Publication
Physica D: Nonlinear Phenomena
Paper

Random fractals: Self-affinity in noise, music, mountains, and clouds

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Abstract

Many of nature's seemingly complex shapes can be effectively characterized and modeled as random fractals based on generalizations of fractional Brownian motion, fBm. As a function of one dimension, t, the trace VH(t) provides a model for the "1/f{hook}" noises. Extending fBm's to higher dimensions gives VH(x,y) as landscapes and VH(x,y,z) as clouds. Although all such fBm's are statistically self-affine, as characterized by the parameter H or the spectral density exponent β, either zerosets or trails of independent fBm's are statistically self-similar and may be represented by the fractal dimension D. © 1989.

Date

01 Jan 1989

Publication

Physica D: Nonlinear Phenomena

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