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Algorithmic art: Technology, and art

Conference Paper · July 2008 DOI: 10.1109/ITI.2008.4588386 · Source: IEEE Xplore

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Abstract. This paper describes algorithmic art, the more narrowly I limit my field of action and i.e. visual art created on the basis of the more I surround myself with obstacles». that completely describe generation of images. So it is not quite sure whether to start painting Algorithmic art is rooted in rational approach to on a blank paper without any constraints is art, technology and application of mathematics. necessarily easier than to have a constraint that, It is based on technology and for example, you only use squares of two sizes. particularly on programming that make The rest of this paper is organized as follows: algorithmic art possible and that influences it In Section 2 we describe relations between art most. Therefore we first explore relations of and technology, while Section 3 presents the role technology and mathematics to art and then of computer technology in development of describe algorithmic art itself. , and particularly of algorithmic art. Section 4 discusses rational approach to art by Keywords. Art, Technology, Computer, presenting approaches of several well known Mathematics, Algorithmic Art. artists. In section 5 rich relations of mathematics and art is described. Section 6 presents the role 1. Introduction of algorithms in generation of visual art pieces from the technical side, while Section 7 gives an Algorithmic art is visual art generated on the overview of algorithmic art, its history and main basis of algorithms that completely describe proponents. Finally, Section 8 presents generation of images. This kind of art is strongly conclusions. related with contemporary computer technology Author of this paper used some of the and especially with computer programming. materials from his earlier texts [2] and [3]. Another influence to algorithmic art is related with mathematics that is used in algorithms for 2. Art and technology image generation. It is clear that it is technically possible to have seen birth of a number of produce images by computer programs based on technologies, especially in the last six centuries. some . However, the question is Some of them are gravure (invented around whether under such strong constraint that image 1400), print (1440), lithography (1796), has to be created by an algorithm (instead of e.g. photography (1830) and serigraphy (1920). use image processing tools like Photoshop where Development of new technologies was always human hand can be involved in creating the a stimulus for artists to try to use them for image) it is possible to create interesting, original creation of new expression, expression that was or even aesthetically valuable visual works. not possible with existing technological tools. Interesting thoughts about producing artworks Although technology is a medium for artistic under constraints come from the famous Russian work, new tools for work very often become composer Igor Stravinsky in his essay “The inspiration for new approaches and give birth to Poetics of Music» [12]. Stravinsky literally new ideas. Visual art is e.g. hardly imaginable without Albrecht Dürer’s engravings, but the fact wrote: «My freedom thus consists in my moving th about within the narrow frame that I have is that artists before 1400 didn’t have gravure at assigned myself for each one of my their disposal. undertakings”. And he also added even more Modern technologies based on and communication, developed in the second half of strongly: “I shall go even further: my freedom th will be so much the greater and more meaningful 20 century, gave a new powerful stimulus for developing of fresh expression. On the first place are computers, then various input devices like mouse or scanner, various output devices like Program generated or processed information is screens, inkjet printers or 3D printers, image used in algorithmic art. processing tools like Photoshop, Internet with its Graphical information that are generated by popular Web and email services, etc. programs or processed after obtained from We will now analyse the main characteristics diverse input devices can be shown on different of computer generated art, also called digital art output devices like screens, printers or . It (although this title doesn’t seem to be very is also possible to create dynamically changing appropriate in the era of digitalisation of image structures, e.g. graphical animations. everything including art). Interactivity with computer can lead to constant changes in image structures that we see on the 3. Computer generated art screen, e.g. as a consequence of changing the position of objects or their temperature “Many years of exploration in art, science distribution that are detected by appropriate and technology have brought us such fields as sensors. Sensors continuously send this detected computer graphics, computer animation and information to the computer program in charge music, scientific visualization and multimedia that uses updated values of input variables and design – all of which are having tremendous on the basis of them generate change of the impact in the artistic, educational, research and image wee see. commercial communities” – C. Harris, Editor of Enormous potential of information and Leonardo Books communication technologies led to numerous Let us first see what new features that were approaches to application of computers in visual not present in earlier generations of visual arts. Some of these are digital imaging (creating technologies are specific for computer as a key 2D images), digital sculpture (creating 3D tool for enabling computer generated art. To images using CAD type of tools), digital begin with, computer is the first tool for symbol installations and virtual reality (e.g. interactive processing in human history, and this means for environments or data-driven installations that use processing of any kind of symbols humans use real-time information obtained from Internet), like numbers, characters, geometric figures and performance and sound art, digital animation and lines, images, sounds, etc. video, software art (e.g. interactive drawing) and Besides that computer is executing operations net art (various art forms that use Internet). that are programmed. It can repeat a huge Description of different forms of digital art number of complex programmed operations and presentation of numerous examples of these extremely fast and precise. This gives the forms can be found in Bruce Wand’s book «Art computer an enormous potential for support of the Digital Age» [15]. developing human creativity, the potential that no technology yet had. Programming and 4. Art and rationality flexible processing of input information also enabled interactivity, again a completely new “A man paints with his brains, not with his technological feature of considerable interest for hands” - Michelangelo art. Programming also enabled animation, a Although art is often considered as an feature used in many art activities. intuitive activity related mostly with emotions Besides, networked computers enabled and inspiration, this is certainly not the only communication, cooperation and transport of approach to art. Finally, artists have to learn information on huge distances, and thus about art theory, technology and techniques in additionally increased abilities of information order to have an appropriate background for technology in many art fields. creating artwork. All these are disciplines based Computer generated visual art is using on rational approach. But rational approach is potential of computers for generation and primarily important in creation of artworks. processing of visual and possibly also other During the history of art numerous techniques information. Information can either be directly were devised in order to obtained particular generated from programs or it can come from artistic effects. This is e.g. the case for various input devices like scanners, mouse or pointillism and cubism. Thus Georges-Pierre different type of databases, to be processed either Seurat developed pointillism as almost analytical by image processing tools or by programs. technique in which painting is done using discrete colour dots with complementary colours being next to each other. Cubism devised of the physical world and that the universe was technique of painting objects from several points ordered and explainable in geometric terms [7]. of view that provided a novel view on portrayed Thus for example two famous Renaissance objects. Studying of colour theory, light, and artists, and Albrecht Dürer perception was also necessary in order to fully were studying and using knowledge on utilize colours and develop desired colouristic , human (especially effects. da Vinci), optics and science of colours in Perspective is another analytic achievement creation of their works. that enabled projection of three-dimensional Another Renaissance figure, Pierro dela objects onto a two-dimensional surface. Linear Francesca, well-known painter from the 15th perspective was used by Islamic artists in the century was one of the greatest authorities for Middle Ages, and rediscovered in Italy in the perspective. He “… had a passion for geometry 15th century, during Renaissance. , and planned all his works mathematically to the so popular in visual arts and architecture, is last detail. The placement of each figure was known from ancient times and was largely calculated so as to be correct in relation to other employed in Renaissance. figures and to the organization of the painting as Rarely was a rational method of creation of an a whole”. [4] artwork described in such detail as in Edgar Alan However, by far the most intensive influence Poe’s essay “The Philosophy of Composition” of mathematics and science on arts began in [10]. In this text E. A. Poe gives reconstruction recent times, in the 20th century. And it was not of steps of development of his famous poem used only in visual arts – one example from the “The Raven”. He literary wrote that “… no one music field is a Hungarian composer Bela Bartok point in its composition is referable either to who applied golden section and Fibonacci accident or to intuition“, and that “the work