Sierpinski signal generates $1/f^α$ spectra

Details Sierpinski signal generates $1/f^α$ spectra Sierpinski signal generates $1/f^α$ spectra

2003-08-14

arxiv.org/abs/cond-mat/0308277v3

Phys. Rev. E 70, 032101 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages (4 figs included). Accepted for publication in Physical Review E

Scientific paper

10.1103/PhysRevE.70.032101

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 $1/f^\alpha$ spectra in a certain class of experimental and natural systems like catalytic reactions and mollusc patterns.

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