Algorithmic Art: Technology, Mathematics and Art Vlatko Ceric Faculty of Economics and Business, Trg J.F.Kennedyja 6, 10000 Zagreb, Croatia [email protected] 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 algorithms 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 computer 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. digital art, 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 Visual arts have seen birth of a number of produce images by computer programs based on technologies, especially in the last six centuries. some algorithm. 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 computers 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 plotters. 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, Leonardo da Vinci and Albrecht Dürer perception was also necessary in order to fully were studying and using knowledge on utilize colours and develop desired colouristic perspective, human body proportions (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. Golden ratio, 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”.