sequence in some of his works. proceeded step by step, to its completion, with Importance of mathematics for artists is the precision and rigid consequence of a emphasized by Max Bill in his well-known text mathematical problem”. Here Poe described how on the mathematical approach in contemporary he decided about the poem length, the effect to art [1]. He wrote that he is convinced that “it is be expressed by the poem, the refrain and its possible to evolve a new form of art in which the sound (“Nevermore”), a creature repeating his artist’s work could be founded to quite a sound (Raven), etc. substantial degree on a mathematical line of Now we will concentrate on relation of art approach to its content”. with mathematics, one of strongest building The best known 20th century artist that was block of human rational thought. influenced by mathematics was probably M. C. Escher. Although he was not mathematically 5. Art and mathematics trained he was interested in mathematics. In mid 1930th he started to develop mathematical "A mathematician, like a painter or poet, is a approach to structure of his prints, and in maker of patterns” - G. K. Hardey, 20th century construction of his famous “impossible objects” mathematician prints he was influenced by mathematician Roger “Mathematics is an invisible art form of Penrose and his father L. S. Penrose. In his profound social and scientific significance. works Escher developed strange perspectives and Computer graphics make mathematics visible” – perspectives on the sphere, and studied the use of H. Ferguson, sculptor of a plane (i.e. regular periodic Mathematics and science had influenced arts divisions of a plane), convergence to a limit, from ancient times: e.g. façade of Parthenon built various transformations of shapes as well as in the fifth century B.C. contains a number of Möbius strip. proportions such as the golden ratio and the His works illustrate the result of his attempts square root of 2, while periodic patterns to visually express various mathematical frequently occur in the Islamic and Moorish concepts like infinity, duality, recursion and self- ornaments. However, it was only in Renaissance similarity. The first stage in process of creation that artists began using science and mathematics of his works Escher devoted to developing a more intensively. They were influenced by the geometric model of image. Escher wrote about rediscovery of Greek philosophy and were his work in this field in the lecture about the convinced that mathematics was the true essence “Regular division of a plane” [5]. Development of computer technology and Among interesting mathematically based particularly graphic cards and software in the artistic objects are sculptures based on second part of the 20th century made an mathematical objects as well as different type of enormous influence on the ability of visualizing perspectives painted on the sphere. One of the mathematics and using these visualizations in leading mathematically oriented sculptors is design and art. , who is using mathematics as One of the best known mathematical a design language for his sculptures [4]. approaches created in the era of computer Ferguson is also an internationally known graphic and exceptionally suited for generating mathematician whose algorithm has been listed attractive visual structures are , a family as one of the top ten in the twentieth century. His of self-similar (they appear similar at all levels of sculptures in stone and bronze have been named magnification) and scale invariant objects that "theorems in bronze and stone". They can be have a simple recursive definition. Fractals were found on many public spaces and were shown in invented by a Polish-French mathematician a number of exhibitions. Benoît Mandelbrot, and the term fractals that he One of the leading artists working with coined was derived from the Latin fractus perspectives painted on a sphere is Dick Termes. meaning "broken" or "fractured". He illustrated He developed his own six-point perspective fractals with computer-based visualizations, and system that he calls Termespheres, being “visual these images were so interesting that they soon environments painted on the surface of spheres became extremely popular. Mandelbrot also that hang and rotate from ceiling motors” [4]. found that fractals are realistic models of many These perspectives show everything that one can real world phenomena like mountains, coastlines, see from one point looking in all directions. It is structure of plants and blood vessels, clustering well known that geometries that fit on the sphere of galaxies, Brownian motion and stock market are totally different from geometries that fit on prices. the plane, and they are related to the study of Some interesting examples of fractals are polyhedra. Six-point perspective is related to the Mandelbrot set and Julia set. Mandelbrot set is cubical polyhedron that extends in all six defined by a family of complex quadratic directions of the space. One of Termes’s well- polynomials. It is a subset of a complex plane, known works is “Paris Opera”, acrylic on a i.e. a set of complex numbers or points in the polycarbonate sphere (40 cm