white. For com- parison at the end of this section, I consider how assuming a Gaussian shape for the diffusion a continuous time and space model can be applied profile. The denominator in the exponential con- to video feedback using reaction-diffusion equa- trols the width of the smoothing with af represent- tions. ing the focus control and a, the intrinsic smoothing The new image I+ , consists of two parts: the in the vidicon. first, the "old image" stored in the photo- A more complete model including the major conductor, and the second, the "incoming image" features of video feedback systems is the following: from the monitor screen. This, and the process of successive feedback of images, can be expressed as I +,(z) = LI(_z) + L'(h(x)~x + sf7(bRz) , (3) an iterated functional equation . The first model of the dynamic T is the following with the parameter L' setting the magnitude of the intensity signal contributed (or leaked) to that at x I +,(x) = LI(x) + sfh(bRx) , (1) during one raster time. Furthermore, the first term in eq. (3) can be where z is a point in Rz. The first term represents modified to include the temporal storage and inte- the old image whose intensity at the point z has gration of images and their successive decay. This decayed by a factor of L each time step. Thus L is can be effected by a weighted sum of past images, the intensity dissipation of the storage elements, including the monitor phosphor, but dominated by the photoconductor. The second term represents the incoming image that is possibly rotated by an angle 0 and spatially magnified by a factor b. R is where the decay parameter L is the same as above. then a simple rotation, This gives equations corresponding to the video feedback system as laid out in fig. 3, _ cos(O) sin(O) R - (-sin(O) cos(¢))' h+ (z)=L(h(x))*+L'(In(x)>x+sfl(bRz) . (4)

due to the relative raster orientations; b corre- For a color system the scalar intensity becomes sponds to the zoom control . If z' = hRx lies out- a vector of red, green, and blue intensities, side of Rz then h(9') = 0. The parameter fE[0, 1] i(g) = (R(-fl, G(x), B(z)). There are also cou-

197' vectorpickup,=extensionstudyin-matrixbethemodel(F,,generalincorrectnon-idealaberrationelectronicasF(IconcentrationalthoughbiologicaloffsignalsdynamicsbebetweenTuringF,onsummarizesLdeveloped=evolutionproposedaFZ,intensitydiagonaltheTuringratescontroladdedrateL~h(x))tThisoftheamplification,andmodel+fordescribingandDERDPformtheseofsameInconvergencescreenintroducedofcolorforcross-talkitalso,theL'toandZIineqFk)APPARATEWELTimperfections,showedcoloraforisthethethatI,ofofvariablesothercolorstheelementsfirstlinesareclearherepartial(4)+representsallowschemicalfeedbackbiologicalphosphortheconcentrationthesecolorvariablesL'~In(z)>xforopticalvariousthephotoelectronsbasedordermatricesandfiltersaworkthatbetweenthat"field"iscausedmanythiscontinuous-timeofforequationsintensitywithoutspatialdifferentialreconstruction,thethesystemsgenerallythiscanonapproximation,nonlinearonthesystemcouplingsthekindmorphogenesiscolorsuchpurposesandImonitor+bythecouplingspatialthesystembeTheirlocalThe=comparisonsrrvariablesdiffusioncouplingaasof(I,,developedcolordecay,dotsevolutionisThedifferentialinnumber"reaction"systemcouplingsequationIZ,complex-calleddiagonalonlygiveselectronfunctiontheissignalstypeofmodelofeasierwhile,vid-Dthisandlin-Forthe,rise[6](5)ofasofIk)ofinisa spatialtheusedthatRHSvideovalidpreviousconsideredderivative(4)anwidelyonfeedbackreaction-diffusion=LI(z)+sfl(bAX)+QPZI(z),"oldthepreviousnaturallydiffusionisandwellcutoffscomputersatisfyintegro-functionaltocanandtospatialequationspatternsthereaction-diffusionrateofequationcomplexityfeedbackForascanAsparametersthatimplementimage",image",Thus,abyEqeqbelowwellmagnificationselectionbeusedarguments,isThewillandspatialthediscussedthedynamicsbeofiteratedcoupling(6)a(7)involveswithderivedasthisthataschemicalbasicmatrixfirstsimulationadditionthemodelusedforthebesimplerclassnaturallyisFurthermore,theandVideofarcanthestructureoflocalatheterms,seencolorspatialfunctionalcriterianexttypeastemporalmodelsresultingabove,hasthetospatialspatialf,fromthesummarizingofoscillateLaplaciandifferentialprovidesverifyingdifferencenotationfeedbackInandofreactionmodelsonb,experimentallyinverytermlastmodelsproposedvideoadirecttakeoftheandofeqL,alreadybiologicalnoiseandthistheandcanpatternssimilarfromisthisequationtemporallythelowisandRHS(7)intodynamicsbecausetemporalmodelthefeedbackaanalogythetemporalnextInoperatorbethedifferstermequationformcontinuousforpassconceptualthecontinuumlaidfact,uponmodelsR,construc-reaction-ofphenom-nonlocaldiffusionaccountsection,systemsandspatialshouldspatio-eqaremodeldownoffiltervideofromstudyofwithcanThefre-dy-dis-Hebe-on(7)eqitsbyasaA

EIGENWELT

plings to . interactions also 1) effect . beams ; These 2) spatial diffusion the . . icon; time 3) ; be . 4) Thus. in ted image. for . A Turing's an . nonlocal a rotation . the In+,(X> (bnx) diffusion namics where . elements di'(x) their dt color . model where early before, could . diffusion . . Along is can "incoming to . coupling. video havior ity . quency model be . reaction-diffusion . video A.M . enology 1952 . described . The reaction-diffusion simplicity . dl feedback I ) (6) this temporal . for . . . The of . eq. . F . . . cretization . . . dynamics . (4), . a digital diffusion . model linear cretization .

198 JAMES P. CRUTCHFIELD

digital simulation, it is a moot point as to which is this framework for some of the more complex better, the iterated functional equation or dynamics. Then a brief description of a movie on reaction-diffusion model. video feedback follows. Stills from the movie illus- Having constructed these models, the burning trate some of the curious features of video feed- question is whether their dynamics describe that back dynamics. And finally, these "experimental" actually found in real video feedback systems. For results will be compared to those from preliminary the very simplest behavior there is hope that the digital computer simulations. equations can be solved analytically . In general, Video feedback dynamics can be roughly catego- though, simulating the models in a more controlled rized as in table II. For the simplest temporal environment on a digital computer, for example, behavior, descriptive terms from dynamical sys- seems to be the only recourse [7] . After describing tems seem appropriate as in the first four behavior the dynamics typically observed in a real video types. At first, let's ignore any possible spatial feedback system in the next section, I will come structure in the images. When a stable time- back to the results ofjust such a digital simulation . independent image is observed, it corresponds to a fixed point in the image space F. Much of the behavior seen for wide ranges of control parame- 4. Video software ters falls into this category. Thus on the large scale video systems are very The models and discussion of video physics in stable, as they should be in order to operate the last section may have given an impression of properly in a wide range of environments . For simplicity and straightforwardness in under- extreme parameter settings, such as small rotation, standing video feedback dynamics. The intent in low contrast, large demagnification, and so on, this section is to balance this with a little bit of the equilibrium images are typically observed. For richness found in an actual color video system. An example, when the zoom is much less than unity overview of the observed dynamics will be then one observes an infinite regression of succes- presented initially from a dynamical systems view- sively smaller images of the monitor within the point. I will also address the appropriateness of monitor within . . . . The image is similar to that

