Digital Creativity 2005, Vol. 16, No. 3, pp. 165–185

Cellular automata in generative electronic music and sonic art: a historical and technical review

Dave Burraston1 and Ernest Edmonds University of Technology, Sydney, Australia [email protected]

Abstract 1 Introduction This paper will review electronic music and sonic This paper will review electronic music and art applications of Cellular automata (CA) in a sonic art applications of Cellular automata historical and technical context. Algorithmic and (CA) in a historical and technical context. computational processes have been of interest Following the main review is a comparative to artists for many years, creating an emerging table highlighting the similarities and culture of generative electronic art. Creating patterns and sequences is necessary for the differences of the different approaches (Table creative artist working spatially and temporally 2). Algorithmic and computational processes within a chosen medium. CA are capable of are an important tool for the technology a wide variety of emergent behaviours and based creative artist producing generative art represent an important generative tool for the systems (Dorin 2001, Candy and Edmonds artist. 2002, Edmonds 2003, McCormack 2003 The sonic artist and musician must be prepared and Miranda 2003). Complex systems such to investigate the theoretical background of as Cellular automata (CA) produce global CA in order to successfully employ their vast

survey behaviour based on the interactions of simple behaviour space within compositional strategy. There is an extensive amount of mathematical units (cells). Their wide variety of ordered, and scientific literature relating to CA, however complex and chaotic behaviour represents much of this is esoteric or difficult to understand. an important generative tool for the artist. Important and accessible CA concepts are CA have been of interest to musicians for presented concisely in a non mathematical many years, assisting an emerging culture context to give sufficient background for the of generative electronic art. An example review. visualisation of ordered, complex and chaotic There have been several approaches at CA behaviour converted to music is shown applying CA in the production of electronic in Figure 1. Example CA evolutions are music and sonic art. Examples exist in the fields of overall structural composition, MIDI shown to the right, the horizontal dimension sequencing and sound synthesis/modification represents the cell space and time is evolving techniques. Applications from academic, horizontally downwards. independent and commercial sectors will be The enabling technologies available to critically reviewed in an artistic, historical and the electronic musician have taken the form of technical context. This will provide the artist and interconnection and sound generation. Musical scientist with a balanced view of this emerging Instrument Digital Interface (MIDI) was the field. first manufacturer wide standard enabling the interconnection of electronic music Keywords: algorithmic composition, cellular automata, electronic music, generative instruments to each other and to computers music, sound synthesis (Rumsey 1994 and Penfold 1995). This made possible to some degree the connecting of electronic musical devices for performance

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Digital Creativity, Vol. 16, No. 3 and Belar1961,Hiller1970). Builtaround the Olson-Belarcomposingmachine (Olson experiments inalgorithmiccomposition was a partoftheprocess.Notableamongearly possibilities andallowingthemachinetobe digital domain,bringingawealthofnew transferred algorithmiccompositiontothe The evolutionoftheelectroniccomputer algorithmic composition(Roads1986). technique oftheirapplicationknownas creative activityofmusic,thetoolsand been utilisedforcenturieswithinthe Formal processesandalgorithmshave 2 Miranda (2002). described inRoads(1996),Russ(1997)and techniques incontemporaryapplicationis field. A solidgroundingoftheprinciplesand cover avastareaandisconstantlyevolving Sound synthesisandprocessingtechniques and control,irrespectiveofmanufacturer. Figure 1.Musicalvisualisationsofordered,complexandchaoticCA

Generative artandalgorithmics Burraston andEdmonds 166 166 Program and in1962completedthe computer toaidthecompositional process large numbers.Xenakislaterprogrammeda 1955, usingthelawsofprobabilityand formulas byhand,notably Xenakis initiallycomposedwithstochastic and over5,000slideprojections.Iannis of uptosevenkeyboardparts,fifty-one tapes HPSCHD later collaborativeworkwithJohnCageon 1997). This providedacommongroundfor computer (HillerandIsaacson1959,Chadabe algorithmic compositionproducedwitha Illiac SuiteforStringQuartet composition in1955,andby1957hadcreated statistical mechanicstoautomatemusical Isaacson beganusinginformationtheoryand event generation.LejarenHillerandLeonard this processcontrolledpitchandrhythmic produced randomnumbers. The resultsof of weightedprobabilitiestoelectronically 1951, thismachineallowedtheassignment (Xenakis1992). , completedin1969andconsisting behaviour. Metastasis 9/16/05, 3:06PM Stochastic Music , thefirstmajor in Cellular automata in generative electronic music and sonic art

states, “Control was an illusion. But I was in Digital Creativity, Vol. 16, No. 3 the loop.” (Chadabe 1997). The generative art process suggested in McCormack (2003) represents genotype as the formal specification and the resultant artwork experience as phenotype. Algorithmic composition can be placed in context with the generative art process as detailed in Figure 2. Algorithmics allows the production of data sets to be mapped to parameters for the generation of musical or sonic outcome. In the centre, the artist may also perform functions upon this data set before application. Feedback and iteration may be factored into this process at all stages. Complexity theory demonstrates that complex systems of simple units, such as the cells in a CA, produce a variety of behaviours. Figure 2. Algorithmic composition and the generative art process. Complex systems produce global behaviour based on the interactions of these simple units. Excellent introductory accounts of the area Symbiosis of interaction and of complexity theory, CA and Artificial Life performance with algorithmic techniques can are described in Levy (1992) and Coveney be seen in the work of Raymond Scott and and Highfield (1995). In their account of Salvatore Martirano. Scott founded Manhatten complexity theory Coveney and Highfield Research Inc. in 1946 and produced a host of define an emergent property as : esoteric machines to sequence and synthesize A global property of a complex system that sound. His Electronomium was a composition consists of many interacting subunits. and performance console utilising electronic A more technical, but also readable, relays. The system’s musical output could introduction to the ideas underlying be modified indirectly by the composer, complexity theory and adaption are described guiding the system to produce a satisfactory in Flake (1999). Adaption with genetic composition. The Electronomium was used algorithms (GA), and complexity theory with in advertising jingles, audio logos and film CA, offer the use of emergent computation soundtracks, as well as by Scott for his and behaviours as compositional aids to the own electronic compositions (Freff 1989). generative process. Biological adaption is a Martirano’s SalMar Construction of 1972, natural creative process of evolution and GA was a realtime performance instrument attempt to model this behaviour, achieving utilising manually and logically driven this through the use of fitness criteria, and touch sensitive switches. A total of 291 processes such as breeding and mutation. switches gave a performer interaction with Approaches to algorithmic composition and four parallel programs controlling a modular generative art through the utilisation of such analogue synthesizer. A zoom feature enabled artificial models, draws much inspiration from movement and change within micro and macro natural and biological processes. structures. Martirano of his performances