diameter) that complex plane the boundary of which does not shows a six-point perspective view of Charles simplify at any magnification. A picture of the Garnier’s design of a Paris Opera. Mandelbrot set can be made by different type of As can be seen, a lot of work in this field has colouring, e.g. by colouring all the points which been done with the goal of visualizing belong to the Mandelbrot set black, and all other mathematical objects. This approach is certainly points white. In the centre of the picture of the valuable for the sake of research in mathematics, Mandelbrot set is the characteristic large but it doesn’t necessarily lead to interesting cardioid-shaped region. visual solutions to the so called fine art or ‘high Various algorithms are used for producing art’ [4]. Too much precision, or computer drawings of the Mandelbrot set. They repetition may look attractive but often isn’t are quite simple, and e.g. the so called “escape regarded as art. However, mathematical time algorithm” has only about a dozen of steps. approach can inspire artists to use their This is an example of a simple mathematical imagination and creativity and to use it in the model generating complex results. process of creation artworks. Some of the other mathematically based Another avenue is to use mathematics as a methods used for generation of attractive images tool in developing artists’ ideas. Following this are genetic algorithms and cellular automata. A approach artists typically use rather simple number of interesting examples of cellular mathematics that enable accomplishment of their automata visualization are presented in the idea but is of no interest from the mathematical Stephen Wolfram’s book “A New Kind of point of view. In such case a lot of experimenting Science” [16]. Cellular automata are also used is typically needed in order to achieve visually for generation of random numbers for the attractive result. It is this kind of approach that is Mathematica software, which is an excellent often used in algorithmic art. example of complex structures generated by a simple algorithm. 6. Algorithms in visual art advantage of computer and its output units is in enormous processing power of contemporary Algorithmic art is based on generation of computers and precision of its output units. visual artworks using algorithms, i.e. precise Because of that they can execute very complex defined procedure that computer executes step by algorithms that include a huge number of step. Algorithms are implemented in computer graphical operations in a rather short time and programs coded in some programming language. without mistake. This enables routine execution Algorithm, or computer program implementing of algorithms that would require years to be it, describe the process of generation of image executed by hand. All this gives computer that we can see either on the screen or as printed. technology a role of enabler of a real revolution Program for image generation contains the in algorithmic art. author’s idea about the image as well as the Another particularly important fact is that technique by which this idea is transformed into analysis of consequences of changes in the an image. It also has to define which graphical algorithm, i.e. in the corresponding computer elements and their structures should be generated program, is considerably simpler and faster in (straight or curved lines, shapes, a group of comparison with repeating of manual elements with a specified structure, etc.), what construction of somewhat changed image. This are values of their parameters (e.g. position of a enables intensive experimentation needed for rectangle, its dimensions and its elevation toward discovering the most appropriate artistic result. axes), colours of lines and shapes, etc. Algorithmic approach to art existed in An elementary algorithm for image classical visual arts. Probably the best known generation could look like this: “come to a example is M. C. Escher whose mathematical specified point, draw the rectangle of certain inclination was already mentioned here. Many of dimensions, elevation toward axes and colour; his artworks are structured in such a way that it is after that move to some other point and draw the possible to write algorithms (computer circle …”. Such algorithms use iteration programs) that generate them. This was indeed procedures that describe related sequence of done by several authors from the computer steps that execute specified actions, e.g. draw a science field. One example is Michael Trott who network of squares with specified positions, in his book “Mathematica Guidebook for sizes, colours, etc. Graphics” [13] constructed a computer program Technically, algorithms use computational that generates image of the Escher’s well-known structures such as loops, subprograms and lithograph . recursion, as well as various mathematical Works of op art pioneer Victor Vasarely were expressions. created on the basis of a deliberate plan of their Algorithmic artists (also called “algorists”) as structure and colouring, as can be seen from a rule don’t use special graphical software but Vasarely’s blueprints. Robert C. Morgan in his rather general program