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Emergence & Moiré


In algorithmic art in the true sense of that word, the artwork is the algorithm. The artistic value of an algorithm is not necessarily purely conceptual, however. Algorithmic art often bridges (or short-circuits) the gap between the conceptual and the "retinal", when the observer is confronted with a surprising or puzzling relation between the algorithm and its visual output – for instance, when a simple procedure yields a complex result, or when a seemingly random process creates striking regularities. This is the art of "emergence": to explore the discrepancies between what is programmed and what is observed; to initiate the "spontaneous" generation of form out of iterated local interactions.

The phenomenon of "Moiré patterns" is an early instance of emergent form: the superposition of two simple patterns gives rise to a new, more complex pattern which is unrelated to each of its constituents: it is an interference pattern, generated by the interaction between the constituents.

The earliest computer art (1960's), also often demonstrates emergent patterns. For instance, an iteration loop repeats a simple shape while transforming it by translation, rotation, scaling, etc.; the result is a new Gestalt which is not perceived in terms of the elementary shapes that constitute it.

More complex algorithms displaying this kind of behaviour are developed in the context of recently developed scientific disciplines such as Computational Mathematics and Artificial Life.


Herbert Brün (1960's)

Bit-101 Laboratory: 2002 january 21; december 1.

Cellular Automata


Moiré patterns

'Moiré' is a French word meaning 'watery' or 'watered silk' and has now been adopted in English. Watered silk and mohair fabric have an appearance that is both shimmery and like the grain of wood. That such patterns could be produced with a pair of diffraction gratings was pointed out by Lord Rayleigh in 1874, who also mentioned that the principle could be useful in making accurate measurements. (. . .)

A diffraction grating is a transparency with ruled parallel lines so close they cannot be seen with the naked eye. But if two such gratings are superimposed, with slightly different rulings, a pattern analogous to the beats of sound becomes entirely visible, in fact a good alternative name for moiré patterns would be 'visible beats'. One is provoked to conjecture that the fundamental nature of matter is based on such a principle. Perhaps all we can observe in nature are moiré fringes produced by something analogous to diffraction gratings in which the distances between adjacent lines are so small that there is no method known for their direct observation, even with an electron microscope. This suggestion would fit in well with the theory of 'winding space', where space is assumed not to close in on itself but to just miss, that is, instead of being a hypersphere it is a sort of hyper-helix.

Good (1971)


I. Amidror: The Theory of the Moiré Phenomenon, Kluwer Academic Publishers (1999).

Gregory Bateson: "The Case of Beats and Moiré Phenomena." In: Mind and Nature.

Irving John Good: "Science in the Flesh." In: Jasia Reichardt (ed.): Cybernetics, Art and Ideas (London: Studio Vista, 1971), pp. 104-106.

J. Guild: Interference Systems of Crossed Diffraction Gratings: Theory of Moiré Fringes. London: Oxford University Press, 1956.

J. Guild: Diffraction Gratings as Measuring Scales. London: Oxford University Press, 1960.

G. Oster and Yasunovi Nishijama: "Moiré Patterns." Scientific American May 1963, pp. 54-63.

Lord Rayleigh: "On the manufacture and theory of diffraction gratings." Scientific Papers 1, p. 209; Philosophical Magazine 47 (1874), pp. 81-93, 193-204.

Online examples and applets.

Circle of Spokes.

Spatial Beats.

Frédéric Durieu: Moiré, 1997-2001


Remko Scha, 2003