Table II Video feedback dynamics

Observed Attractor in image space

equilibrium image fixed point temporally repeating images limit cycle temporally aperiodic images chaotic attractor random relaxation oscillation limit cycle with noise-modulated stability spatially decorrelated dynamics quasi-attractor with (e.g. dislocations) local temporal dynamics : fixed point limit cycle chaotic attractor spatially complex image spatial attractor: fixed point limit cycle chaotic attractor (?j spatially and temporally aperiodic nontrivial combination of the above

199 EIGENWELT DER APPARATEWELT

seen when two mirrors face each other. With a bit simple fixed point or limit cycle. The closer in of rotation the infinitely regressing image takes on parameters to aperiodic behavior, the longer the an overall "logarithmic spiral" shape that winds transients. The simple dynamics discussed so far into the origin. are globally stable in just this sense of returning to When the parameters are set to moderate values, the same image(s) when perturbed. Of course, one one of the first non-trivial dynamics to appear is a can perturb the system too much, knocking it into simple oscillation. This would be a limit cycle in another basin of attraction and so losing the image space: a sequence of dissimilar images that original behavior. It is a common experience, in after some time repeats. Because entire images fact, that hand-waving perturbations will leave the repeat, individual points on the screen exhibit screen dark, with the system requiring a "positive" periodic behavior. Consequently, the values of stimulus of light from some source to get back to intensity at a point cycle repetitively. its initial attractor. At parameter values nearby often lie temporally At large zoom, or spatial magnification, the aperiodic image sequences. Chaotic attractors in system noise is readily (and exponentially) image space are most likely a good description of amplified. This regime is dominated by bursts of this behavior type in the simplest cases* . When light and color. Depending on the controls, the non-repeating images are reached from limit cycles bursts can come at regular intervals or at random with the change of a parameter, the bifurcation times. Also, the particular features of the bursts, occurs in one of (at least) three ways: such as color, intensity, or even the pattern, can be 1) Simple lengthening of the limit cycle period, the same or aparently randomly selected. This until it is sufficiently long to be effectively aperi- behavior is quite reminiscent of a limit cycle with odic: for example, going from -a limit cycle of 10 (noise) modulated stability [9]. seconds to one of hours. New images are intro- The dynamics discussed so far is simple in the duced, but are not sufficiently similar to be consid- sense that its temporal features are the dominant ered as close "recurrences" . aspect. No reference was made to spatial structure 2) The introduction of subharmonics at fre- as the temporal dynamics was readily distinguished quencies lower than that of the original limit cycle: from it. A more precise way to make this dis- these subharmonics are small modulations of the tinction is in terms of whether the behavior at a image's geometric structure. The overall image suitably chosen point captures the dynamics [8]. sequence remains the same, but differs in the Using intensity data from this point, if a simple modulated detail. attractor can be reconstructed, then the behavior is 3) Suddenly at some critical parameter value, of a simple type that can be decomposed into the limit cycle disappears and aperiodicity set in. temporal and spatial components. The last entries A very telling indication that complex behavior in table 11 are an attempt to indicate that there is lies at nearby parameter settings comes from much more than this simple decomposable dynam- slightly perturbing the system. This can be done ics. Indeed, the spatial structure and its interaction most conveniently by waving a finger between the with the temporal dynamics are what makes video monitor and camera. Once perturbed, the nearby feedback different from other systems with com- complexity reveals itself by long and convoluted plex dynamics, like chaotic nonlit»ar oscillators. transients as the system settles down to its original But this difference presents various (intriguing) difficulties, especially because a dynamcal system description does not exist for spatial complexity [10]. Nonetheless, a qualitative description is possi- * In this case, given atime series of intensity values at a point, it is possible to "reconstruct" a state space picture of the ble and, hopefully, will lead to the proper the- attractor [8]. oretical understanding of spatial dynamics.

20 0 JAMES P. CRUTCHFIELD

Much of the following description, and the boundaries between segment ends form the dis- categorization used in table II, is based on observed locations. They can move regularly or wander similarities in spatial structure. While it may be erratically. Dislocations form in pairs when a stripe very difficult to unambiguously state what.a com- breaks in two. They also annihilate by coalescing plex image is, we as human beings can easily two stripes. Dislocations make for very complex, discern between two images and can even say some detailed patterns whose temporal evolution is are "closer" than others in structure. I am not difficult to describe in terms of dynamical systems currently aware, however, of any mathematical because of their irregular creation and annihi- definition of "closeness" for spatial structure that lation. Nonetheless, when perturbed very similar is of help with the dynamics observed in video images reappear. A quasi-attractor would be asso- feedback. Such a concept would be of immense ciated with global features, such as the relative value in sorting out complex dynamics not only in areas of regular stripe arrays and dislocation re- video feedback but in many other branches of gions, the time-averaged number of dislocations, science. or the pattern's gross symmetry. To denote images that are observed to be simi- Dislocations fall into the behavior class of spa- lar, but different in spatial detail, I introduce the tially decorrelated dynamics. Moving away from phrase "quasi-attractor" for the associated object one point on the screen, the spatial correlations in state space. These state space objects appear to decay rapidly enough so that eventually there is no be globally stable to small perturbations and it is phase relationship between the behavior of in this sense that they are attractors. Once per- different regions. The governing dynamics in any turbed, the video system returns to similar images, one area is similar to that of other areas. The local although in spatial detail they may be slightly behavior, however, can take on the character of a altered from the original. fixed point, limit cycle, or chaotic attractor. Thus A good example of quasi-attractors is the class while globally stable, the entire image cannot be of images displaying dislocations . This terminology described by a single attractor in the conventional is borrowed from fluid dynamics, where dis- sense of dynamical systems theory. This behavior locations refer to the broken structure of con- type has been studied quantitatively in simple vective rolls in an otherwise simple array. Dis- nonlinear lattice models [13]. Spatially decorrelated locations are regions of broken symmetry where dynamics apparently is the cause of heart the flow field has a singularity. The formation of fibrilation that results in sudden cardiac death [14] . this singularity typically requires a small, but The existence of spatial attractors that describe significant, energy expenditure* . In video feed- an image is another useful notion in classifying back, dislocations appear as inter-digitated light video dynamics. Intensity values as a function of a and dark stripes. The overall pattern can be com- "pseudo-time" can be obtained by following along posed of regularparallel arrays of alternating light a simple parametrized curve on the screen. These and dark stripes with no dislocations, and con- values then can be used to reconstruct a "state voluted, maze-like regions where stripes break up space" picture [8] that captures some features ofan into shorter segments with many dislocations. The image's structure. These features naturally depend on the type of curve selected . For example, data from a circle of fixed radius elucidates the rota- Both Couette flow [1l] and Benard convection [12] exhibit tional symmetry in an image. Similarly, data from this phenomenon. In nematic liquid crystal flow these are called along a radial line allows one to study radial wave disctinations . Similar structures appear in spin systems, such as magnetic bubble devices, and in the formation of crystals. propagation caused by magnification . The recon- Turing's discussion [6] of "dappled patterns" in a two- struction of spatial attractors has been carried out dimensional morphogen system is also relevant here. for the above-mentioned lattice models [13].

