Dresden 2003 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.76: Poster
Donnerstag, 27. März 2003, 15:30–18:00, P1
Sierpinski signals: 1/fα from cellular automata — •Jens Christian Claussen1, Jan Nagler2, and Heinz Georg Schuster1 — 1Theoret. Physics, Univ. Kiel — 2Theoret. Physics, University Bremen, Germany
From the Sierpinski triangle pattern, which can be generated by a cellular automaton, by sea shells, or reaction-diffusion-systems, a time-dependent measurement quantity (here referred to as Sierpinski signal) is simply defined by the row sum, or total number of active lattice sites.
Using an exact solution (that can be dated back at least to Kummer [2]), the spectrum of the Sierpinski signal can be calculated analytically; apart from large fluctuations in the structure, it shows a power law spectrum with exponent near to one [1]. Such behaviour may be generic in deterministic self-affine spatiotemporal dynamics.
As a new result[3], it is shown that in arbitrary dimensions always a cellular automaton rule exists that generates a 1/fα spectrum in the total activity of the lattice. However, the Sierpinski signal also scales exponentially with dimension, which on the other hand is irrelevant for the d≤3 case of e.g. catalytic experiments (where similar signals resp. spectra were observed).
[1] J. C. Claussen, J. Nagler, H. G. Schuster (1999), to be published
[2] E. E. Kummer, J reine angew Math, 44, 93-146 (1852)
[3] J. C. Claussen (2002), unpublished