Power-law-distributed level crossings define fractal behavior.
A relationship is established between the autocorrelation function of continuous Gaussian and non-Gaussian stochastic processes and the discrete process that describes their zero or level crossings. Random fractals occur when the distribution for the number of crossings is described by a class of Markov processes whose singlefold statistics are the discrete analog of the Lévy-stable continuous probability densities.
Hopcraft
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School of Mathematical Sciences, Applied Mathematics Division, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
Ingrey
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Jakeman
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