Even Wolfgang Amadeus Mozart developed a "musical game of dice"[1] that contained most of the elements that today are associated with generative tools. The piece carries the explanatory subtitle "Composing waltzes with two dice without knowing music or understanding anything about composing. For this, Mozart composed 176 bars of music, from which sixteen were chosen from a list using dice, which then produced a new piece when performed on a piano. Sixteen bars, each with eleven possibilities, can result in 1,116 unique pieces of music. Using this historical example, the methodology of generative art can be appropriately described as the rigorous application of predefined principles of action for the intentional exclusion of, or substitution for, individual aesthetical decisions that sets in motion the generation of new artistic content out of material provided for that purpose. With regard to the piece of music mentioned, it was not a matter of a unique playing by the composer. A work sheet for Adagio KV 516 shows an outline developed from principles similar to those that apply to the game of dice. It can be assumed that behind this process was a serious method that Mozartsometimes used for his compositions. To describe this method, musicologists introduced the concept of "aleatoric music"[2]. The name is derived from the Latin " aleator" (the dice player), and could not be more appropriate for the above example. In aleatoric music, the principles of chance enter into the composition process. A considerable number of musical pieces belong to this genre. A few of these compositions will be presented here in the context of generative tools because fundamental artistic requirements were postulated in those pieces that have to be introduced in the current discussion on generative art. In an exemplary overview, it will be shown in the following that there is no standard artistic position connected with the concept of "generative", but rather, a method of artistic work which was and is employed with the most diverse motives. At the same time, it is interesting to observe that this way of working appears not only in connection with a certain genre, but has in fact established itself in nearly every area of artistic practice (music, literature [3], the fine arts). The works to be presented in this article were chosen as examples depicting basic artistic starting points of "art

in defined dependencies". With examples of three artistic viewpoints from music history of the nineteen fifties, it will be first pointed out how different the paths to achieving a goal can be, even though all three artists used aleatoric or serial methods. Beside any considerations of musical theory, the question that needs to be discussed is what contextual and formal possibilities the application of such methods offer. John Cage used chance as a defined rule in a rigorous fashion to exclude predetermined connections. He was concerned with making sounds possible in a way completely independent of the composer. To do this, Cage for example used sound carriers (instruments) which were completely independent of his composition. In "Imaginary Landscape No. 4" (1951), he wrote a piece for 24 radios. He laid out rhythms and sequences Using traditional notation. The result, however, remained unplanned, dependent upon the place and time of the performance, broadcast frequencies and radio programme structures. Cage's efforts culminated in the piece entitle "4'33" (1952). There is only one hard and fast parameter: the length of the piece. Without any help from musicians, theresulting sound is produced from the moment the piece starts from different accompanying noises; for example, the rustling and the clearing of throats by the public, or the rush of traffic. His artistic goal was to have the sounds sort themselves out. Serial music, which developed out of the tradition of aleatoric works[4], mainly represented by Karlheinz Stockhausen, Pierre Boulez, Henri Pousseur or Gottfried Michael Koenig, took the exact opposite approach in the nineteen fifties. Serial compositions subordinate all acoustic characteristics, such as pitch, duration, touch, tone colouring, and loudness independently of each other to the same principles of order; for example, number ratios. In this way, it is possible to force separate musical aspects into a complete relationship on a higher order. As a system of order, mostly series (dependent upon the twelve-tone system) or continuous tones are used, which, in order to avoid repetition, vary constantly. Aesthetic criteria of music are subordinated to the principles of order. This method gives the composer total control over every imaginable detail of composition. The work is independent from the nuances of interpretation and

