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Automatic art generation as an optimization problem

In most approaches to algorithmic art, a (possibly very large or infinite) set of images is specified by means of a constructive mathematical definition (a grammar, an algebra, or a cellular automaton), and an algorithm is implemented which computes and displays the visual appearance of the resulting images –– either enumerating them all, or drawing random samples, or allowing the spectator to explore the space of possibilities. The constructive definition is the artwork. It is concept art made visible: the output refers back to the abstract structures that underly its generation.

Note that this kind of "art generation" has nothing in common with human art production. There is no distinction between a "mental image" and the detailed description of its concrete realization; there is no incremental process of beginning, addition, judgment and improvement. The artificial artist is blind: when he perceives his output, he merely remembers how he produced it.

There have been proposals, however, to construe artificial art more along the lines of simulating human art production. A historically important example is the following statement by Frieder Nake (1974), pp. 34-40:

    Die 5 Dinge, die [. . .] ein ästhetisches Programm bestimmen, sind: das "Zeichenrepertoire" Z, die "Transformationsmenge" T, die "Ablauffunktion" a, die "Bewertungsfunktion" b und "Zielmenge" K. [. . .] Wir haben es demnach bei dem ästhetischen Programm mit einem Modell folgender Art zu tun: ein Künstler ist sich seiner Mittel (Z, T) und Ziele (K) bewußt: er kennt operationale Definitionen seiner Kriterien (b) und weiß a priori auf welche Art er sein Ziel erreichen will oder welche Konstruktionsschritte er sich selbst zugesteht (a). [. . .]
     Wir machen einen Unterschied zwischen den von einem ästhetischen Programm P erzeugbaren ästhetischen Objekten und den bezüglich P akzeptablen Objekten, die eine Untermenge der erzeugbaren sind. Ein vorliegendes ästhetisches Objekt ist also nicht notwendig "akzeptabel" (der Begriff "akzeptabel" ist rein operational, obwohl er natürlich auf das traditionelle "schön" reflektiert). [. . .]
      Hätten wir aber vielleicht besser getan, eine generative Grammatik für die Beschreibung des ästhetischen Programms zu wählen? Der Generationsprozeß formaler Grammatiken läuft in der Regel "blind", "zufällig", nicht zielgerichtet ab. Das soll heißen, das nicht versucht wird, ein vorgegebenes Ziel zu erreichen [. . .]. Da wir aber ausdrücklich die Zielgerichtetheit des ästhetischen Realisationsprozesses im Auge behalten wollen, scheint der eingeschlagene Weg der bessere zu sein.

Nake defines automatic art generation as an optimization problem: find, within the set of all images, the ones that best satisfy one's aesthetic criteria (the most "beautiful" ones). To implement this approach, one must make two conceptual decisions and solve one technical problem:
   (1) Define the set of all possible images.
   (2) Define the aesthetic evaluation criterion.
   (3) Develop an effective method to search the space of possible images.

Decision (1) is crucial. It determines how the program thinks about images, how it describes them. If we define the set of images in a broad but mindlessly reductionist way (as pixel grids, for instance), the formulation of evaluation criteria and search strategies becomes impossibly difficult. But if we define them by means of a specific style grammar, we impose arbitrary boundaries which may turn out to be too narrow. The ideal definition would avoid arbitrary reductionisms as well as arbitrary styles; it would define images in terms of the elements and constructions that are actually employed by the human cognitive system in its perception of images.

Decision (2) is supposed to be the artistically interesting one: it articulates the system's values, its criteria for success or failure. If these criteria are to resemble those employed by a human artist, the system must be able to "see" its output, i.e., it must handle representations of the Gestalt structures that a human person would perceive in the output. (Note that this is beyond the state of the art; cf. our page on Gestalt perception.) A more impersonal version of this approach might try to implement a general notion of "beauty"; it could lean on proposals to formalize the notion of beauty that were put forth by Birkhoff (1950), Gunzenhäuser (1975) and others. Note, however, that the scope of these proposals is extremely limited, and that the notion of "beauty" which they try to capture is somewhat boring. (Cf. Scha & Bod, 1993.)

Problem (3) gets us into a particular area within the field of Artificial Intelligence: heuristic search. When the set of data to be considered is large, and the evaluation criteria are complex, finding optimal solutions is a matter of trial an error; one may try to detect properties of the search space which can be exploited to enhance the success rate of this search process. Many techniques exploit the local coherence of the search space (hill-climbing, simulated annealing). When the number of dimensions is very large, one often resorts to "simulated evolution": genetic algorithms.

So far, the conceptual difficulties haunting the project of the "simulated artist" seem to be unsurmountable. I do not know of any serious efforts to carry it out on a non-trivial scale. (This includes Nake's own work, which is much closer to the "grammar-based" approach than his theory seems to demand.)

Several art generation systems exist which technically fall under the optimization approach: they use genetic algorithms to search a large space. And their aesthetic ideal is to simulate a very conventional artist: they search for the most "beautiful" images in their search space, appreciated by the largest number of human observers. Nevertheless, these systems do not constitute bona fide realizations of Nake's research program, because they do not implement any formal evaluation criteria, using an "oracle" instead: human persons vote for what they like best ("supervised learning").


G.D. Birkhoff: Collected Mathematical Papers, New York: American Mathematical Society, 1950.

D. Boekee & J. van der Lubbe: "Discrete Informatie." In: Informatietheorie. Delft: Delftse Uitgeversmaatschappij, 1988. [In Reader 1991]

R. Gunzenhäuser: "Die Theorie Birkhoff's unter Informationsästhetischem Aspekt." In: Maß und Information als ästhetische Kategorien. Baden-Baden: Agis Verlag, 1975.

R. Gunzenhäuser: "Superzeichenredundanz." In: Maß und Information als ästhetische Kategorien. Baden-Baden: Agis Verlag, 1975.

Lev Manovich: Thinking Beyond Information, 1997.

Frieder Nake: Ästhetik als Informationsverarbeitung. Grundlagen und Anwendungen der Informatik im Bereich ästhetischer Produktion und Kritik. Vienna / New York: Springer Verlag, 1974.

J. Pierce: "Information Theory and Art." In: Symbols, Signals and Noise. London: Hutchinson and Co., 1962. [In Reader 1991]

Remko Scha & Rens Bod: "Computational Esthetics." Informatie en Informatiebeleid 11, 1 (1993), pp. 54-63.


Remko Scha, April 1, 2007