Last edited 21mar03 by andy schwieter

illiBarnsley: Fractals by the MRCM Method

Abstract

Fractals can be generated in many different ways, one of which is the iterated function system (IFS). There are two main methods of drawing the attractor of the IFS, the fractal: the deterministic algorithm and the random iteration algorithm. I use the somewhat more computation intensive deterministic algorithm in my program. With it, many common fractals can be drawn from a small amount of information, usually 24 or less numbers. It can be proven that if two IFS's have values "close" to each other, then their attractors (fractals) are also "close" to each other. I have programs which demonstrate this by transforming one well-known fractal, such as the Sierpinski Gasket, Barnsley's fern, or the tree, into another in a given number of steps. The knowledgeable programmer could, with relative ease, use my algorithm to create fractals in three dimensions, such as the tetrahedral analog to the Sierpinski Gasket. Unfortunately, I am currently unable to do this. Also, one could vary the speed with which the fractals are drawn so as to better show the process of their creation.