languages that enable book «Vasarely» [9] wrote: «He created drawing basic graphical elements like line, circle algorithmic systems that in many ways parallel or rectangle (and most programming languages, the development of the computer», and also: including various dialects of Basic language, «Vasarely made his own visual software in the have this feature). Such approach requires more form of mathematics, referring to the blueprints work but as a reward offers much more of his works as programs». flexibility and freedom in expression. Using Since algorithmic art consists of generation of general program languages algorists develop images on the basis of algorithms, algorithms can their own software in which they embed their be viewed as a notation, and notation is artistic ideas. After the image is generated no something that music has but visual arts in further intervention with image processing tools general miss. There are further parallels of like Photoshop is done. Interventions for algorithmic notation with music. First, is not the changing image are done merely by changing the author but the computer that executes the algorithm (i.e. the corresponding computer algorithm. Moreover, algorithm can be executed program). by different computers, using different operation The algorithms could also be executed by systems, programmed in different software and human hand, and they have been executed by presented by diverse output devices with various humans before computers came into arena (and resolutions and other characteristics. sometimes even after that). However, the evident 7. Algorithmic art 1968 she began to use a computer to assist her. She started to create a series of abstract works “Without the aid of a computer, it would not generated from a procedure in which simple be possible to materialize quite so faithfully an geometrical shapes and their combination were image that previously existed only in the artist's successively altered in small steps, and she mind. This may sound paradoxical, but the wanted to find which alteration lead to the machine, which is thought to be cold and aesthetically most appealing result. inhuman, can help to realize what is most Jean-Pierre Hébert was born in Calais, subjective, unattainable, and profound in a France, in 1939. He is educated as a classic artist human being” – Vera Molnar, algorithmic artist and he started to create digital conceptual We review here some of the key events in the algorithmic art in 1974, while in 1979 he history of computer generated art and present engaged in intensive experimentations in some of the best known authors from the field of creating drawings with computers. His algorithmic art. professional background in engineering and First experiments with usage of computers in computer programming languages originally led visual art were performed in late 1950th and early to a consulting career, though he maintained his 1960th. More intensive development of interests in arts and mathematics. In 1983 he algorithmic art began in early 1960th, and moved to United States and ceased consulting to pioneers were two researchers in the area of devote himself fully to art. Hébert is computer graphics, Dr. A. Michael Noll from experimenting with various media from paper, USA and Prof. Frieder Nake from Germany. Dr. glass and mirror to wood, steel, and sand. He is Noll also wrote the first computer generated also working on digital video animations, ballet in 1965. computerized kinetic sculptures, and organic In 1963 first competition was algorithmic drawing devices such as paint- held, sponsored by the U.S. journal “Computers dripping pendulums. In 2003 Hébert was and Automation”. In 1965 first computer art appointed Artist in Residence at the Kavli exhibitions were held at Technische Hochschule Institute for Theoretical Physics at University of in Stuttgart and at Howard Wise Gallery in New California at Santa Barbara. York. In 1971 Herbert Franke published the book was born in Tarrs, “Computer Graphics - Computer Art” [6] in Pennsylvania, in 1929. He was educated as artist which he described the tools and principles of and historian, but spent 16 years as a Benedictine computer generated graphics, its artistic monk. In the beginning of 1980th, after 30 years applications, history of computer art and its of work as a traditional visual artist, he started theoretical foundations. In 1976 Ruth Leavitt working with algorithmic graphics using edited the book “The Computer in the Visual classical pen plotter. He is one of the most Arts” [8] which presented texts of three dozen of original algorithmic artists, and besides a early computer artists like Vera Molnar, Manfred voluminous art production he also wrote a Mohr, Edward Zajec and Charles Csuri. number of essays on algorithmic art and on his Several authors proposed the name own methods of work. He is using the term “algorithmic art” and “algorists”, and Benois epigenetic to describe the algorithmic procedures Mandelbrot, mathematician who discovered in his work, identifying the biological analogues fractals, also wrote that “… astonishingly for art works executed with algorithms created complex and beautiful graphics can be