English

Sierpinski signal generates $1/f^\alpha$ spectra

Statistical Mechanics 2007-05-23 v3

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/fα1/f^\alpha spectra in a certain class of experimental and natural systems like catalytic reactions and mollusc patterns.

Keywords

Cite

@article{arxiv.cond-mat/0308277,
  title  = {Sierpinski signal generates $1/f^\alpha$ spectra},
  author = {Jens Christian Claussen and Jan Nagler and Heinz Georg Schuster},
  journal= {arXiv preprint arXiv:cond-mat/0308277},
  year   = {2007}
}

Comments

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