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Digital Creativity, Vol. 16, No. 3 example space-timeplotsoftheir behaviour. Figure 3.Langton’s schematicofCA rulespaceand the areaforpurposeofthisreview. CA presented togiveasufficient backgroundin quantities, everythingisassumedtobegrainy. Space andtimeinthisviewarediscrete computed withunknowabledeterminism. much likeaCA,deterministicinnaturebut that thedigitalmechanicsofuniverseis nature’ (Fredkin1992).Fredkinbelieves his owndigitalphilosophytermed‘finite universe isdigital(grainy)andhasdeveloped standing CA scientist,isconvincedthatthe digital, analogorhybrid?”.EdFredkin,along poses thecontroversialquestion:“Isnature ‘calculating space’ (Zuse1969).HereZuse was introducedbyKonradZuseandtermed of theuniverseasatypeCA computer growths ofform(Burks1970). The concept to studytheprocessofreproductionand Ulam andJohnvonNeumanninaneffort units. CA wereconceivedbyStanislaw behaviour basedontheinteractionsofsimple Complex systemssuchasCA produceglobal 3

(CA) Background on cellular automata Some importantCA conceptsarenow Burraston andEdmonds 168 168 rule. Figure 4.Exampleofanattractorbasinforachaotic Class 4:Patternsgrowintocomplexforms, Class 3:Patternsbecomechaoticandnever Class 2:Patternsevolvetoafixed size Class 1:Patternsdisappearwithtimeor with oneoffourbehaviours(Wolfram 1984). were qualitatively classed by Stephen Wolfram specified neighbourhoodaroundeachcell.CA rule. The localtransitionruleisappliedtoa each cellisspecified byalocaltransition states. The simultaneouschangeofstate cell canhaveoneofanumberpossible process operatingonthisarrayofcells.Each common forms. The CA algorithmisaparallel dimensional arraysofcellsbeingthemost of dimensions,singlelineararraysortwo time arediscrete. They mayhaveanumber are dynamicsystemsinwhichspaceand spatially andtemporally. exhibiting localized structures moving both states. repeat, formingaperiodicandrandom number ofstates. periodic structurescyclingthroughafixed forming structuresthatrepeatindefinitely, become fixed. 9/16/05, 3:06PM Cellular automata in generative electronic music and sonic art

the λ parameter appears quite useful it should Digital Creativity, Vol. 16, No. 3 be used with care. Langton points out that it does have weaknesses and will not always be able to work correctly. The λ parameter is seen as a useful tool when dealing with CA of higher number of states and neighbourhood size. Langton produced an example schematic illustrating his view of rule space shown in Figure 3. We have included spacetime plots of example 1D CA evolutions for each class. The evolutions show space (cells) in the horizontal and time runs vertically downwards. It is important to note on this diagram that the boundary between order and chaos contains Figure 5. Example of Wuensche’s automatic CA rule space complex behaviour within it. This implies classification using a random sampling of >10,000 5 neighbour 1D that the transition from order to chaos as λ binary CA (v2k5). increases, may occur in a discontinuous jump to chaos or may pass through a region of Other methods of behaviour complex behaviour. classification have been devised, an example Langton also supported and promoted of six categories is given in Li, Packard work on the global dynamics of CA and Langton (1990). It is known that it is (Wuensche and Lesser 1992), which offers undecidable to assign a CA to a Wolfram a new perspective based on the topology of class (McIntosh 1990) and there are several attractor basins, rule symmetry categories and behaviour prediction parameters, five of rule clustering. In their work an atlas of these which have been surveyed in (Oliveira, basins is presented for a variety of small CA Oliveira and Omar 2001). The relatively rare sizes up to about 15 cells depending on the complex behaviour of class 4 was shown to particular rule. Here one can compare basin occur between ordered (class 1 and 2) and topologies and measures between rules to chaotic (class 3), termed the ‘edge of chaos’ gain insight into different rule behaviours. (Langton 1990, 1991). Langton introduced Attractor basin topology reflects the dynamics the £f parameter, a kind of virtual tuning knob of a CA rule and can be used as a method through the classes of CA rule space. Although of identifying ordered, complex and chaotic

Figure 6. Example of increase in chaotic rules demonstrated by Wuensche’s automatic CA rule space classification using a random sampling of >10,000 v2k6 (left) and v2k7 (right).

