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Enumerating everything: All Grids

The major conceptual challenge of algorithmic art is to develop a cognitively viable characterization of the set of all images. To take on this challenge, is to engage in a long-term research agenda concerning visual Gestalt perception – to understand and formalize the structure of the "space of all images", as Frieder Nake called it. In the 1990's, a more straightforward response to this challenge was developed and implemented independently by several artists: to enumerate all pixel grids.

  •     Lars Eijssen & Boele Klopman: "The Wishing Well" (Enschede, 1991). Program printing out all configurations of a 71 by 71 black & white pixel grid. With a graphical interface for "looking into the future" and an "inverse mapping" which calculates for any picture when it will be produced. (Pascal program running on IBM-compatible PC's under MSDOS.)
    This piece was displayed as an installation at the 1991 TART Festival, University of Twente, the Netherlands; it was mentioned in: Remko Scha: "The Artificial Artist." Natuur en Techniek 60, 7 (1992), pp. 526-539.
  •   Jochem van der Spek: "Borges" (Amsterdam, 1993).
  •   John F. Simon Jr.: "Every Icon" (New York, 1996). Enumeration of all configurations of a 32 by 32 black & white pixel grid. (Platform-independent Java-applet.)
  •   Leander Seige: "Imagen" (Leipzig, 2000). Enumeration of all configurations of various pixel grids. E.g.: up to 150 by 150 black & white; up to 64 by 64 grey or RGB (up to 16 bit). [This program has been accessible online, and may become accessible again. See .]

An esthetic experience evoked by these pieces: Even if the number of n x n black-and-white images is finite, it is extremely large. The mental representation of such an image set is experienced as a sublime vertigo. (Cf. Kant: "Das physikalische Erhabene.") [Computer Science correlary: Theory of randomness: Almost all of these images lack structure. Regularity is rare.]



Minos: In predicate (2), you speak of 'any transversal': a little while ago, you spoke of 'every exterior angle.' Do you make any distinction between 'any' and 'every'?
Euclid: Where the things spoken of are limited in number, I use 'every'; where infinite, I use 'any' in order to bring the idea within the grasp of our finite intellects. For instance, you may talk of 'every grain of sand in the world': there are, no doubt, what country-folk would call 'a good few' of them, but still the number is limited, and the mind can just grasp the idea. But if you tell me that 'every cubic inch of Space contains eight cubic half-inches,' my mind is unable to form a distinct conception of the subject of your Proposition: you would convey the same truth, and in a form I could grasp, by saying 'any cubic inch.'

Charles L. Dodgson: Euclid and his modern rivals. London: Macmillan, 1879. [Second edition, 1885, p. 25.]

Man kann soweit gehen, große Teile des ästhetischen Produktionsprozesses unter dem Anzahlaspekt zu betrachten: Künstler wechseln den ästhetischen Raum, wenn eine genügend große Anzahl von Objekten darin realisiert worden ist - vom Künstler selbst oder von anderen; wenn sie herausfinden, daß ein solcher Raum schon besetzt ist; Künstler suchen sich "große", "offene" Räume. Die Definition der ästhetischen Räume selbst ist natürlich das eigentliche Problem. Die zwei extremfälle sind der Raum aller überhaupt möglicher Bilder, der alle anderen ästhetischen Räume enthält, sowie die durch jedes einzelne realisierte Bild definierten Räume, die keinen anderen Raum enthalten.

Frieder Nake: Ästhetik als Informationsverarbeitung. Vienna/New York: Springer Verlag, 1974, p. 104.

Quoi que l'artiste veuille faire, y compris n'importe quoi, une oeuvre au hasard par example, il lui faut bien faire quelque chose. En d'autres termes, il ne peut pas tout faire, sa finitude l'interdit.

Thierry de Duve: Au nom de l'art. Pour une archéologie de la modernité. Paris: Les Éditions de Minuit, 1989, p. 133.



Remko Scha, 2001