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Regensburg 2002 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.26: Poster

Donnerstag, 14. März 2002, 15:30–18:00, D

1/f noise in Sierpinski signals — •Jens Christian Claussen1, Jan Nagler1,2, and Heinz Georg Schuster11Institut für Theoretische Physik und Astrophysik, Leibnizstr. 15, 24098 Universität Kiel, Germany — 2Institut für Theoretische Physik, Universität Bremen

The extremely simple Sierpinski automaton xi(t+1)= (xi+1(t)+xi−1(t)) mod 2 which can generate complex patterns, is investigated on its capability to generate 1/f-noise. By definig a sum signal X(t)=∑i xi(t), we obtain a time series which power spectrum (periodogram) can be calculated analytically giving a power law with exponent 1.15.
In some cases Sierpinski-like structures can be observed in nature: Sierpinski patterns occur in reaction diffusion systems, pmost prominent in the patterns generated by sea shells. A Sierpinski-sum-signal-like time series has also been measured in a catalytic process. Other recent measurements have reported 1/f noise in chemical reactions.
Although our model describes an infinitely growing process (which is limited by system size), it gives an interesting viewpoint on an interesting observable of fractal generating processes.

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