Practical Synthesis of Accurate Fractal Images

Abstract

This paper compares the synthesis of fractal images using both wavelets and a modified form of the random midpoint displacement algorithm. The accuracy of the generated fractal is investigated by an analysis of its second-order temporal statistics. It is shown that, although wavelets can be used to produce a good approximation to fractional Brownian motion, a technique based on the random midpoint displacement algorithm is in practice much simpler to implement, faster to generate, and results in a comparable accuracy. Furthermore the proposed method is shown to be considerably more efficient computationally.