11Fractal and multifractal methods with ANN

This chapter covers the following items:

–Basic fractal explanations (definitions and descriptions)

–Multifractal methods

–LVQ algorithm application to datasets obtained from multifractal methods

–Examples and applications

11.1Basic descriptions of fractal

The word fractal is derived from Latin fractus, which means “broken.” Mathematician Benoit Mandelbrot coined this term in 1975 [1], in the book The Fractal Geometry of Nature. In this work, fractal is defined as “a fragmented or rough geometric shape of a geometric object which is possible to be split into parts, and each of such parts is (at least approximately) a reduced-size copy of the whole.”

One of the most familiar fractal patterns is the ...

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