Fractals and Multifractals

Stephen Lynch
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Stephen Lynch: Manchester Metropolitan University School of Computing, Mathematics & Digital Technology, Department of Computing and Mathematics

Chapter Chapter 6 in Dynamical Systems with Applications using MATLAB®, 2014, pp 107-138 from Springer

Abstract: Abstract 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 MATLAB; • 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.

Keywords: Fractal Dimension; Chaotic Attractor; Multifractal Analysis; Multifractal Spectrum; Graph Paper (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-06820-6_6

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