Phys. Rev. E 70, 032101 (2004) [4 pages]Sierpinski signal generates 1∕fα spectraReceived 18 August 2003; accepted 23 January 2004; published 14 September 2004 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∕fα spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns. © 2004 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.70.032101
DOI:
10.1103/PhysRevE.70.032101
PACS:
05.40.−a, 05.45.Df, 82.40.Np, 45.70.Qj
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