Sierpinski signal generates 1/fα spectra

Jens Christian Claussen; Jan Nagler; Heinz Georg Schuster

doi:10.1103/PhysRevE.70.032101

Sierpinski signal generates 1/f^α spectra

Jens Christian Claussen^*
, Jan Nagler
, Heinz Georg Schuster

^*Corresponding author for this work

College of Engineering and Physical Sciences

Universität Bremen
Christian-Albrechts-Universität zu Kiel

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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∕fα spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.

Original language	English
Article number	032101
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	70
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevE.70.032101
Publication status	Published - 14 Sept 2004

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10.1103/PhysRevE.70.032101

https://arxiv.org/pdf/cond-mat/0308277.pdf

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title = "Sierpinski signal generates 1/fα spectra",

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∕fα spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns. ",

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AU - Schuster, Heinz Georg

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N2 - 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.

AB - 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.

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Sierpinski signal generates 1/f^α spectra

Abstract

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