Sierpinski signal generates 1/fα spectra

Jens Christian Claussen*, Jan Nagler, Heinz Georg Schuster

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number032101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
Publication statusPublished - 14 Sept 2004


Dive into the research topics of 'Sierpinski signal generates 1/fα spectra'. Together they form a unique fingerprint.

Cite this