201 EIGENWELT DER APPARATEWELT

The rough classification is not yet complete. One image out of a long limit cycle is shown in There are also image sequences that appear to be plate 2. The limit cycle period was approximately combinations of spatially-decorrelated dynamics 7 seconds . Initially, a green disk nucleates at the and complex spatial attractors. The latter entries in center of a homogeneous light blue disk. The green table II indicate these possibilities. disk grows to fill 80% of the illuminated area The interaction of spatial and temporal dynam- leaving a blue annulus. A red disk then nucleates ics makes it very difficult to describe the more inside the green disk, along with an outside ring of complex behavior in any concise manner. To alle- nine dots. The oscillation consists largely of the viate this problem a short video tape was prepared radially outward moving red disk, that Nntercepts to illustrate the types of behavior in table II [4]. the inward propagating dots. The still is taken at The movie is particularly effective in giving a sense the moment of collision. The disk expands en- ofthe temporal evolution, stability, and richness of gulfing the dots and the green annulus, then itself video feedback dynamics. An appreciation of the is over taken by the inside boundary of the blue spatial complexity can be gleaned in a few stills annulus that moves inward . The outer boundary of from the movie. (See plates 1-7.) This will com- the red disk then recedes before the blue annulus. pensate hopefully those readers who do not have The screen then eventually becomes entirely light access to a video feedback system or who have not blue, at which moment the center nucleates a seen the movie. growing green disk, and the cycle repeats. This The examples have a few common features. limit cycle was stabilized by a very small marking Regarding parameter settings, they were all made near the screen's center*. at rotations of approximately 40 degrees and with Plate 3 shows a still from a sequence of images spatial magnifications slightly less than unity, un- with slowly moving dislocations. Toward the out- less otherwise noted. The discreteness caused by side there is a "laminar" region of stripes. Moving the finite resolution is apparent in each figure. Note inward from this, the first ring of nine dislocations that the spatial structures are typically many pixels is encountered. These were seen to move smoothly in extent, so that the discreteness does not play a counter-clockwise. The center, however, period- dominant role. ically ejected thin white annuli that propagated out Plate 1 presents a typical nontrivial equilibrium radially, only slowly acquiring clockwise rotation. image, or fixed point. It has an approximate nine- The interface between the inner and outer regions fold symmetry that comes from the rotation angle: caused the intervening maze-like dislocation pat- 360/40 = 9. The intensity at each point as a func- tern. The entire image shows a high degree of tion of angle is periodic, with periods not greater nine-fold symmetry although in the dislocation than nine. The overall spatial symmetry as a region it is quite complex. function of rotation 0 exhibits a "symmetry lock- Spiral patterns are quite abundant, as one ex- ing" highly reminiscent of that found in temporal pects from a transformation with rotation and frequency locking in nonlinear oscillators [3]. One magnification . Plate 4 illustrates a logarithmic noteworthy similarity is that the parameter win- spiral that dynamically circulates clockwise dow for which a given symmetry dominates de- outward. Temporally, the behavior is periodic with creases in width with increased order of the sym- color and structure flowing outward from the metry. For example, spatially symmetric images of center. The rotation here is 0 = - 30 degrees. The period 31 occur for a much smaller rotation range logarithmic spiral can be easily described as a those with period 9 symmetry. parametrized curve with angle (k and scaling b 'One evening this cycle was allowed to oscillate for two controls as follows hours with no apparent deviation from periodicity before the power was turned off. (x, y) = (bt cos(o log t), bt sin(o log t)) ,

202 JAMES P. CRUTCHFIELD

with tE[0, 1]. Such structure and periodic coloring correct. It is still an open question as to whether occur often in organisms, such as budding ferns they reproduce the detailed spatio-temporal dy- and conch shells. namics. Such comparison is a difficult proposition With relatively high zoom, or large spatial even in modeling temporal chaos alone. Digital magnification greater than unity, noise in intensity simulations are many orders of magnitude slower and spatial structure is exponentially amplified . A than the space-time analog simulations of video common manifestation of this is periodic or ran- feedback. And for this reason it is difficult, given dom bursts. Plate 5 shows a snapshot of a devel- model equations, to verify in detail and at numer- oped burst that had spiralled counterclockwise out ous parameter settings their validity. To date digi- ofthe center in about one second. After a burst the tal simulations [7] have reproduced the following screen goes dark with faint flickering, until another features typical of video feedback: fluctuation occurs of sufficient magnitude to be 1) equilibrium images with spatial symmetry amplified into a spiralling burst. The video sys- analogous to Turing's waves [6]; tem's finite resolution can be seen as a graininess 2) fixed point images stable under perturbation; on a scale larger than the intrinsic discreteness. 3) meta-stability of fixed point images: Luminance inversion stabilizes images by ampli- sufficiently large perturbations destroy the image; fying contrast. Black regions map into white and 4) logarithmic spirals; colors map to their opposite. This sharpens bound- 5) logarithmic divergence when the rasters are aries between dark, light, and colored areas in an not centered. image. Section VI ofref. 2 discusses this stabilizing At this preliminary stage of digital simulation it effect in more detail. Plate 6 shows an example of is not possible to discuss much in detail. In fact, it the "pinwheels" that dominate the images found may be a long time until extensive digital simu- with luminance inversion*. The rotation for this lations are carried out on the proposed models. photo was 0 = -90 degrees. By adjusting the The construction of, or use of pre-existing, special rotation, focus, and/or hue, controls the pinwheels purpose digital image processors to simulate video are seen to move either clockwise or counter- feedback may be more feasible than using con- clockwise. Winfree discusses similar "rotating ventional digital computers . The next and final waves" of electrical impulses that cause the heart's section comes back to address these questions of coordinated beating. Plate 6 should be compared future prospects for understanding video feedback. to the figure on page 145 of ref. 14. Plate 7, also made with luminance inversion, is a snapshot of outward spiralling "color waves" . .5. Variations on a light theme These are very reminiscent of the ion concentration waves found in the Belousov-Zhabotinsky chem- Video feedback is a fast and inexpensive way to ical reaction [15] . The rotation parameter here is perform a certain class of space-time simulations. roughly 0 = -40 degrees. As in the above pin- It also provides an experimental system with very wheels, every point in the image has a well-defined rich dynamics that is describable in some temporal phase, except for the center where there regimes by dynamical systems theory, while ,in is a phase singularity . other regimes it poses interesting questions about A digital simulation based on eqs. (4) and (7) extending our current descriptive language to spa- captures some of the gross features of video feed- tial complexity. back. To this extent the proposed models are One goal in studying video feedback is to see whether it could be used as a simulator for dynam- ' Bob Lansdon introduced me to these pinwheel images. See ics in other fields. Turing's original proposal of also ref. 2. reaction-diffusion equations for biological mor-

203 EIGENWELT DER APPARATEWELT

phogenesis comes to mind, as well as the image configuration. With video feedback one has simple processing [16] and hallucinogenic dynamics [17] of control over the nonlocality of the rules using the visual cortex. Naturally, the first task in this is rotation and spatial magnification, and over the to understand video feedback itself as completely number of neighboring pixels using the focus. as possible. Toward this immediate end, I have A monochrome system, employing an intensity proposed models based on video physics and threshold to give crisp black and white images, presented an overview of the possible behavior in could be used to simulate binary cellular automata. a particular color video system. The next steps in This restriction on the intensity range falls far this program are to make a more quantitive study short of the possible pixel information in video of the attractors and bifurcations with calibrated systems. Indeed, as discussed in the appendix, video components. Data from these experiments color systems are capable of transmitting roughly would be analyzed using techniques from dynam- 20 bits of information per pixel. This includes a ical systems to (i) reconstruct state space pictures random "noise floor" for small signals. Gener- of the simpler attractors, and (ii) quantify the alizing cellular automata, from a few states per site unpredictability of the simple aperiodic behavior. to many, leads to lattice dynamical systems [13]. A second approach to understanding video feed- This corresponds in the video system to removing back dynamics is to study other configurations of the above thresholding. Thus this video video components. The possibilities include: configuration will be especially useful in the experi- 1) masking portions of the screen to study the mental study of lattice dynamical systems and in effect of boundary conditions; the verification of analytic and numerical results, 2) optical processing with filters, lenses, mirrors, such as spatial period-doubling, found in some and the like; nonlinear lattices [13]. 3) using magnets to modulate the monitor elec- A number of video image processors are avail- tron beam scanning; able, both analog and digital. Many have been 4) connecting two camera-monitor pairs seri- constructed solely according to their aesthetic ally, thus giving twice as many controls; value by video artists . Certainly, among this group 5) nonlinear electronic processing of the video there is a tremendous amount of qualitative under- signal; standing of video dynamics. At the other extreme 6) inserting a digital computer into the feedback of the technical spectrum, some of the emerging loop via a video frame buffer. supercomputers have adopted architectures very The possible modifications are endless. But, similar to that of video feedback systems. These hopefully, they will help point to further under- machines would be most useful in detailed quan- standing and lead to applications in other fields. titative simulations. And, in turn, video feedback Variations (5) and (6) may lead to the most might provide an inexpensive avenue for initial fruitful applications of video feedback. For exam- study of simulations planned for these large ma- ple, they allow one to alter the governing rules in chines. simulations of two-dimensional local and nonlocal Physics has begun only recently to address com- automata. In this process an image is stored each plex dynamical behavior. Looking back over its raster time. Each pixel and its neighbors are oper- intellectual history, the very great progress in ated on by some (nonlinear) function. For rapid understanding the natural world, with the simple ("real-time") simulation this function is stored in notions of equilibrium and utter randomness, is a "look-up" table. The pixel value and those ofits astounding. For the world about us is replete with neighbors form the input to the table. The table's complexity arising from its intimate inter- result then becomes the pixel's new value that is connectedness. This takes two forms. The first is stored and displayed . This is a very general the recycling of information from one moment to