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Digital Creativity, Vol. 16, No. 3 deviations andentropyvalues awayfromthe complex rulestendtohavehigher standard entropy withalowstandarddeviation, and and standarddeviation,chaoticrulesincrease Ordered ruleswilltendtodecreaseentropy type ofbehaviourhasitsown‘signature’. variation oftheentropyovertime).Each disorder) againstitsstandarddeviation(the on meanentropy(ameasureofamount rule spacefromrandomsamplesbased emerge. are requiredbeforecomplexbehaviourcan more cellsforlarger neighbourhoodsizes, of thisbackground. At least150cells,and glider canbeseenasadislocationordefect over auniformorperiodicbackground. A particles orself-sustainingpatternsexisting random initialconditionstoformgliders, emerges (self-organises) inspacetimefrom in (Wuensche 1997).Complex behaviour various parametersandexamplerulesisgiven characteristics, itsautomaticclassification by images. A thoroughaccountofbehaviour on asubjectiveassessmentofitsspacetime the endofthissection. automatic rulespaceclassification anduntil the followingbriefoutlineofhisworkon numbering terminologyfrom terminology. We willuse Wuensche’s in thefollowingsectionsadopt Wolfram’s Most oftheCA musicliteraturereviewed even numbers of cells within a neighbourhood. Wuensche’s numberingscheme allows for states andrastheneighbourhoodradius. numbering schemeofkasthenumber by k. This differs slightlyfrom Wolfram’s and thenumberofcellsinneighbourhood the numberofstatevaluesisrepresentedbyv chaotic ruleisshowninFigure4.In of CA. An exampleattractorbasinfora 2005), aswellmanyotherimportantaspects exploration ofglobaldynamics(Wuensche Lab behaviour. Wuensche’s ( DDLab DDLab CA behaviourisoftendescribedbased ) softwareallowsforthe canautomaticallyclassify Burraston andEdmonds 170 Discrete Dynamics DDLab DDLab in 170 highly likelytobeachaoticrule,whichhas is thatifarulegeneratedatrandomit top leftoftheplots. The implicationofthis a chaotictowerasthemainfeaturein shown for6and7neighbourrulesshowing clearly inFigure6wheresimilarplotsare rules risesverysharply. This canbeseen size isincreased,theproportionofchaotic with thismethodthatastheneighbourhood Wolfram’s. Wuensche hasimportantlyshown v2k5 in Wuensche’s terminologyork2r2in here arethe5neighbourhood1Dbinaryrules, over 10,000ruleswasmeasured. The rules seen inFigure5wherearandomsampleof extremes. An exampleofthismethodcanbe rules canbegroupedinto88 equivalence the totalnumberofrules. The 1Dv2k3 increased thereisadramatic increase in of 3to7cells. As theneighbourhoodis rules for1DbinaryCA withneighbourhoods 1 showsasummaryofthetotalnumber rule andcontainsatotalof256rules. Table three neighbourhoodcellsistermedav2k3 of theneighbourhood. A twostaterulewith function ofthenumberstatesandsize one dimension. Table 1. Total numberofCA rulesforv2k3tov2k7of commented onthe5neighbourrules: is extremelylarge, Wentian Li(1989)has systems inartisticendeavour. implications fortheserendipitoususeofthese half, itstillrequires asolid69years. to-1 transformations,whichcutthetimeby due toequivalencebetweenrulesupon0- all therules.Consideringredundancy going to take about 138 years to run through pattern from eachrulein1second,itis Even ifwecanproduce aspatial-temporal The totalnumberofCA rulesisa The magnitudeofthenumbersrules 9/16/05, 3:06PM Cellular automata in generative electronic music and sonic art

developments include both a 1D hardware CA Digital Creativity, Vol. 16, No. 3 (Sipper 1997) and the Bio Wall, an interactive 2D self-replicating CA display (Stauffer and Sipper 2002). In addition to the references already citied CA have a substantial and wide ranging body of research (Toffoli and Margolus 1985, Adamatzky 1994, Sipper 1998, Adamatzky 2001, Wolfram 2002, Griffeath and Moore 2003 and Meinhardt 2003) which will continue to influence many artists in the future. An extensive bibliography of CA can be found in Nisho (1975). Figure 7. Noyzelab’s digital prints of CA compositional data. 4 Generative electronic music and rule classes, with a maximum of four rules sonic art with CA per equivalence class by the application of There have been several approaches at simple rule table transformations (Walker and applying CA in the production of electronic Aadryan 1971). Global behaviour of rules music and sonic art. Iannis Xenakis used within an equivalence class is identical and CA calculated with his ‘pocket computer’ to the spacetime patterns are simply changed by determine the succession of chords within being negative, mirror image or both. The 88 a rational, perceptible structure for his equivalence classes can be further grouped composition Horos in 1986. Xenakis was into a total of 48 rule clusters by another attracted by the simplicity of the CA process simple rule table transformation (Wuensche to produce a rich output (Varga 1996). David and Lesser 1992). In this case the equivalence Weinstein’s graphical music score for his classes become grouped in clusters of related Illuminated Man (Davies 1986), a 20ft square global dynamic properties, although their textile dye on canvas, is a 2D arrangement of spacetime patterns are often different. Another black and white squares which suggests a CA popular method of reducing the number of influence. Joel Ryan, in collaboration with the rules for a chosen neighbourhood size is to artist Ray Edgar, created LINA, an installation simply take the sum of these cells (Wolfram piece (Edgar and Ryan 1986, Beyls 1989). 1983). Rules computed in this manner are LINA utilised a single CA, with mappings termed ‘totalistic’ and are a very small subset applied to the MIDI and visual domains. of each vnkn rule type. There are only 64 Sound was produced by the use of a pair of totalistic v2k5 rules, reducing further to 20 Yamaha TX7 MIDI synthesizers and video by rule clusters (Wuensche and Lesser 1992). a Fairlight video synthesizer. Isle Ex exhibits A more manageable number, but also a large on the internet philosophical transmusical reduction of the possible behaviour. The v2k3 renderings based on 2D CA. A variety of 2D rules are also termed the ‘elementary’ rules rules have undergone transformation to MIDI and only one equivalence class (rule 110 and by ‘musification maps’ and these may be its 3 equivalents) is said to produce complex viewed online (IsleEx 2005). behaviour (Wolfram 2002). Bill Vorn has utilised 2D Life (Gardner Another interesting area is the research 1970) for his noise art installation EVIL/LIVE into hardware, which will have a bearing on (Vorn 2005). Vorn used an 8x8 matrix of future application of CA technology. These halogen lights suspended from the ceiling

