Evolving IFS Art

Julien Sprott has taken a different approach to automatic generation of interesting computer images. He selects a category, iterated function systems (IFS) for instance. Each image (the attractor of the IFS) is determied uniquely by fixing the parameters for that IFS. Each function is determined by six values, so the collection of all two-function IFSs is described by a 12-dimensional parameter space. Most points in the parameter space give rise to uninteresting attractors, so a purely random search would be boring. Sprott's approach to this problem is to test a collection of attractors for their interest level, and compare this with some computable number attached to the IFS, the dimension for instance. Having determined a range of dimensions giving interesting attractors, Sprott's program searches randomly through parameter space, but generates only the attractors of those IFSs with dimensions in this range. More details can be found at http://sprott.physics.wisc.edu/fractals.html

Here is an example of one of his IFS images. Click to enlarge.

A natural question is "Is it possible to map the regions in IFS parameter space having attractors of a given dimension?" With the difficulty of computing dimensions of self-affine fractals (pieces have different scalings in the x- and y-directions), probably the answer is "No." Some element of randomness and search appears to be necessary in this approach.