Self-similar fractal sets: theory and procedure

The presented algorithm generates approximations of self-similar fractal sets. The algorithm is based on a pattern rewriting system that draws a geometric pattern repeatedly after suitable mappings. A program developed from the algorithm reproduces Mandelbrot's self-similar fractals. We begin by discussing fractals and dimension theory, then present the algorithm, and conclude by using fractal set theory to calculate the dimensions of self-similar sets from their generators.<<ETX>>