20 4 JAMES P . CRUTCHFIELD

the next, a temporal inter-connectedness . This is on the photoconductive properties of certain semi- feedback. The second is the coupling at a given conductors (such as selenium). When light is inci- time between different physical variables. In glob- dent on these materials their electrical resistance is ally stable systems, this often gives rise to non- reduced . Photoconductors can have quite large linearities. This inter-connectedness lends structure quantum efficiencies, approaching 100%, with vir- to the chaos of microscopic physical reality that tually all the incident photon energy being con- completely transcends descriptions based on our verted to mobilizing electrons in the material. Once traditional appreciation of dynamical behavior. energized these electrons diffuse in an ambient From a slightly abstract viewpoint, closer to my electric field. personal predelictions, video feedback provides a The vidicon takes advantage of these mobile creative stimulus of behavior that apparently goes electrons in the following way. (Refer to fig. 3.) An beyond the current conceptual framework of dy- image is focused on a thin photoconducting layer namical systems. Video feedback poses significant (A) approximately one square inch in size. Spatial questions, and perhaps will facilitate their answer. variation in an image's light intensity sets up a I believe that an appreciation of video feedback is spatial distribution of mobile electrons. Under an intermediary step, prerequisite for our compre- influence of a small bias field these diffuse toward hending the complex dynamics of life. and are collected at the transparent video signal pickup conductor (B). During operation the photoconductor/pickup sandwich acts as a leaky Acknowledgements capacitor with spatially varying leakage: the more incident light, the larger the local leakage current. I am particularly indebted to Ralph Abraham The electron beam (C) from the vidicon's cathode for introducing me to video feedback a number scans the back side of the photoconductor depos- years ago. Special thanks are due to Doyne Farmer iting electrons, restoring the charge that has leaked and the Center for Nonlinear Studies, Los Alamos away, and hence, bringing it to a potential com- National Laboratory, for the support and encour- mensurate with the cathode. The coils (D) supply agement of this project. Larry Cuba generously the scanning field that moves the electron beam loaned his video equipment for Plates 6 and 7. over the photoconductor . They are driven syn- Elaine Ruhe was especially helpful in the prepara- chronously with the horizontal and vertical raster tion of the video tape and stills. I would also like timing circuits (top of diagram). The output video to thank the Automata Workshop participants signal corresponds to the amount of charge locally who played with the video feedback demonstration deposited by the beam at a given position during and discussed their ideas with me. Particular its scan. This charge causes a change in the leakage thanks go to Bob Lansdon, Alice Roos, Otto current and this change is picked up capacitively Rossler, and Art Winfree, for useful discussions on and then amplified . video feedback. The important features of this conversion pro- cess, aside from the raster scanning geometry already described, are Appendix A 1) the diffusion of electrons as they traverse the Video physics photoconductor; and 2) the local storage and integration of charge There are many types of camera pickup tubes, associated with the light incident during each raster but for concreteness I will concentrate on the time. common vidicon tube and describe how it converts The diffusion process directly limits the attainable an image to an electronic signal. The vidicon relies spatial resolution. This places an upper bound on

205 EIGENWELT DER APPARATEWELT

the number of horizontal lines and the number of adjusting it to one side of exact focus the diffusion pixels (distinct picture elements) within each line. orientation can be inverted. Very small changes in The effect on spatial patterns is that there can be the zoom, or spatial magnification, can have quite no structure smaller than this diffusion limit. An- large qualitative effects because the image informa- other interpretation of this is that, over the period tion repetitively circulates in the feedback loop. A of several rasters, there is a diffusive coupling spatial magnification greater than unity increases between elements of an image. exponentially with the number of passes through The high spatial frequency cutoff can be easily the loop. Similarly, adjusting the admitted light estimated. The electron beam forms a dot on the with the f/stop can cause the light in an image to photoconductor's backside approximately 1 to 2 dissipate completely when set below some intrinsic mils in diameter. Diffusion then spreads this out to threshold. roughly twice this size by the time these electrons The image intensity can again be adjusted with have traversed the layer, yielding an effective 3 to the brightness control on the monitor, perhaps to 4 mils minimum resolution. Fora vidicon with a compensate for the camera's f/stop setting. The one inch square photoconducting target, this re- brightness adjusts the DC intensity level of the sults in a limit of 250 to 300 pixels horizontally and video signal, while the contrast amplifies its dy- the same number of lines vertically. These are in namic range, or the AC portion of the video signal. fact nominal specifications for consumer quality High contrast will amplify any noise or spurious cameras. Additionally, although the raster geome- signal into an observable flickering ofthe image. A try breaks the image into horizontal lines, the monochrome monitor's screen (E) is coated with a resolution within each line is very close to that uniform layer of phosphor that emits light when given by the number of scan lines. It will be a struck by the electron beam (G). Using the mon- reasonable approximation, therefore, to assume itor's driving coils (D), the raster synchronizing that the spatial frequency cutoff is isotropic. circuits move the beam to the appropriate position In a similar manner the charge storage and on the screen for the incoming video signal. This integration during each raster time places an upper signal modulates the beam's intensity (F). The limit on the temporal frequency response of the screen's spatial resolution is effectively continuous system. In fact, this storage time T, can be quite a with a lower bound significantly less than that bit longer than the raster time T r of 1/30 second. A imposed by the vidicon resolution and by the finite rough approximation to this would be number of scan lines. Additionally, the phosphor ,r, ;z- IOT, z 1/3 second. Thus the system's frequency stores each raster for a short time to reduce response should always be slower than 3 Hz. And flickering. Thus there is another image storage this is what is observed experimentally . Even the element in the feedback loop. The phosphor's simplest (linear) model for video feedback must persistence is typically a single raster time and so contain spatial and temporal low pass filters corre- it can be neglected compared to the vidicon's sponding to the above limitations . storage time. The optical system that forms the image on the There are a number of sources of error, or photoconductor has spatial and temporal band- deviations from the idealized video feedback sys- widths many orders of magnitude greater than the tem. Here I will briefly mention a few that could vidicon itself. Hence these intrinsic optical lim- be taken, more or less easily, into account in the itations can be neglected . The optical system con- modeling, but for simplicities sake will not be trols, however, are quite significant . The focus, for included. The first omission that I have made in example, can affect an easily manipulated spatial describing the functioning of video systems, is that diffusion by moving the image focal plane before the bulk of them transmit two interlaced half- or behind the photoconductor . In addition, by rasters, or fields, every sixtieth of a second. A