can therefore be seen in a larger context. It therefore appears logical that for work on serial compositions, electronic instruments were used. "In principal, it is not at all a matter of the use of unusual sounds, but rather that the musical order in the vibrational structure of the sound processes is driven out, so that sounds that occur in a composition are integral components of this and only this piece, and come about from the rules used to construct it " [5]. With the help of the instruments, sound could be constructed from the individual parameters. The introduction of electronic devices made the translation of the composer's directions into machine-readable instructions necessary, so that mathematical operations came in during the process of composing. With "Studie II" (1954), Karlheinz Stockhausen was the first to publish a score for electronic music, indicating the exact placement of instruments and describing how the piece would unfold. In 1959, however, Stockhausen opened up his compositional work to subjective interpretation. In "Zyklus für einen Schlagzeuger" (cycle for a percussionist) , individual decision possibilities were again allowed, determinedby the presence of a musician. Yannis (Iannis) Xenakis rejected the introduction of series and constructed his serial music (like virtually no other composer) from mathematical, architectonic, and even geological calculations. In establishing his principles of order, he was striving for a working connection between the different spheres of art. He was seeking the threedimensional sound that unites music and architecture. His active collaboration in the studio of Le Corbusier during the 1950s, enabled Xenakis, who had studied architecture in Athens, to introduce his musical skills into architecture. He designed "Pans de Verre Ondulatoires" [6], the window arrangement of the cloister, and the principal façade of "La Tourette" [7] (1955-1959) according to criteria of musical rhythm (see also the "Philips Pavillion" from the 1958 World's Fair in Brussels). Above and beyond this, Xenakis made crucial contributions to the development of the computer programme called UPIC (Unité Polyagogique Informatique du CEMAMu), [8] which translated graphics into music. Complex, computer-controlled universal music was supposed to serve in simplifying the composing and democratising of music. The goal was to

create a programme structure understandable even by laymen, but which nevertheless implemented nuanced facets of constructed sounds. It should be stressed that, through the introduction of a higher order system of rules, and its consistent implementation, works of art were created that succeeded in producing connections between apparently disparate structures and aspects, and this resulted in unique, complex and diverse sounds. A prerequisite for this was ensuring that each musical parameter would be viewed as being independent from every other, that each would be treated as structurally equal, and that the resulting sound would be understood in connection to the time factor. In Cage and Stockhausen, different artistic interpretations of the same working method produced two artists who could not be more different from each other. An area of work was therefore created in which opposite poles could be related to each other. Within this region, bounded by these two extreme positions, Xenakis united music with the working structures of the natural sciences, architecture and the other arts. He tried to apply their principles of order to his music and to influencethem with his own music. It must, however, be stressed that besides anyintellectual considerations which stand behind each position referred to above, the question of design or form was what provided the crucial impetus for artistic work. The general artistic goal, which each of these artists pursued in different ways, was to free sounds from the will of the composer. In this respect, three fundamental thought structures for artistic work with generative elements are indicated that are valid not only for music but also occupy artists in other fields. Generative methodology places its own demands on the fine arts. Since the late 1960s, individual pioneers of computer art have set out to establish generally valid rules for creating generated artistic works. In the following, using works by Max Bense, Manfred Mohr, Harold Cohen and John Horton Conway as examples, four fundamental conditions are presented below for employing generative methodology in the fine arts. By 1965, Max Bense had already introduced the concept of 'generative aesthetics' and defined it as "[…] the combination of all operations, rules and theorems […], that can be applied to a number of material elements functioning as symbols

