Algorithmic worlds

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2009-06-14 Kusama's patterns

2009-06-04 Piling hexagons

2009-05-02 Voronoi patterns

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June 14th 2009

Kusama's patterns

Yesterday, I wandered in the art galleries of Chelsea. Here are some great artists I discovered :

James Surls

Robert Courtright

Greg Parker

Dustin Yellin

But the most inspirational exhibition was probably the one by Yayoi Kusama at the Gagosian Gallery. Among other works, she had paintings displaying various patterns covering uniformly the canvas, without being periodic. In particular, I love the dot pattern displayed below.

YAYOI KUSAMA, COSMIC SPACE(TWBBAA), 2008, Acrylic on canvas, 51 1/4 x 51 1/4 inches (130.3 x 130.3 cm), Gagosian gallery

This type of patterns are precisely the ones which are interesting for "pattern piling" (see the explanations here), the technique used to build my works. So I started thinking a bit about how to draw this pattern with an algorithm.

The most natural way to draw it would be in a gradual way, by throwing randomly disks of various size on the surface of the image, with the requirement that they do not overlap. But as is explained here, the algorithms that Ultra Fractal can use have to work "pixel by pixel": they accept the coordinates of the pixel as basic data, out of which they must return a color. The image is produced by running the same algorithm for each of its pixels. This makes the implementation of the natural algorithm we hinted to more cumbersome. First we would have to store the information about the size and the location of each disk, and then for every pixel, to check whether it belongs to some disk. For pattern piling applications, we need patterns containing a very large number of disks, what would lead this type of algorithm to require huge quantities of memory and a lot of computations.

So we have to find a better way of drawing this pattern. One simple but not very satisfying solution would be to draw a periodic pattern. For instance the background of Yayoi Kusama's website is periodic, even if this is not immediately obvious. If we restrict ourselves to a periodic pattern, then the previous algorithm has to be applied only on a relatively small elementary tile, so the memory and computing problems disappear. But this is not suited for pattern piling, because the periodicity would be obvious for the small scale (ie. zoomed out) copies of the pattern.

A smarter idea would be to draw it as a Truchet pattern. A set of decorated square tiles is chosen such that all the decorations intersect the boundary of the tiles in a unique way. Then, by choosing randomly the decoration of each tiles of a square tiling, we get a non-periodic pattern. It is not difficult to imagine a set of Truchet tiles decorated by the pattern of Kuzama. Still, the fact that the decorations have to coincide on the boundary would give this pattern a pseudoperiodicity which would not be very appealing in my opinion.

I believe there is an much better way of drawing this pattern algorithmically. Hopefully I'll be able find some time to implement it, and if it works, I will describe it in a future blog post.