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 Schuster1 — 1Institut 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.