206 JAMES P . CRUTCHFIELD

complete raster is still formed every thirtieth of a [2] G. Ferrano and G. Hausler, "TV Optical Feedback Sys- second, but the successive images appear to flicker tems", Opt . Eng. 19 (1980) 442; see references in section 5 of S.A. Collins and K.C. Wasmundt, "Optical Feedback less than without interlaced fields. Since the time and Bistability: a review", Opt. Eng. 19 (1980) 478 . scale of this is much less than the image storage [3] B. van der Pol, "Frequency Demultiplication", Nature 120 and integration time of the vidicon it can be (1927) 363 . C. Hayashi, Forced Oscillations in Nonlinear Systems (Nippon, Osaka, Japan, 1953). neglected. [4] J.P . Crutchfield, "Dynamics in the Space of Images", 1983; A second and important error source is the 12 min . video tape : U-matic, VMS, and Beta formats . intrinsic noise of the intensity signal. A number of [5] See for example R. Abraham and C.D . Shaw, physical processes contribute to this noise. The Dynamics-The Geometry of Behavior, vols. I and II, Aerial Press (1982), P.O. Box 1360, Santa Cruz, California discreteness of the quantum processes and the 95061; D.R .J. Chillingsworth, Differential Topology with electron charge produce resistive noise in the pho- a View to Applications (Pitman London, 1976); or P. toconductor. The electronic amplifiers for the sig- Collet and J.-P . Eckmann, Iterated Maps on the Interval as Dynamical Systems (Birkhauser, Boston 1980). nal also introduce noise. The net effect though is [6] A.M. Turing, "A Chemical Basis for Biological Mor- a signal to noise ratio of about 40 db. This trans- phogenesis", Phil. Trans. Roy. Soc. (London), Ser. B, 237 lates into about 10 mV white noise superimposed (1952) 37. signal, or into about 1 [7] J.P . Crutchfield, in preparation. on the 1 V standard video [8] N.H. Packard, J.P. Crutchfield, J.D . Farmer and R.S . fluctuation in the intensity of pixels on the mon- Shaw, "Geometry from aTime Series", Phys . Rev. Lett. 45 itor's screen . (1980) 712 . See also H. Froehling, J.P. Crutchfield, J.D . Farmer, N . The photoconductor's monotonic, but non- .H Packard and R.S . Shaw, "On Determining the Dimension of Chaotic Flows", Physica 3D (1981) 605 . linear, current output io as a function of light [9] See section 9 of ref. 6 and J.D . Farmer, "Sensitive De- intensity I, adds a third error. For vidicons io - I;, pendence to Noise without Sensitive Dependence to Initial with 7 e[0.6, 0;9]. Furthermore, this response func- Conditions", LANL Preprint . [10] For one approach to quantifying spatial complexity see tion saturates above some intensity threshold I, J.P . Crutchfield, Noisy Chaos, Ph.D . dissertation, Univer- Vidicon photoconductors also exhibit a non- sity of California, Santa Cruz (1983). uniform sensitivity of about 1% over the target [11] R.J. Donnelly, K. Park, R.S . Shaw and R.W. Walden, "Early Non-periodic Transition in Couette Flow", Phys . region. Rev . Lett. 44 (1980) 987. When the camera is very close to the monitor, [12] K.E. Heikes and F.H . Busse, "Weakly Nonlinear Tur- there is significant geometric distortion due to the bulence in a Rotating Convection Layer", New York screen's curvature. Geometric distortion also arises Acad . Sci . 357 (1980) 28 . [13] J.P. Crutchfield, "Spatial Complexityin Lattice Dynamical from other errors in the system, such as the Systems: The Logistic and Circle Lattices", in preparation . adjustment of the horizontal and vertical raster [14] A.T. Winfree, "Sudden Cardiac Death: A Problem in scanning circuitry. These distortions can be re- Topology", Sci. Amer . 248(5) (1983) 144 . [15] See for example AT. Winfree, "Singular Filaments Or- duced to within a few percent over the image area. ganize Chemical Waves in Three Dimensions: Parts 1, 2, Finally, within the monitor there are saturating and 3", Physics 8D (1983) 35; 9D (1983) 65 ; and to be nonlinearities in its response to large intensity published. Herault, G. Bouvier and A. Chehikan, "A New Algo- signals high brightness high contrast set- [16] J. and or rithm for Image Processing based on the Properties of tings. This list is by no means exhaustive, but at Neutral Nets", J. Phys. Lett. 41 (1980) L-75 . least it does give a sense of the types of errors and [17] J.D . Cowan, "Spontaneous Symmetry Breaking in Large their relative importance . Scale Nervous Activity", Int . J. Quant. Chem . 22 (1982) 1059 .

References

[1] R. Abraham, "Simulation of Cascades by Video Feed- back", Lect. Notes in Math. 525 (1976) 10.

207 NOTES FOR AN EARLY ANIMATION DEVICE

Lee Harrison

Thefollowing paper is reprinted infacsimileform as the most primary and authentic source of Lee Harrison's original conceptfor electronic animation. These notes eventually materialized as the ANIMAL animation system. -D.D.

21O EIGENWELT DER APPARATEWELT

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211 LEE HARRISON

v cIU1W cu6c*uau .c %J;rE-coMM4TATOR, oR MWOUIWLLfit ,6RqDIi " e ' ((~~SMV) MSM'I ouTilq" ~ 41 IS THE tNMW OF I C MONp6TA6lk %ULT1VIblAT'O~", C4RWC~~oPeN' St~~f N~ -i~ 1 AN T_I-FcThpwiC contrlUTAlok WHICH OPEN9 , ;k . In C. I t )~ A 5f4UJgN}IAL cLOsT35 A Si:NCE TkOCtDE To DRAW ThF AKMS Ago . A CFIAIJGE 19 VOLTA66 tAVWC_%%S "OPEN" TIME DUpIN6 THAT"pLAcrMtIQT'.'T3oAE DRAWIAIG,TNE l,T:IV`I ou7PUTS . THIS VoLtA6t IS O«LIRS oN owe .of 1Ts .' IS BLANKED ouT) NIA 6E .QL"ED Calf A-585011-, USlo TO OPEN ._A NUM%ER of .SAits CcowKTED To IT. THE MSMV AUTO - `r WHFJJ -NE `QPfA'_'TIME HAS LAP5tD, AS M*iJTIDNI^D 6fTroTtT,/ -NT_ LXN6TH of TIME ORIGINALSTATE CSTM0: MX.nCkt1.%1 FUF5 BACK INTO ITS Omit IS gem"ImED JoaMIE DRwIN6T11E AT'"SMV Amtr. w 1m o,6lihrl wb C1W+6TyS %A.- 170E ouTPuT 6'1 R M THE IIJTb6TLAL RC . NETWORK, THUS PJ4 G.LnSINCr -fNE FUP-6NGk~ GAT'ES,TIII,LS THEM. DUQIN6 VAR%IoG of THE RXSISTNOCES ASSJcu(TED WITli THE -E THAT cAUStb TN'a~ A PULSE LIMtLAR To PAC-l1 ThSMV-ctC-NT'11NORlt;J A1d aprRATeR IS ABLE TO CTrNERATep AudTFIER oLRPUT' OT11WwAL FUP_ IS . A " p" A Fte uei OTL CNARAcTE R NWE THE DESIRE THE MEXT M%%AV 10 SLf-U TO DoluT, MIb :TN"CE IS SENT To WC1tALL STTLUCTUt2E HE ~_~_ -P£RA=IJ OCCUXSJ THUS "BONE" LEN6TH5, +i1JD .. ALSO 111e CAP'll1 WetRE A SIMILAR IN T115 SETUP PRoctbUQE ~bI.TF-IZhINE5 -Mt- &ECIIUEWC` OPEN11J6 Tub NE*T 6RaUP. Of A559cIATED GATES - ASSOCIATED*NTN IN WHICH_].Ht PArne-LILAt %oNrS WILL bt DRAWN. IAI A TIME_ Dfl51;RIDr-D PA Tills R DETt=RMINh'TII S NE I: NECCESSAR 4rAT11J6 NCT15tl coWIIKIES ?n° M5MuALL . _ llg5 -Comm CONNtQ101J Z 'jI'~ .I-LII)1j~,K~ p,1,A11KIN6 Gti hSKV 'S 114E tMA1W HAVE soNC TNQLL L&ML -MS- IN IN rbblTlal4 Tb bMbMIA1r- 141D 581106' UP '-MT: WkRTO I- .-IRSLAMIMMIALL CKLES, . FSor,,E LEW&Th5 . -ME -DbIlINGo1.UPIAT. Df THE H51iv 5 (SmiAM lei I I FIC-T.). ISySE To plff2weM A vlUtIB7:Q of TA51;5 . CopNUT1+TINCr ?O _ I -(wE M5Mi1 cNAim IS A SWIT[HIv3G - EOCL EIUMRLL,:-T1115 OWTNu7 "MA ISE USED NExWoRJC WdtCa1 R6ULAES THE OtuioG )AND cWSINb Cw ttq - _~j, TZoNK SW ETCHES ACROSS THE- T11E `;QN6 6AT'tS''1~TH1= VARIouSTAsKs wHIcg Ir KQWRMS CouLD 8E powb IN aTBi:R WA45 LSuc11 AS lahM>aHA01cAL . 545TTMS(b .) PIVAR4 muKMR 5~5M5 WTTH AN9~4,L DwhA WTWO&S e.) OTMbILbLKSRoNIC ARRAA6EM61JT5 d")q,6clWb Mrcw,utr.I,L 54SMM5