and through which aesthetic conditions (distributions or arrangements) can be produced deliberately and methodically [9]. By using the laws of statistics, Bense hoped to achieve a rational basis for creating images. He subdivided picture surfaces into tiny squares and investigated the individual colour values, looking for internal connections in order to be able to create new images according to predetermined criteria. But he was unsuccessful in this endeavour and gave up this method. From then on, Bense dedicated himself to semiotic examination, thereby pursuing the artistic goal of "[ &] a rational production of art […]"[10] through a rational production of symbols. The target of his investigations therefore remained the aesthetic process. "Actually, such aesthetic systems, just like information, are expressions of a distribution and selection process, and both the relative frequency of a symbol as well as the relative freedom that one has to choose it from among other available possibilities, are generally, at the beginning of the aesthetic process, in no way statistically preferable with respect to frequency or choices of other symbols (which are in general set in advance). On the whole, theprobabilities of being chosen and of appearing are, at first, equal for all the symbols in the available group"[11] .The aesthetic act of formation however belongs to "that class of processes that start with purely stochastic equal probabilities in the course of which, however, the probability with which certain symbols can be chosen and appear becomes greater and greater while the probability for certain others […] becomes smaller and smaller, and finally disappears" [12]. Manfred Mohr[13] worked under the theoretical influence of Bense. He attempted to respond to calls for the creation of a rational art, also known as artificial art , through the realisation of logical and unemotional concepts, organized in such a way that all aesthetic decisions were taken over by a computer programme. In the series Cubic Limit (1973-1977) a normal twelve-edged cube is systematically dismantled in order to produce the pictures. The cube remained the form in Mohr's work, later being extended into the four-dimensional, so-called, hypercube with 32 edges. Through the systematic application of operations such as rotation, addition/subtraction etc., an inexhaustible number of aesthetic signs was

generated and became the material of Mohr s artistic work. For the cycle Frühe Algorithmische Arbeiten (early algorithmic works) (1969-1972), Mohr added text to his pictures, thus making the procedures used to make graphics by computer more accessible, and, at the same time, demystifying the role of the artist by underlining the automated nature of the decision-making process. At the beginning of the 1970s, Harold Cohen developed the computer programme Aaron[14]. This drawing machine first produced abstract and then figurative drawings, to which Cohen later added colour. In the 1980s, Cohen succeeded in equipping the programme with the ability to make independent colour choices as well as to apply the colours itself. The programme became functional with a complex set of rules in which Cohen formulated generally accepted aesthetic requirements for lines, surfaces, forms and colours and analysed their arrangement on a sheet of paper. In this way, he worked out the generally accepted characteristics of each of the elements and provided them with small inaccuracies for purposes of variation. Automated creation then, must first of all proceed from ageneralizable representability, not from the individual characteristics of a form. What is represented is not a tree, but rather the principle. Bense and Cohen attempted to turn aesthetic decision-making processes into algorithms, that is, to analyse the basic creative questions and break them down into workable units. This method clearly differs from that of image generation by means of fractal sets, something which was becoming very popular and which merely translated mathematical approximation processes into points of colour. So a canon was created with possible rules for automated application of creative decisions. In 1970, the American mathematician John Horton Conway developed his Game of Life[15] as one of a series of so-called simulation games. This simulation involves the development of succeeding generations of cells on a chessboard-type grid. Depending on their neighbouring cells, they either remain alive, die or create new life. The development of the following generation depends on certain rules, specified for its predecessor generation. Even with relatively simple output configurations, it is extremely difficult to foresee the next-generation constellation. It has to be

played, and only by playing can one experience the perpetual surprises. Game of Life is very highly regarded among the rule-dependent designs and has gained a cult status among very different groups of users. Its rules interested mathematicians, the clarity of design attracted many of an artistic persuasion and, last but not least, the players were enthusiastic. A great many computer programmes were developed that copied Game of Life, and during the seventies and eighties it caught the attention of many computer users. The life spans and graphic forms of the most varied populations of cells were observed and analysed. Alongside the short-lived organisms, stable populations develop from connections made with two or three neighbouring cells_these Conway referred to as still lifes. The constellations were systematically given names like Blinker, Glider or Eater. From the meetings of such constellations, glider guns for example, can develop after thirty generations. There were numerous investigations, some of which continued down to the 1,102nd generation, reported a stable population and described it in detail. The fascination of the game was to be found both in itscomplexity and its predictable unpredictability. Game of Life made it possible to subordinate graphic aspects to a continuous system and, in so doing, to generate forms independent of the individual: this was achieved by basing it on an algorithm modelled on the life cycle. For many of the artists who became involved with generative methodology, Conway's Game of Life represented a comprehensible starting point. In March 2001, the interdisciplinary artist Brian Eno gave a lecture on his method of composition with reference to Conway's Game of Life at the London ICA and introduced the term generative to the music scene. His work Generative Music 1 was first performed in 1996 at the Urban Aboriginals XI Festival in the Parochial Church in Berlin. With Generative Music 1 , Eno, who had already created important works featuring varying changeable sounds for his ambient music in the mid-seventies, reduced the task of the composer to defining the connection between sound and individual parameters, and the choice of the available sound characteristics. The implementation of generative music allowed the technical development of commercial software[16],

