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Sierpinski signal generates $1/f^α$ spectra

Jens Christian Claussen·Jan Nagler·Heinz Georg Schuster
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Abstract

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for $1/f^α$ spectra in a certain class of experimental and natural systems like catalytic reactions and mollusc patterns.

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Jens Christian Claussen, Jan Nagler, Heinz Georg Schuster. 2004-05-15. Sierpinski signal generates $1/f^α$ spectra. https://doi.org/10.1103/physreve.70.032101

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