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Digital Creativity, Vol. 16, No. 3 these surfaces.Dorinalsomakes thesoftware to pitchesdependentontheir position upon a different MIDIchannel.Cellsareassigned degree. Eachsurfaceofthecubeismappedto order toinfluencethesonicoutcomesome cube. CA activitymaybealteredbytheuserin interconnected andpresentedassurfacesofa six 2DCA grids(Dorin2002). These CA were polyrythmic patternsbythearrangementof installation piececalled stage. Alan Dorincreatedaninteractive to recruitvolunteersinteractatthedesign software beforeinstallationwithouthaving Life artwork. This enabledthetestingof for with automaticallygeneratedfitness data spaces. gallery areadjustabletosimulatedifferent real gallery. The dimensionsoftheartificial the movementandreactionsofpeopleina artificial galleryspace,designedtomimic lattice gasCA togeneratethemodelofan and Thompson 2002). CA andgalleryspaceis are availableforfreeat(DelicateEar2005). controlled byCA. Cellsound Filter. the basisforCycling74 of a1024bandfilteravailable. Thisisalso cell movementismappedtocontrolfrequency created ftp server(IRCAM2005).DelicateEarhave Max These formpartoftheIRCAMlibrary objects for1Dbinary, 2DLifeand3DLife. Max created alibraryofobjectsforCycling74’s rhythmic patternsandstructures. Vorn also are triggeredbythecellactivitytoproduce with thecellularspace.Soundssamples human location,creatingaparallelinteraction space becominganinfluential input,by sensors withinthesameroom. The physical controlled byboth2DLifeandamatrixof The SoundGallery objects andisavailablefromIRCAM’s in 1996called Another DelicateEarCA applicationis Another installationworkconnecting GalSim Life Filter , inwhichupto25sinewavesare was usedtoprovideaGA Burraston andEdmonds usingthe Life Filter Life Tools 172 , aninteractive A- GalSim Liquiprism GalSim Pluggo Harmonic Life and , containingCA uses a2D (Woolf object, where Cellsound to produce 172 Figure 8.PeterBeyls’ patterns. be inducedtoadjusttheworkings ofthegrid based on2DLifeoruserdefined rulesmay interacting processes. A mutationsystem are createdbyavarietyofmutatingand symbiosis. Gridbasedsequencepatterns of machineaestheticsandhuman-machine the medium. The systemisacelebration and thecomputerarealsoconsideredtobe composition processinwhichthesoftware The interfaceallowsasemiinteractive throw awaymusic(RobotSoftware2005). software artworkbasedonthenotionof (2005a, 2005b,2005c). Burraston andEdmonds(2004), and moredatavisualisationsarepresentedin is showninFig7.Experimentalcompositions digital printsinagallerycontext,anexample compositional datahavealsobeenexhibitedas Some alternativemethodsofvisualisingCA juxtaposed withmanualkeyboardtechniques. sometimes controllingotheralgorithmsand Here CA havebeenusedinmanyforms, and pre-processedalgorithmictechniques. compositions wererecordedusinginteractive CA, andotheralgorithmicprocesses. These musical recordingsbasedon1Dand2D available forfreedownload(Dorin2005). Cellular GridMachine Noyzelab exhibitsanumberof Interactive cellularautomata 9/16/05, 3:06PM isagenerative . Cellular automata in generative electronic music and sonic art

South neighbours extracted Digital Creativity, Vol. 16, No. 3 from previous and future generations respectively. Further experiments included feedback from cell neighbourhood evaluation into the rule set itself and history tracking to include selected previous generations into the computation. A 2D wave propagation CA, based on the interaction of moving particles, was also investigated using a mouse to select areas of the wave field. Beyls wanted a flexible MIDI mapping process for Figure 9. Dale Millen’s Cellular Automata Music. real-time composition and performance, after his earlier work in non real-time. This mapping drew from the CA history evaluation, 5 CA systems in the MIDI domain a user defined root and the current cell value. Selection of MIDI channel was by cell index CA have been utilised in a number of number, using the modulus function to map novel applications in the MIDI domain. to the available number of MIDI channels. Predominantly these applications have Durational values were computed by matching been in the area of MIDI sequencing, using the CA cell value with a condition in a large a multiplicity of CA types and mapping decision tree. methodologies. A review of CA in the MIDI Beyls further expanded this work domain is presented in (Burraston, Edmonds, by investigating a small network of Livingstone and Miranda 2004). Two early interconnected 2D CA and the use of MIDI experimenters of CA were Peter Beyls Langton’s Lambda parameter within a realtime and Dale Millen, working independently in system (Beyls 1991). Three 2D CA of 8x8 academia on slightly different systems. cells were used with the first CA accepting Beyls’ early work (Beyls 1980, 1989, physical input gestures. The second CA is 1990), one of the first examples of a CA music influenced by its own transition rules and system, is interesting both technically and the output of the first CA. The transition also from a music industry standpoint as it rules of the second CA may be tuned with was later commercially sponsored by Atari the Lambda parameter by the user and also and Yamaha (Beyls 89). The types of CA by a ‘subtle feedback mechanism’. The third investigated were varied and novel, drawing CA is used to generate MIDI messages on from a mixture of 1 and 2 Dimensions. A up to 16 MIDI channels by a process similar further interesting avenue was the use of to activation/inhibition and is fed from the time dependent rules, where the rule itself output of the second CA. An active cell in the changes during the CA evolution. 2D rules second CA causes a non-linear increase in its were also applied to a 1D CA, the North and corresponding cell in the third CA, also with

