IFS Matlab Generator: A Computer Tool for Displaying IFS Fractals

Abstract

Fractals are among the most exciting and intriguing mathematical objects ever discovered. A particular type of fractals, the Iterated Function Systems (IFS), has received a lot of attention due to its appealing combination of conceptual simplicity, computational efficiency and great ability to reproduce natural formations and complex phenomena. This paper introduces a new Matlab program, called "IFS Matlab Generator", for generating and rendering IFS fractals. In addition to providing a gentle introduction to the mathematical basis of IFS, two of the most important rendering algorithms, the deterministic algorithm and the probabilistic algorithm (also called "chaos game" algorithm), are briefly outlined. A critical point of chaos game is the choice of the set of probabilities associated with the iterated functions. This issue will be briefly discussed in this paper: we analyze the efficiency of the chaos game algorithm, comparing the standard method for choosing the probabilities proposed by Michael Barnsley with another method based on a new multifractal technique. The latter method optimizes the rendering process by obtaining the most efficient set of probabilities. Some examples aimed at illustrating this technique along with a gallery of beautiful two-dimensional fractal objects are also given.