capable of producing perpetually changing music. Brian Eno is reported to have said: I think our grandchildren will probably look at us in wonder and say: 'You mean you used to listen to exactly the same thing over and over again?[17] It's an idea that clearly relates to current ambitions within generative art_to create a constantly evolving form, a form that exhausts its potential for development as a result of this process. Rules are unavoidable for this kind of art because continuous decisions on the further development of particular stages have to be taken which, in turn will influence what follows. The specific rules necessary here are to be understood in terms of value-free systems for algorithmic process control. An algorithm is a finite list of well-defined instructions . For each problem within a class of problems, an algorithm, after going through many steps, will finally arrive at a solution by implementing the instructions one after the other [18]. If then, a complex set of rules such as that provided by an algorithm is to be the basis for generating form, it begs the question of what requirements must be met in order to lend expression to a form. Strictly speaking there are two different andpartial aspects to be addressed here. First of all, generally accepted rules have to be found by which forms and colours can be generated (see Bense and Cohen). Secondly a system for the continuous change and variation of the forms to be generated needs to be devised which will take the first set of rules into account (see Conway). Against this background, the artistic fascination with generative methodology concentrated henceforth on continuous processes. The technology used plays a major role. It substantially determines both the possibilities and the extent of the systematic application of rules as was shown with all the work presented so far (cube synthesizer or computer, for example). The Internet offers ideal conditions for the generation of art by continuous processes, providing an interface by which many people can simultaneously work on a project. In addition, it opens an almost inexhaustible pool of new forms and subject matter for collective access. What is remarkable is that despite the rapid spread of this medium since the 1990s and the concomitant idea of democratisation and de-individualization of a process-governed form, no fundamentally new artistic positions

with reference to generative methods were developed. What is special about the Internet is that it is not restricted simply to one use, it moves across genres, finding applications in every conceivable field of artistic activity. It makes connections possible between the most diverse artistic fields and disciplines. For example, process visualization, animation, installations, sample music, programmed applications etc. The following selected examples from these fields illustrate the versatility and range of applications for generative methodology in the Internet age. In a kind of automated collage creation, websites such as http://www.potatoland.com/shredder search for pictures by means of search engines, or by entering URLs, and assemble them in line with given parameters to create independent artistic works. In Drawing Machines 1-12[19], Marius Watz documents the information flow on the Norwegian government s server. He draws distinctions between micro and macro structures in the dataflow, generating artistic works from this over a specified period of time. At the end of the nineties, the group of artists from Cologne known as Knowbotic Research created a work theycalled IO_dencies[20] (a model for several city projects), in which they made visible the urban force fields such as the city of Tokyo (1997), for example. Ten city areas, selected for their density of traffic and business activity, were declared "intensity zones" on the basis of this energy potential. They could be divided into sub-groups (humans, information, economy, traffic, architecture) and could be altered graphically, either individually or together. In 2002, the group of artists called Mashica programmed their work Hommage to Walter Marchetti_movements of a fly on window between 8 am and 7 pm one day in May, 1967 on a Website http://mosca.mashica.com. A number of flies from 0 to 99 move at random across the imaginary window of the computer screen. The only link on the page leads to a listing of the mouse positions traced by the user during the session. A symbolic fly then crawls once more over the mouse route, thereby visually representing the fact that the users' behaviour is just as aimless and random as that of the other flies. The forms and figures generated in this animation appear to have independent life, and, freed from linear dramaturgy, to have overcome defining