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Digital Creativity, Vol. 16, No. 3 of 1DCA andthe numberofcellsispresetin The OSXversionutilisesthree different types available forfreedownload(Millen2005). OSX (Millen2004),showninFig9.is Macintosh andanewversionfor pitch valuestotheCA rule.CAMrunson the arbitrarymappingofmusicallyrelated 1D k2r2CA rule(Millen1992). This involved musical structureswithCAM,usingacyclic later investigatedthegenerationofformal by automaticseedingofLifeforms.Millen can beenteredgraphicallywiththemouseor number ofmethods,inthecase2DLifethis seeding oftheCA canbeachievedbya the calculateddurationisalsoscalable. The automatically, exceptinthe3Dcasewhere and durationsareappliedbytheprogram selected. Pitchesareenteredasasetofvalues allowing anyofthe2 as a32bitpatternbyon/off switches,thus 100. The 1Dk2r2ruleiscompletelydefinable The 1Dand2Dlatticesizesarescalableupto to pitchanddurationvalues(Millen1990). Life and3DCA bymappingtheresults Arkansas. Musiciscreatedfrom1Dk2r2,2D created byDaleMillenattheUniversityof a votingrule(Beyls2004). the latestincarnationconsistsoftwoCA with subject tomutationandcross-overoperations, viewed asgenotypesandare (Beyls 2003). The CA are his CA the Lambdaparameterwith algorithms andfurtheruseof selections basedongenetic extended hisworktoinclude is showninFig8.Beylshas Cellular Automata screen shotofhis 1997, 1998,2000)anda field ofmultipleCA (Beyls continues with his work in the of itsneighbours.Beyls the effect offadingsome Cellular Automata Music Explorer Burraston andEdmonds program Interactive program 32 174 possiblerulestobe (CAM)was Figure 10.EduardoMiranda’s 174 five sizesuptoamaximumof700cells. musical passages. of theCA tocontrol theplaybackofdiscrete control ofacomposition,usingtheoutput data. This workwentontodescribehighlevel form ofMIDIcontrollersorsystemexclusive blocks. Datastreammappingscouldtakethe by thearbitrarypartitioningofCA into under thecontrolofcomposer, constructed MIDI instruments. These datastreamswere the parametriccontrolofelectroacousticand could beusedtoconstructdatastreamsfor work wastheidentification thatCA output evolution. An importantoutcomeofthis simple extractionofasubsetfromtheCA by usingapitchmaskfeature,allowingthe perform live.Cellswereallowedtobemuted through CA generationstotestmappingsor pitch, thecomposerbeingabletomove could consistofanactivecellcontrolling to musicalparameters. The basicmapping evolution tomapparticularareasofinterest The composercouldalsozoominonan neighbourhood sizeandnumberofcells. adjust parameterssuchasrulenumber, Kirk andOrton1991). The composercould interact withCA processinrealtime(Hunt, which attemptedtoallowthecomposer dimensional ‘Cellular Automata Workstation’, the Universityof York developedaone The Music Technology Groupat CAMUS 3D. 9/16/05, 3:06PM Cellular automata in generative electronic music and sonic art

In CAMUS and CAMUS 3D Eduardo of one morphogen over an another, in order Digital Creativity, Vol. 16, No. 3 Miranda investigated whether CA that exhibit to further impart the algorithm on the note pattern propagation behaviour could be stream. Multiple instrument mappings were utilised to model musical pattern propagation possible by assigning them to a subset of cell (Miranda 2003). The chosen CA were Life and parameters. Martin implemented the system in Demon Cyclic Space (Dewdney 1989), both Forth, but later produced a Max based version occupying fixed grid sizes,CAMUS using 2D specifically as a drum machine. CA and CAMUS 3D extending the concept to FractMus 2000 is an algorithmic 3D CA, shown in Figure 10. In CAMUS, Life composition system for Windows with the is used to determine the intervals of a triad ability to perform 1D binary CA based pitch based on the x/y locations of active cells on a sequencing. The system will allow for up column by column basis. CAMUS 3D uses the to sixteen CA mapped to individual MIDI additional z coordinate to create a four note channels. Each MIDI channel is based grouping. CAMUS applies temporal coding on an event structure. This allows for CA to these intervals based on the neighbouring parameters to change over time and for much cells and in CAMUS 3D by using a first experimentation with rule, size and initial order Markov Chain. In both programs the conditions and its effect on pitch. The number corresponding cell of Demon Cyclic Space of cells is restricted to values between 128 determines the orchestration of the output to and 512. Experiments by the authors have a MIDI channel corresponding to its current produced interesting pitch sequences, but the state. Both programs allow for a good deal program does not allow investigation into any of interaction and manipulation of musical other types of CA mapping. FractMus 2000 is parameters, and some adjustment of the CA available on the internet at (FractMus 2005). rule space. CAMUS and CAMUS 3D are both Harmony Seeker, an interactive available on CD-ROM (Miranda 2001). application developed at the University of Andrew Martin investigated the Calabria, Italy, represents an interesting application of Reaction-Diffusion (R-D) hybrid approach and uses genetic algorithms systems (Meinhardt 2003, Turing 1952 to breed/select multiple types of 1D CA, with and Turk 1991), to produce MIDI based k=2 or higher, and renders successful fitness algorithmic compositions (Martin 1994, matches as a batch of MIDI files (Bilotta et 1996a and 1996b) at the Australian Centre al. 2000, Bilotta and Pantano 2001, Bilotta for the Arts and Technology (ACAT). The and Pantano 2002). A mapping is achieved R-D application is an interesting approach, through the use of ‘musification codes’, of differing from the pure computational logic which three types have been identified, local, approach. Martin used a 24x24 grid of R-D global and mixed. Local codes view the CA cells, scanning rows from left to right and top as a piano roll and the presence of an active to bottom, giving the effect of ‘self-modifying cell causes a note event to occur. Global codes repetition’. Each cell produced a number of which view the CA as a whole and extract values, the concentration of two morphogens musical passages based on measures taken and their second derivatives. These cell from the input-entropy and the evolution values were assigned to control tempo, note over time. Mixed codes extract sections from durations, note onset, note velocity and the the CA and map these to note and tempo note value itself. The note value was selected parameters. The software is in an early beta from a discrete set within a specified limit. A stage and can generate a large number of cells morphogen value could also be assigned MIDI sequences, although there is no capacity to an event mask, based on the dominance to map CA to loudness dynamics. These codes