generated by artists. In his own words: “The epigenesis of by surprisingly plain algorithms. Hence the term organisms is the process whereby a mature life algorithmic art, which I use at present” [4]. form grows from its seed. In this analogy the Some of the best known algorithmic artists software may be viewed as genotype or the seed we present here are Vera Molnar, Jean-Pierre that contains all the information necessary for Hébert, Roman Verostko and Manfred Mohr. growing the mature form.” What is particularly interesting is their Manfred Mohr was born in Pforzheim, background and how they approach algorithmic Germany, in 1938, He was educated as an artist, art. but he also used to play tenor-saxophone and Vera Molnar was born in Budapest, Hungary oboe in a jazz group. In 1969 he made his first in 1924. She was a classical artist using drawings with a computer. From early 1970ties geometric themes, and her aim was to create he began his artistic work on a cube structure, valuable works of art in a conscious way. In and in 1977 he begins to work with the 4-D hypercube and graph theory. In late 1980ths he James Faure Walker, classical artist who is extends work to the 5-D and 6-D hypercube. In also intensively working with computer art, in 1998, after using exclusively black and white his quite informal book “Painting the Digital colours for three decades, he starts using colours River» [14] gives a personal view on computer to show the complexity of the work through art. As a painter, critic and educator he analyses differentiation. In his own words: “What digital art culture and compares it with classical interests me, are the two-dimensional signs art. As already mentioned in this text, Bruce (graphics) and their visual ambiguity resulting Wands in his book: “Art of the Digital Age» [15] from the projection of the lines of the cubes from gives a description of different forms of digital higher dimensions into two-dimensions”. art and presents a number of examples of these Manfred Mohr received a number of forms. international prizes for his work. Since 1981 he lives and works in New York. 9. References

8. Conclusions [1] Bill M. The Mathematical Way of Thinking in the Visual Art of Our Time. Werk 1949, One could possibly think that since 3. algorithmic art is generated by a program, its [2] Ceric V. Legitimacy of Algorithmic Graphic author doesn't need to use any aesthetic Art (I) (in Croatian). Grafika 2005/06; 3(7- judgments. However, as James Faure Walker 8): 18-22. argues in his book “Painting the Digital River” [3] Ceric V. Legitimacy of Algorithmic Graphic [14]: "… these artists make aesthetic decisions Art (II) (in Croatian). Grafika 2006/07; all the way through - how to start a drawing, 4(10-11): 68-73. what materials to use, how to decide when it is [4] Emmer M., editor. The Visual Mind: Art complete, and which drawings actually work". I and Mathematics, The MIT Press; 1995. might add to this that nothing can be created [5] Escher M. C. Escher on Escher: Exploring without the initial idea about the artwork. the Infinite, New York: Harry N. Abrams, Besides, the author constantly evaluates visual Inc.; 1989. outputs obtained during experimentation with the [6] Franke H. W. Computer Graphics – program and on the basis of this makes changes Computer Art. Phaidon Press Ltd.; 1971. to the program until satisfactory visual results are [7] Kline M. Mathematics in Western Culture, obtained. Oxford University Press, 1964. This also indicates a specific character of [8] Leavitt R. The Computer in the Visual Arts, algorithmic art: the author has to possess rational Harmony Books; 1976. abilities required to compose the algorithm and [9] Morgan R. C. Vasarely, New York: George write the corresponding computer code correctly Braziller, Inc.; 2004. from both the syntactic and semantic point of [10] Poe E. A. The Philosophy of a Composition, view, but he also needs intuitive and aesthetic Graham’s Magazine 1846. abilities required to select visually promising [11] Spalter A. M. The Computer in the Visual alternatives. Arts, Addison Wesley; 1999. We have already discussed the potential for [12] Stravinsky I. The Poetics of Music – in the experimentation in algorithmic art as well as its form of six lessons. Oxford University importance in achieving good artistic results. Press; 1947. Undoubtedly, experimentation is also present and [13] Trott M. Mathematica Guidebook for important in a traditional art, but algorithmic art Graphics, Springer; 2004. is using its full potential. [14] Walker J. F. Painting the Digital River, At the end I would like to recommend readers Upper Saddle River, NJ: Prentice Hall; several of the most interesting and informative 2006. recently published books on computer art. Anne [15] Wands, B. Art of the Digital Age, Thames Morgan Spalter’s book “The Computer in the & Hudson; 2006. Visual Arts” [11] is the first book devoted to [16] Wolfram, S. A New Kind of Science, detail description of principles and art Wolfram Media; 2002. applications of numerous technologies used in computer art like digital painting, electronic colour, printing, rendering, multimedia and Web.

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