Fractals: classification, generation and applications

Abstract

An overview of the types of fractals, their generating methods, and their applications is given. Fractals come in two major variations, deterministic fractals and random fractals. The first category consists of those fractals that are composed of several scaled down and related copies of itself, such as the Koch curve. They are called geometric fractals. The Julia set also falls into the same category because the whole set can be obtained by applying a nonlinear iterated map to an arbitrarily small section of it. Thus, the structure of the Julia set is already contained in any small fraction. They are called algebraic fractals. Hence, both geometric and algebraic fractals are deterministic fractals. The second category, i.e., random fractals, includes those fractals which have an additional element of randomness, allowing for simulation of natural phenomenon. They exhibit the property of statistical self-similarity. Several techniques for generating fractals have been developed and used to produce fascinating images. Two techniques popularized by Mandelbrot, the Koch construction and the function iteration in the complex domain, are discussed. >