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Digital Creativity, Vol. 16, No. 3 higher computationalcostof digital signal evolved ataslowerpace,mostly duetothe of approaches. This fieldhasnaturally domain hasbeeninvestigatedbyavariety The applicationofCA intheaudio 6 domain isinthehandsofprogrammer. The applicationoftheCA output totheMIDI and otherreseedingbasedonthecurrentstate. reseeded randomlyorbyauserspecified seed, or frozenevolutionstobeautomatically matrix modules. Tests canbemadeforstatic implemented asoptionswithin and 1D Wolfram binaryCA. These CA are many otheresotericmodulesareLife,HiLife, 2005). CA modulesincludedamongthe the constructionofMIDIsequencers(Dunn the PCby Algorithmic Arts, designedfor algorithmic developmentapplicationfor (Miranda 2001). of those using non-pitched sounds. A beta version sound domains,especially methodologies oralternative encourage newermapping of CA rules,anddoesnot its breedingandselection ‘musical consonance’ for practice byassumingthis barriers tocontemporary also retainsmanyofthe consonance. The approach boundaries setbymusical limits itselfbyretainingthe contemporary music,italso for theproductionof approach toutilisingCA this remainsaninteresting and Pantano2000). While ‘musical consonance’ (Bilotta are basedonafitnesstestfor

Harmony Seeker processing domains CA systemsinthesynthesisand Softstep is acommercialmodular Burraston andEdmonds isavailableonCD-ROM 176 Softstep Figure 11. JacquesChareyron’s ’s 176 of thevisualoutput”. behaviour andnotmerelybe “a representation mapping ofthealgorithmshouldparallelits importantly identified thatthemusical level organisation ofsonicgrains.Bowcott Roads’ conceptoftendencymasksforthehigh previous granularsynthesismethodsused of screens’ (Xenakis1992),whereasmost Bowcott wasalsoinspiredbyXenakis’ ‘book synthesis instruments(Bowcott1989). generate scoredataforCsoundgranular stamped x/ycoordinatesoflivecellsto 2D Life.Bowcott’s methodextractedtime a compositionalcontrolstrategyutilising this suggestionPeterBowcottproposed synthesis method(Truax 1988).Following systems mayprovideusefulmodelsforthis Truax furthersuggestedthatself-organising synthesis (Roads1978,1996)andBarry first computerimplementationsofgranular (Xenakis 1992).CurtisRoadsdevelopedthe a compositionaltheoryforgrainsofsound 1947), Xenakisbeingthefirst todevelop Gabor’s quantumapproachtosound(Gabor known asgranularsynthesis,basedonDenis CA andsoundsynthesisutilisedatechnique processing. Initialexperimentscombining Linear Automata Synthesis(LASy) 9/16/05, 3:06PM . Cellular automata in generative electronic music and sonic art

Chareyron demonstrated that Digital Creativity, Vol. 16, No. 3 this process can be viewed as the operation of a digital filter on a time-limited signal. By using the sum of two neighbouring cells he went on to show that the basic Karplus-Strong plucked string algorithm (Karplus and Strong 1983) could be simulated. Interaction is via computer keyboard, mouse Figure 12. NYR Sound’s Chaosynth. and MIDI in order to play and modify sounds. Sounds are The University of York’s Cellular organised as banks of instruments specifying Automata Workstation (Hunt, Kirk and Orton the CA rule, an initial waveform and envelope 1991), described in the previous section, was settings. LASy runs on the Macintosh platform used to map the CA output to the tendency and is part of the University of Milan’s masks of a granular synthesizer (Orton, Hunt computer music workbench called Intelligent and Kirk 1991) to assist in the process of Music Workstation (IMW) and is also generating a large amount of control data. available on CD-ROM(Miranda 2002). York produced another graphical 1D CA Chaosynth produces sound tool (Katrami, Kirk and Myatt 1991) which by using a 2D CA to drive a granular allowed timbral manipulation of a phase synthesizer, originally implemented on a vocoder (PV) (Flanagan and Golden 1966, Cray supercomputer at Edinburgh Parallel Roads 1996). Timbral manipulation was Computing Centre (Miranda 2003). The CA achieved by using the CA output in two is modelled as a matrix of cells, where each approaches, as frequency filters for the PV cell is an identical electronic circuit existing analysis data and also by applying the CA in a state of polarisation, depolarisation or directly to the PV resynthesis process. The collapse. The program allows some interaction system used a fixed mapping of 512 pixels, the on the part of the user for adjusting CA circuit CA being scaled if not of this size. parameters, shown in Figure 12. These being LASy (Linear Automata Synthesis) was two resistors within a potential divider and a an inspired attempt by Jacques Chareyron capacitor regulating the rate of depolarisation. at forging an original direction for CA Equal sections of the CA grid are chosen from synthesis, using a 1D CA to create a model a ‘frequency pool’ to control an oscillator, of sound evolution (Chareyron 1988 and creating transitions from initial configurations 1990). LASy creates a broad range of timbres into oscillatory patterns. Chaosynth also from simple to complex and a screenshot is allows post processing of the CA output by shown in Figure 11. The 1D CA is viewed multi-mode filters, ring modulators, envelope as a wavetable and the cell values equate to generators, low frequency oscillators, sample sample values. Each generation of the CA and holds, and a modulation matrix. This thus becomes a time slice of the resultant post CA section is very similar in architecture sound stream, creating a self-modifying and use to a traditional analogue synthesizer. waveform based on the CA transition rules. Chaosynth is available as a commercial