$oNE 6/TE5 . bti v DRIVEN ASSoc1AYED WITH ENCH SOME I AND Walt A ?r1 Il S MV of 111'E fn6MV CHA I!4!I- .ARE GATT-S% 5 A NUMBER OF FLECT LOt4IG. f.~ bUT ~~"`ie; ^IED AR-. NORMALL`1 CLoSEDI . 16%1 TtM RLdl."LAP. WAVE f-RM REcE IVEZVROhj p4 VApl11AJo1W D .C . INPUT Tlve -MIRI5 Gm Ls THEIR DRIVING. MunVIbRlOoR . luraf Is AA1 OurPUT u5ED "To COMPLTHB #4Y.ULNR Po6I11oN Core. May eF 1 UM.LF1) "R-TA-f1 .NMAL Pa-sirlopi - Fit 01"I 1NTi 6KM ONL4 DaRWG THt"oPE?J " PERIOD ) OT- T14 Skits 00 -ME jl,sooE AND T11E f4~E oR coxgKm2 c.IF "x15 ouTfmT . 6lJV E12 NED By D.DD Ill-1JAL QVE5 NAH 6b GrSSID 10 51F111,AI2 D . J THE INPLCT PIW&L. -if: 14t INPUT 15 A .C S"AL ., VA S1"11 To C-NT?tOL ¢sTHf R PARAMtMj2S of TNb e - SlJcH AS I OTEostTLi - MILL. BE A cnRRl66PC*l 1) 114C D-I: BON ~c;T&YueF fd'c TWN-11CtOtATPttT sink WAU6 slGwAL 4) C5lrkua\h it TlAt INPUT IS A OUTPtAT WILL 141 Ii_5UTDJo 6ATE5 cAttrb _ O. x.ND +' SEND oTZ aT11ER SIMPER SIGNAL ) THE IN -TtlLIQ 516NAIs'Tb.~ I LooK LI Kb '111 - IW PUT .) amBa WcRAS "T"S 1 AAaL~P2~DUUNG IT N114 N~TW o1zIC5 %ATE PRSSFS M..ALwWS TO PASS 1HRU . TkfrS Ay ALSO 4F SbM' mCmAL MT-t5 PRf~,&rt AT It's INAa Dule1Nc, . % : ITo toRRvSWND INC- Cm"NMS pF 1"~K5 TAP6 Rbr-o"GR THE"CPEN-PER -Pf .uf; 6mb. ~ so THAT DUQ11162, PIltiBMK THESE MLALTIPLLAD - WILL 1-Kt- "1NE GATES faR EACH epmE (IRE IN LLM,. ' SKI.IALs bRIVt: "Nb AAJp SKINPRob11C11JCr SEW s16MS ~\9Ot'CjAANISMS OF AWD CPethTt. SlM1ALTAt~641.15L`1 AND ; TA6 MKE IllAS AIATar"IATcALL4 _ DITTfet-vf PAIff'S cf -Fllf; Dtvr-F- 10 o~D I_T_ PRobtkc(AIG TIVE PMI0MRI RSC.DRDED Movbm6lJM _ TO N5 . PSSd_IpiTjD "MWt.'- BONES AND COOTl2-L 11iti1~`n~WSfll° of THE fl~NB i AA¢TS, SPAC.$. -A 6mD D.C WAVEFJRM the. WILL IN PAIJE . :Kr .CTIVS sc- s"ou1N LATER) MAKES A STRA16a -1Nti oUTPUlS a , CON5>CL O GATES ftR'& A GKT'ED _=SHAPED "WAVBi~RN1 WIL<_ P1AKE A LLL QED INTO THE "O*- SINt-C S'MC FUNtnod-66N61* ofBow E r a WNo!;e AXIS 15 OCT STRAI6 "T I AND SIMItA1zLy -ME-. OUTPlr*1 1 GATES IArlO BUT NAS -Mj II.IlEGRATT:~D~ ) VECIGRJAI. DIRBCMN 111 I: + SI NE. co-AA6 f ut)M-N Cep . 9NAPED INPUT . _. (oa SNAPF) m I -D er1 TNS ~!`11 T1Ib U .C . Vdl7A6E APPLIED iI lbE "Lt- (d) TdA1 THE '' TO -mv Titz5T_GAm b?NE _MAKES LN7H THE X -AXIS op THE D!SPLA4 M VARMg . A _VkRIA6Iyt POnWIP 612 tIAt1 b kstD To YAWCl16 INPUT VOOME, coT11ER MEANS D 6Ab r1Ati I-- ,5r-r,,_,c coupSE) . TIAF sbC<+J I 1~45ED. IJTRaL_ F,~AI6 LE -NAT TNb T+X"tf PLAN INSiMILAft 051110N

214 EIGENWELT DER APPARATEWELT

- Castor- FuWcT%OAT 6ENLRATolL .,1 .

