# John Shier

All of these space-filling images were constructed using the same random fractal algorithm. It is a universal algorithm for any shape, based upon computational studies of around 100 varied shapes. The number of random trials needed to place n shapes obeys a power law versus n, so the algorithm does not halt. The (infinite) sequence of areas is constructed as a power law versus shape number (with exponent -c) such that the sum of all the areas equals the area of the boundary. In two dimensions the fractal dimension is D=2/c.

The ability to use any shape (or 10 mixed shapes as with the numbers) offers interesting possibilities for art.

The picture shows nine images, all made with the same "statistical geometry" algorithm. The algorithm is simple enough to write down in half a page, but can produce quite varied results. It was discovered in 2010. The first publication in a refereed journal has been accepted by Computer Graphics Forum (with co-author Paul Bourke). For mathematical detail see

http://paulbourke.net/papers/shier2013/