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Digital Creativity, Vol. 16, No. 3 Table 2.CA musicsystemscomparison. Burraston andEdmonds 178 178 9/16/05, 3:06PM Cellular automata in generative electronic music and sonic art

application for Windows and an older free the result as a sound file. The CA module Digital Creativity, Vol. 16, No. 3 Mac OS9 version by NYR Sound (NYR consists of a fixed 1D binary 32 cell CA 2005). additive synthesizer based on a user defined The MIDI R-D systems investigated fundamental frequency. The frequency by Andrew Martin at ACAT, described in the mapping is selectable as linear or logarithmic. previous section, were also applied to the The neighbourhood look up table uses 16 synthesis of sound (Martin 1995, 1996a and user definable sets of 4 cells, which is an 1996b). These investigations were primarily unusual choice. The majority of published with 1D R-D systems of both 24 and 32 1D CA research often has a symmetrical cells. The output of the R-D systems created neighbourhood of 3 or 5 cells. The number scores for an additive/FM CSound system, the of generations is restricted from 1 to 100, number of FM instruments being equivalent to mapped to a total sound duration of between the number of R-D cells. The temporal nature 100 and 10,000 ms. Further sound synthesis of timbre was emphasized in this study, with control includes a variable smoothing instruments having R-D control mappings for function, affecting the attack and decay of the peak amplitude, FM rate, FM depth, attack spectral components. and decay characteristics. Martin further expanded this work to include multiple linked 7 Reflections R-D systems of one and two dimensions with an interactive graphic interface and Presented in Table 2 is a general comparison also utilising the Karplus-Strong algorithm of the CA music systems reviewed, based (Karplus and Strong 1983). Parameters were on the main features. CA music systems are extended to include panning position/speed notated in the left column and features are and pluck index. The R-D systems were identified in the top row. We are now able to connected in a tree branching structure in compare differences and similarities between order to control the overall parameters of a work in this field. The first four features relate sonic composition. Later work at ACAT by to the architectures of the CA system used. We Tim Kreger investigated the use of 1D binary can easily see differences in the architectures CA to control a Fourier based spectral filter based on numbers of dimensions, cells and (Kreger 1997 and 1999). Here the CA was states, and of the rule types implemented. used to create an evolving band-pass filter, Following this are two further columns each cell determines if the respective band in identifying the number of CA within each the Fourier analysis will be resynthesised. system, and their seeding mechanisms. The The Centre for Computer Music at last two columns indicate the particular the University of Cincinnati have produced domains of application, MIDI or audio. a real-time granular processing tool called It is immediately apparent that the ca (Vaidhyanathan et al. 1999) for the SGI MIDI domain has proved more popular platform. A sound sample is selected and with researchers. The rule types used show decomposed into grains, which are then passed a reasonable degree of diversity. The one through a bank of filters. A 32 cell binary 1D dimensional CA is a popular choice for both CA evolution controls the parameters of this domains and, perhaps not surprisingly due bank of filters, transforming the harmonic to its wider popularity, 2D/3D Life has also structure of the grains. influenced researchers. A wide range of choice Virtual Waves was an early commercial in the number of cells used is apparent, with Windows application by Synoptic for building Chaosynth allowing up to 999x999 cells on a modular synthesis systems and rendering sufficiently powerful machine. It is surprising

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Digital Creativity, Vol. 16, No. 3 parameters havebeenthemost widely somewhat difficult.Noteand duration though interesting,makesdirect comparison and domainsusedintheseapplications, values withinthetable. wavetable, whichmaybeanycombinationof special caseandthestartingconditionsarea at anequilibriumvalue. Reaction-Diffusion systemsareusuallystarted referred toasLifeforms. Andrew Martin’s have beendocumentedandtheseareoften In 2D/3DLifemanystartingcombinations seeds arethenormforlogicbasedsystems. where random,singlecellanduserspecified Seeding mechanismsforCA arequitegeneric, within alarger programmingenvironment. allows thisastheCA arespecifiedasmodules compositional structures. Martin’s workhavebeencreatedasnetworked and multiple,inthecaseof Andrew chosen isquitewellbalancedbetweensingle a 4096stateCA.OverallthenumberofCA 12 bitsynthesizedaudiostream,resultingin in thatthenumberofstatesisequalto MIDI domains. approach atinvestigationofbothaudioand work areprimeexamplesofaunified and Andrew Martin’s Reaction-Diffusion high powereddesktops. power wassignificantlylowerthantoday’s systems were created in an age when computer and itshouldbenotedthatmanyofthese cells willconsumemorecomputerresources exhibit complexbehaviour. A larger numberof k2r1 rule110 (andits3otherequivalents)will is variablefrom128to512cells,butonly restricted tofive fixedsettings.Fractmus2000 produce complexbehaviour, butcellsizeis around 150cellsarerequired.CAMOSXwill it wasshownthatareasonableminimumof knowledge ofCA introducedinSection3 emerge. With thebenefit ofthebackground have enoughcellsforcomplexbehaviourto that manyofthelogicbasedsystemsdonot The diversityofCA,mappings York’s Cellular Automata Workstation LASy Burraston andEdmonds 180 is particularlynotable LASy SoftStep represents a theoretically 180

synthesis hasbeenthemostpopularmethodof investigation intheaudiodomain.Granular rather thanprocessingformedthemajorityof lack ofimplementation.Soundsynthesis as welltempoandtiming,hasamarked musical parametersofloudness/notevelocity, note valuesfromtheCA output.Important are generatingeithersingleormultiple a specifiedpitchset,whereastheremainder note specification threesystemschoosefrom off theshelfCA system.Inthedomainof and, unliketheothersdoesnotrepresentan but thesemustbeconstructedbytheuser offers thecapabilitytoexplore allparameters, investigated intheMIDIdomain. CA algorithmsin Common LispMusic. an interestingsectiononimplementing notes onalgorithmiccomposition include in Musicand Acoustics (CCRMA)course University CenterforComputerResearch composition invariousforms. The Stanford for deeperinvestigationofCA foralgorithmic mapping strategiescanthenbeformed. Following thissteptheseeding,evolutionand to obtainmorethanoneCA definition. CA. This partoftheprocessmayberepeated chosen comprisethedefinition oftherequired The architecturalandrulesetvariablesonce this isnotalwaysapparentornecessary. a specificationfordesiredbehaviour, but generative music. The processmayinclude perspective ofthecriteriaandflow useful for visualised inFigure13. This presentsa an overviewoftheCA designprocessis Mac OS9andiscertainlyworthinvestigation. developed, but synthesis obtainable intheMIDIdomain.Forsound CAMUS 2/3Dprogramsarethemosteasily not allarepubliclyaccessible.CAMand Although manysystemshavebeendescribed Chaosynth of parametriccontrolisevidentinCAW, mapping theCA output. The implementation Music basedacademicresourcesexist Based onthereviewspresented Chaosynth and theworkof Andrew Martin. LASy is theonlyonestillbeing can stillbeusedunder 9/16/05, 3:06PM Softstep Cellular automata in generative electronic music and sonic art

consumer, artistic or scientific? How much Digital Creativity, Vol. 16, No. 3 space would a device occupy in a studio? What are the differences between hardware and software implementation? How would the interface be presented? To date the only music industry interest in these systems was brief, during the early work of Peter Beyls. Music industry interest would surely require an evaluation of cost, technical requirements and development time.