~.laLFhn~ .a..{,r,.l+v ~t THL11L ART 'A SINE -0351WE fume-Tlo~AjJfRATDR5 . :ONE RtCENE5 JTs ISIPwr FtaomlT£ O -6ATC-5~ -me csmLR-7n.m - !He -MIL OWPI.tT OFTNE DfLA4 MV . IS DIFFEQI:AMATED EAcH rsuLQKTm HAS t cxmPUTs - ACA INW . AND CLIPMb, So -TNAT .OmL4 APULSE R*PR>:SENTiA(r 44 1Hti RANGE CE VOLIA6ES AT THE 1 4PILE 6ENT TILE - 11-AILING EDGE OF lUE CPAA6t- CF-STATES IS pmmwr AV44 Dum1=.D AWSL$LAiL P051 -THE ST= NT ON To -MT-- NARROI4- PULSE h5 M V, gowE I Auu'tNE-TWavwncE ourpRT5 HAVE 11fE Q;.LA- roN of THE SIME AND COSIAE RESPECM) 1H6 IuPUT To THE NAKROw PuLSt M5hV IS 4OMM41P" (3ETc,G-eNEQNL TNEOQ4 NA,RR.W ~TTLI SfAe PULSE

A. HIGH GA1t1 AMPLI t I EP 'MX- INnGAkfoll_Is _. obfkIMED NAS A r-TEb%AcK CAPACITOR 1a Its ` 5 IM'ERMlDIATE vMWS MAN BE_ 134 comTl4uou I?ADo0 Fun3GTIDt4 Is ro PERF-)Rri COM1~IWIN6 ALL THRFE 4NTE6Wo1~_ allTPLITS nJ oi'Ss THE 5"ALS 'PATSSNTED T b 1'f5 . 11J . IIIb12E PAoPER "WOO AMOUAT3,- MW -T1lll5 ALL.WIaI- 1 AR-E THMf ctwoRS 1N-10.t BONE GC- W CKRmpt of THE- woke Tb . VIT-L) )OF t F&{ -tNE mWE FOR T;1~It^CooaOllJf.T'6V 7(,1A ;Z 6blECT OR FIG KRC -FRohl Aj.)L1 Po5fTIotu I -Me 11. . 4-LfA6E~ IF THE WET TO AA Mt6WCfO2 i. D.G FUIYC.Twt~ oT- cor1t51A11Jb. 'MESS wiK12Arca cwrPuT5 IVITIAL cr~IDIfI.I S -T11f olitp%fr IS P RAMP F"NC.spN  Tile 11.1 A PLoPB2 FASf11o0J IS CAVAteb. OUT 6ti THC THE ouTPtkr WFIKM bereRn1AE (aTNRTWO VoLThG2fa OR "CAMERA 1.1J6LC- NSTWRgy?o 6b waiS50 LATU, ~ -at STAnoN` PfefaT of EAC-H 6ONE 00 THE DISPLA4) % P W IsETtawIHEA ISh THE Y.LTA6E AcDoSS iNE fEtlylDGL' yb~ -vrj ypr.cIToR , K Ale-t- OF 111 AT tHt; VU=I Of VOLTAGE p1LbStAMD To T1IE IMPUT cd c--ct~W~Li'000~1, 1,I~6RNIO~I cjF ' Au IIdPE61LRINZ ~t;TE4HINES. TI1b RATE of tk1+J66 7owcu A SL.~~IUE(N]Ce OT .D,C . `4OLTA6f5 0ILL- tE e~ w&WAQF hr T11E ourPWr, (slurs), zc Tu M"WMer%1 . TOGFf"rR:; WHtot116R THE CAPA4To(Z IS DKL4ARGBb lwPIITVoLTAe_E5 ta TbE X ANA Y INTE-MTO RkPRESEIJT 4044 oa, IhioKssc C. L CPODMON 4OLTncfS Aa>: THE Go5 O AND SW 8 %tesPScnvrly US" -ME ANn Tns USPU,y UAM *.A OIMPkr OPT41F ImTEGRKr0R5 .WHLN D F1ED RtTU"S TO R?ARGeR STIJLfIN&P'OSIT1ON . INTO T11t rtorMc,urAL AND vtltTr-nL A"PUF"S oN rTtle PL4BtCiC__SA9CSAT To p5E WSCR1b$D PfPICWhS h 61SPLALJ StbM WILL CAaUSE T1+E 6" Ta DRAW Our _~ lot FI4NCTWN of SHORTIUr. A LIME am THE SCOPE WHOSE /ANGLE To THE ppyal&Mul(r-lift VUPAC,1Tolk AS mslR*D OR Rfqu'RvP 1-1o21z,NTAL . Is O. - ._ _ To WW A Ff61LfLe OR IM&6$ . P

_W___ "_- .- ~ . . JnI,(onelropT ori o - .IU RS Ia11ttj PILt FW IVO CAMCF AN4Iw°4fa .. mt THE w A11 MMQNJ-111E DISPLA!I,WlLL 614E1Hf__ . D9nwN) . PiI.o7EcTiOM o* THE F16kkL CO R IMAe-IE- $I

21 5 LEE HARRISON

216 EIGENWELT DER APPARATEWELT

,Tt%s FuNCCww cF T116 F4PRFCK NETWOW l, o 11011T our CA DISCNAfJ& THE CAPAc%TORS. ASSOC W(Th TtrE C~ "~t,u NTTWdRK~ WTE6RKTOtLS~ AT . bt51RZb TIMES Dud~ ~yS Na TIE CNb OF Gvk `VCL 'THE FkUcJntbJ ¢FTIIE SKIN NETW-tit IS To AL6ENOAiCN.Lt/ 6F 1snmC5 AND AT- F Boob CLIMHINT Tit' VAI1IOgS . VoLTAaf. RZPAra .N77R1o1JS "'j . GENEFlkTIOIJ, DISCHA"IWw OF -Mr. CAPACITbP-S CUSSS .3111 n cnn n AI n I e~S "~ IC,t~ k,t Kits' alv%kt I " :"fN>r DUM oA TIIT r,PLAY1 CRT To FLL1 8AC.1; TO 11A4 cos kyt AWO ih.a. VIDEo sluihal - A; T~ 6IVE T1E i SfARPUb (bSITION . . __ .. PlZoP£R FotMULAMA-nc ktpQ:tSLMTATItiJS of TN>: AN LLFCTRQNIL SWITC14 DISrHARfT5 THE CAPA.C.ITOR. GEOMETRIC. PROJVCT1a"S e3F THE FIGLA121= oR ObJE(T PULSES WNIclA CLOSETAE SW1" eontfaet-T Aly AMPUFIbQ BEIUG 6T:N1` TT.'D. Fo0.QUlGK RETtRkA~UL 1 A er TIO . Wluc.A 1S 1A joh) f1

:S, THIS PuLSF t=LIPS THE ,SM4 DC . VALUES OT- VOLTAGE. WHOSE QFLATI-ASHIP f 4110 AND IT`" ouTP&-c-d41S:kS THE' SWITcU1=S 17n, C4-S1=, CoS IS AS E 1-1"16 pup COSH d111E ' AN61E ~ . i~11dIS v5smy .SQ"SL .LJ 7114 '~cuSfQ"Slmb Llt4TIlt IT grCl'1Jg5 AOJOT1SQ. IAIPLf(` WHIG" PIU-SG "15 TIME KIt~ RAMP R1NCilot4S Of VOLTt~6E, THE OUTPUTS !P2oM TNT:. CpW.ITft3, THE PuLSb CnMES sxkmh k.t,~ of IAITE6RA1mc, X, y ANb Z R1=SPba1VbLy t wutom('-p lc1{ STA~ Tk'1n 4it,rJ of _ IHslr. v 'S, K,t t Tke wwsmw K, is A, ScAtlw& . _ rAobES_OomvEST l4t~ of I%kF PIALst IAIPwr5 Ta FACTOT~~A~' ~~,,WHICH Is p'bEuict- FukGtlo1J of -ME ~ 1A1: AMPLIFIER I~AIcB. AcniAZ65 1N6 51iitKRA5 So AS 6a%NS C* DISPLIw1 AwPUFlt IDFTAa 6Alu5 OFTHE uITT36RAT1Ne- -Tim PRE,)E^An ruLSES r,F~EOIoa bkcK IARo TAr- AMbL1PItI6 ACID AOjA A wAIcMotJ aF Tt1E AMPLITUbt (%-THE: 6prcs Amt, ~aL? aF SE vtNCB IWPur SINE NOD QaSIWC- WAVES TO Tl1t IMTE6RAToKs. roR . 1 . :11tE- .f1.Ett~q IJIL._ 31elIfLNSs U6Ma1 t1o55D UuR1tiiG SIMPLIctr1 -rAESIE Eltv-Ts AILE accomrirl" FOR ek TNE (Ass At DuaAP:!_'~ PuLSF r 1Wa 6E R L-06- o!L of Iil(5 "LUMPED COAS?AAT ' KI ,