rules. The soda group works in the same domain with its project sodaconstructor [21]. This involves the building of a graphical creature that moves back and forth with simulated independence. The joints of the structure can be moved with the mouse and it can be turned, pushed or distorted. Alternatively, it can be influenced by virtual gravitation, collisions or friction. The structure can be equipped with other mass constellations, even reconstructed, and can produce sounds. Carsten Nicolai used generative methodology in his installation bausatz noto (construction kit noto infinity), at the Galerie Eigen + Art in Leipzig in 1998. Four record turntables (Technics MKII) were placed next to one another, set within a table. On each of the turntables lay a record. On a total of 48 grooves loops were added which could be played over headphones or external loudspeakers in the gallery foyer. Because of the high variability of the playing, an infinite variety of versions could be generated by the individual elements. Carsten Nicolai supplied the material and the equipment; the public (as the DJ) produced the sounds. The results depended on chance and were not repeatable. With his Fünf Räumeproject was developed in the course of a research scholarship at the Institute for Media Design. http://www.img.fh-mainz.de/~sbauer. (five rooms) project (2003), Sven Bauer made the task of the serial composers visual_the freeing of form from the artist. He sees his artistic work as research. Bauer prepares his research results in an almost didactic way. Using an approach similar to that of the serial composers, he isolated five design parameters (colour, substance, position, inclination and abstraction) and subjected the form to the so-called attractor principle, borrowed from astronomy. In each of the five rooms, formative influence is assigned to the three attractors, which rotate around the three-dimensional form (the cube as initial form). The 15 attractors (three per room) are assigned continuously controllable degrees of freedom. They may therefore suddenly change their movement, and by so doing, partially shift the influence radius on the object, they may slow down or even come to a complete stop. By this means, Bauer succeeds in carrying out test arrangements for detailed settings as well as giving free rein to chance aspects and making possible the combination of both. The respective parameters are transferred to a two-dimensional graphic which then endlessly reflects the interaction

(modifiable within the predetermined framework) of all attractors. In contrast to the application-oriented examples mentioned above, there is a smaller number of artists for whom rules and instructions play a central role in artistic endeavour [software art][22]. For them it is not a case of applying foreign systems and rules in order to free the form from the individual, but rather to define the system of rules itself as a work of art. "dot-walk"[23] from socialfiction.org raises regimentation to an art form by giving instructions for a walk through a city. These instructions correspond to an algorithm and can be traced back to a simple computer programme: //Classic.walk Repeat [ 1 st street left 2 nd street right 2 nd street left ] The psychogeographical project "dot.walk" supplies instructions (software) on how to use a city (hardware). In principle, however, this artistic position offers no compelling case for involvement with programmed software, providing instead a general reflection on rules and their use. The artistic interest in this case is concentrated on the instruction. In conclusion we can say that generative methodology was adopted across genres and over a wide time span. The middle years of the last centurywitnessed the emergence of artistic approaches in which this method was seen not only as an aid, but also as an integral part of artists' work. The method itself however was not central in their view, but, recognised as the principle suited to the realisation of their artistic goals, was used accordingly. At the same time, computer artists were involved in searching for ways of generating forms. With the spread of the Internet, a tool was available which carried the principle of generation within itself. It was appropriated into all areas of artistic creation and offered new dimensions in representation, distribution and interdisciplinary co-operation. From this, many areas of application were discovered in which the generative method could be used. Along with all these application-oriented uses, the rules involved, as well as their programming, began to attract the interest of artists. What was of interest now was not the rule as a means to create form, but rather the rule as such. On the basis of the works referred to here, we can say that as a principle, generative art justifies from within itself the necessity of its being generative.