8 Conclusions and future work There is difficulty with comparatively assessing the diverse work published so far because it draws from a variety of different technologies and mapping strategies. The difference in creative media technology application from scientific computing application is not a distinct boundary and crossover does occur. There does not appear Figure 13. Process overview of generative music CA. to have been much interdisciplinary working between the scientific world and the art world. Binary CA of one and two dimensions are The sonic artist and musician must investigated and course notes are available be prepared to investigate the theoretical (CCRMA 2005). Queensland University background in order to successfully employ of Technology offer a 1D rhythmic CA, this vast behaviour space within their described in greater detail in (Brown 2005) compositional strategy. In using CA for and 2D Life as examples for the jMusic generative music successful and sensitive programming language. Under the leadership application requires understanding of the of Rudy Rucker the San Jose State University science by the artist. Global dynamics and have created a 1D CA sound synthesis Java rule clustering are important concepts for applet (Rucker 2005). The Kyma Capybara the generative artist intent on using CA, and sound design environment from Symbolic more importantly not esoteric or difficult Sound Corporation includes 1D CA objects as to understand. The creation of scalable CA part of its standard library. Kyma offers these architectures and systems targeted at music as harmonic and rhythmic interpretations of applications can only be achieved by deeper the CA evolution (Scaletti 1997). The popular research into this area. CA behaviour space and free Super Collider program also has a CA will remain an untamed wilderness for class library available at (SCOL 2005). music application unless these concepts are A number of open questions occur acknowledged. when reflecting on using CA for generative Although much work has been done music. Is it currently possible for an engineer, with CA in music and sonic art, the diversity artist or scientist to buy a CA chip or hardware and growth of the field will require further module of any kind? Is there a market for such research with MIDI and sound. The majority a device in any type of appliance, whether of work so far has been conducted in the

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Digital Creativity, Vol. 16, No. 3 Beyls, P. (1990) Musicalmorphologiesfromself- Beyls, P. (1989) The musicaluniverseofcellular Beyls, P. (1980) Bentley, P. (ed.) (2001) Adamatzky, A. (2001) Adamatzky, A. (1994) References 1 The truespiritoftheunderground, Iainvon Note Burraston using computed andgraphedforthispaperbyDave in Wuensche (1997,1999)andhavebeen of Figures5and6areoriginallypresented made with allowing ustousedataandpresentimages Wuensche forhiscontinued supportin The authorswouldliketothank Andrew Acknowledgements ever showaninterest? electronic musicalinstrumentmanufacturers has alongandinterestinghistory. Will the Their placeinthefield ofgenerativemusic mechanism asCA provides‘patternforfree’. variety ofbehaviourcapablebysuchasimple received lessattentiontodate. The astounding dynamics, andothertemporalparameters,has imperative. The domainofMIDIloudness alone andfurtherinvestigationsarestill MIDI domain,particularlyinnotesequencing Association, pp.34–41. Music Conference Proceedings ofthe1989InternationalComputer automata. In Wells, T. andButler, D. (eds) Editions, Belgium. systems. Physics Publishing. media andautomatacollectives automata. this paperisdedicatedtoyourmemory. completed. A greatfriendandfellowmusician, Trapp, diedtragicallyasthispaperwasbeing Morgan Kaufmann. Taylor andFrancis,Oxford. DDLab Action DDLab Burraston andEdmonds . InternationalComputerMusic software. The entropyplots Computing innonlinear Identification ofcellular . Exhibitioncatalogue,Kindt Creative evolutionary 182 . . Instituteof 182 Beyls, P. (2000) Beyls, P. (1998)Interactivecellularautomata. Beyls, P. (1997) Aesthetic navigation. Beyls, P. (1991)Self-organising controlstructures Burraston, D.andEdmonds,E.(2004).Global Burks, A. (ed.)(1970) Brown, A. (2005)Exploringrhythmicautomata. Bilotta, E.andPantano,P. (2002)Synthetic Bilotta, E.andPantano,P. (2001) Artificial life Bilotta, E.andPantano,P. (2000)Insearchfor Bilotta, E.,Pantano,P. and Talarico, V. (2000) Bowcott, P. (1989)Cellularautomataasameans Beyls, P. (2004)Cellularautomatamapping Beyls, P. (2003)Selectionistmusicalautomata: Marseille). (Laboratoire MusiqueetInformatiquede Intersens etNouvelles Technologies, MIM and MerseysideOn-LineLtd. Evolution 2.0 of theJIMConference Computer Music Association. pp.254–257. Conference. of the1991InternationalComputerMusic using multiplecellularautomata. Music Research organising systems. automata. experiments withonedimensional cellular dynamics approachtogenerative music Univ. ofIllinoisPress. Evolutionary Musicand Art. Proceedings ofthe3rd European Workshop on harmonies: recentresults. Workshop). Models forMusical Applications music tellsofcomplexity. Musicological Review, SpecialIssue musical fitness onconsonance. GA2000 to givelifestrangecreatures. Music generationthroughcellularautomata:how Music Conference Proceedings ofthe1989InternationalComputer of highlevelcontrolgranularsynthesis. Computer MusicConference procedures. P Music algorithms. Integrating explicitinstructionandevolutionary . BrazilianComputingSociety. , Milano,Italia. Proceedings ofthe2004 Australasian IX BrazilianSymposiumonComputer Montreal,Canada:International CD-ROM,Liverpool Art School roceedings ofthe2004International Synthetic creatures incontext

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