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.
KeywordsChaotic Attractor Iterate Function System Multifractal Analysis Multifractal Spectrum Graph Paper
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