Fractals and Multifractals

Aims and Objectives

• To provide a brief introduction to fractals.

• To introduce the notion of fractal dimension.

• To provide a brief introduction to multifractals and define a multifractal formalism.

• To consider some very simple examples.

On completion of this chapter, the reader should be able to

• plot early-stage generations of certain fractals using either graph paper, pencil, and rule, or the Maple package;

• determine the fractal dimension of some mathematical fractals;

• estimate the fractal dimension using simple box-counting techniques;

• distinguish between homogeneous and heterogeneous fractals;

• appreciate how multifractal theory is being applied in the real world;

• construct multifractal Cantor sets and Koch curves and plot graphs of their respective multifractal spectra.