Sirs K,t " SI,t NOD cl-s(IJE WAVE FutOcilo~S Coy WIwSF 'pQr,? tltVJC,L1 (Toe IIIaK F"6MG4) IS pt"itm11.1m et1 AMD IJ1hsr -lC1~ s AMPLITUDE 15, COW51or-PLED To bE EQlLAAL _ 10 I C ONE 4NIT)" (Vdl A 110RMAL MkMV1N1c1AL a IIEPRLSfiNT1R4~IJ UI1Lt o NA4F to US6 Q Sln 9-Lt . "A . . DEMOTE '1%11S WAVE 15UT Of- siy. 1~PL_tv-4 TNrt ExFRyW . LTaMIA6 0,,= a la ,i"} , tWkit11 k*r, e a6vl lotaft P"!

cAPITAL. A, IS USE4 Tb MNCTf A0 3161~p.L WHICH r1W1ffS FRs~(V1~9Tt~ .-.SKao $ckom"ER, THIS IS ), Wlbt DA 1=SIeoJIIL Aamr-l wllcsf uprrt2 FR~tA~A~tis !,.l~2lt NIa -rt-'YO 1"16EMNC CkIJCT104S ARg Pe krIED P}1 .'RIF %2M014 -M SHOW THE INvrk-fmLmogSH1P ~* 'iN 1~41s dPTNE moick WNICf1 we UILLlht SKIIJ VJETWORK, 316Np.LS, A PICTo6RAPA 1s 61gcw bL~LoI,~FoR ~. ULMELI{ MIULTIPLICkno4 Awo ADD(T1ON, Ba"FS AS SodpTFp WtTN EACH MIALTRUER AW ARE INPUT AND OUTPUT AMPLIttERS I WHIct1 A" imq'QoNIcAity WEc--SSA2y TO ALLOW Au MIOW6Ut MutMPUFR10 PEkl-eNl TIIti TASK of )qIAImpLlcpwlolj . QP MUI-TIPLMRS P-lgUI A"cegrt.R TAP° IINPUT~TgUS IALMQ(JE12 pf .C9 9IS6lI- Mx-E IMP-RTA9T -MIIJG H "T11E PAR71cUU.1ZTALIC I OUT THAT WE-QQ- PERFwkm IT .

ADD'ET15 ME HrsmL4 RzSISm Z pT5C1,bIZ1C5 WHICH ADD 1NF UAIQIWAS S16p)AI-5 PRE-St4MP -rt., IT.

XL4,t0RAICAL.W SPEAKING, Trt SKIIJ NETWORK TxK65 -mb ~vIoust?~I PltwTP ;i& 916NALS AI,Ib c'Ytela6S THEM So THAT

z _- k,tz si,, +A cos o~skit

HERE '1L I, AND ,'L kt-PRE ~~ A )L,% AMD 'f VrtCToi1AL.~ COMPWJL" W,Am .9`1 PIESf1JT1U/G M H a, of T1I f%f S l6 U hLS TO THE X A 1J D y apw" DiSvW( cfT I -rat R*SULTIuG btAtA111G WILL DE T, peo-TFC.n-N dr-Tilt S blPI&Js101 AL F161IRr 00 -ME PLANS MlERM)td6D t1 TIIE COMPol1COT5 SeLIMED I I1'1 -ME GEOP1MOAc" SSLEatna AND G0MbWKT1o1J of ALL1HICFE -"MESb COMPw'JCOM, A+IIA ulsw twfflft oR PR°TtrCw t, cT 11It- 3 DIrt8AstalkL }s161ARD 00,11 86 --

21 7 LEE HARRISON

Z 18 EIGENWELT DER APPARATEWELT

/7 t--~~, - . .~.6n~*h-N~t.rz WFTAORK . \6'~'~

Tm puaclfo 0 of THE CmTeP, "LIE WWOSM is TO RLCV&LAY~LIM (4")D 1N45 C90o"TTTZKPLL 1IJE. I ! 'flit V, 1, Awl) z compowtwTS OF TH t` DIM~Kal gVf1+TuAtL`1~we'LL USE 4Zo& zoLl0G- SA O- H31-orb-n3 tFiC1,m 10 suds f,, ~H_~._yNfR AS To AL '' WR -01 Pesin-W '/NF' sNAPTS O i-+, So THAT -MF CAMFR), ' OTT1fE PCESEWNTMIJ Of ~S`l'^ MCTION OR V17EW We. Lt5 MA"i bt Ot-CMAED olJ 'n{b -CoOTRot_-Tx.PS F1611m Ofto TAI_ cuTPu?$~F T%1s atria-av ARZ- E£~nR.D~~~~e~~- ALopc- W+~cT11Mo'TI+E2 camp--LLi4cr 111FUoR1 P~ mF A" CRT 1R'eSEtireD Zb `f14b .XILNbY cskNNFLS DKPum . INOWQ VA.V+7,WE'LL *VvCa2D _ S161*L5 lo WH%Ckk TNb" SE.e-J o 5 W &L RT)~CT , THUS 0fpRPW%- -RAE e ? MA t&OkC FtWCTPNS A(X- PER.Fn12M6D - THE FIRST AN e-LT;S 15 MuLt1tLKATIa[,L_el A C)D1JSTPIJT, THE SECOND IS

THE "ntiLnPucAncN hsti A coWSrw1JT" 15 " 14 VFEEC.T" TN1=" n.K11JCr of t t E 5113E N* Cp411JE OF TH E 'VC"oQ- Wb 1,S_ lc~ccMPUSNE<~ lVi A NfTWWK OF YA+LImt_~ Slde~. SIN~ Porewilomu6K. ADP111M1,j t'. PFRfbRmBD u5LIJ6 A ftxLD Pzv-StstJ,ACr- N6r4uRK .

PN6LE$ O._CTRL^_ PR1Mfi) IND ~~ ~PNI PRIME 1 PLAIJf ~BXtr ropwTSEF.tr 7116. RorAT1oW of THF X J 111E X Axis AND TNT- XZ 7EA9au1' 1H& AxIS. .ww w4rees 1 Si 1J -Co9r.f PoTS GM16ED Tbr.ETH ER (IR r bN A COMMwj . SNArr) is -me HECAAU151"1 FOR WRWRyYL 31E P2opb"-RtWED MULTIPaCAMN By CWSt*N3 u , 1Px%oV 1pt smlY+ CC611JE5 M lite PR-Pm RELATIc4shlP? Twt;l~a apt -n%- su4i MbCPNu15M5 . RaTAT1o0 aF 111E SNAFr 0 . .oNE,CoaWoL.s 7H E VIfWIW-, AN6LE LE-O'. T1lE an+Fl; . cArLm~ls f.' MPL(FIrAS AsSWaf ; _ WlfW '121E_l19I1+pax_ of Sink:- coslAr . Par-5 ARE AN _ pLxrn"At NIe"1m - _ K~ ourpuT~i cF - IS WTbL-*K ARf FED Ivfo THY"~,Cp~NNtl;. dr -m b15PlJM C"RT E 1~D RtPRC-SFN~ ;, 7b 1NP -7~.r.8~=4WWL IIIlbo"* rtceSSM OW t

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21 9 LEE HARRISON

22 0 EIGENWELT DER APPARATEWELT

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22 1 LEE HARRISON

22 2 EIGENWELT DER APPARATEWELT

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22 3 LEE HARRISON