Fractals and Multifractals

Abstract

• 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.