Genetic Algorithms for the 1-D Fractal Inverse Problem.

Abstract

We describe the basics of one-dimensional IFS type fractals including their generation, the forward problem, and their encoding, the inverse problem. We also describe the details of a solution of the latter by a Genetic Algorithm. The resultant algorithm converges remarkably well, and, when parallelized as described, achieves a 600 fold speed-up using 12 processors. 1 Fractal Sets Generated by Iterated Function Systems Let W = {w1,w2,...,wn}be a finite set of affine maps of the unit interval I =[0,1] into itself, that is maps of the form w(x)=sx + a, 0 ≤ x ≤ 1. Here the parameter s is the scale factor and the parameter a is the translation. Alternatively, putting l = a and r = s + a, then