# Dresden 2009 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

# DY: Fachverband Dynamik und Statistische Physik

## DY 12: Poster I

### DY 12.42: Poster

### Dienstag, 24. März 2009, 14:30–16:30, P1A

**Rule 150 cellular automata on 2D and Bethe lattices** — •Jens Christian Claussen — Neuro- und Bioinformatik, U zu Lübeck — Theoret. Phys. & Astrophys., CAU Kiel

The rule 150 cellular automaton is a remarkable discrete dynamical system, as it shows 1/*f*^{α} spectra if started from a single seed [1].
Despite its simplicity, a feasible solution for its time behavior is not obvious. Its self-similarity does not follow a one-step iteration like other elementary cellular automata. In this contribution [2] it is shown how its time behavior can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length. This allows us to compute the total activity time series more efficiently than by simulating the whole spatiotemporal process or even by using the closed expression. The results are further extended to the generalization of rule 150 to the two-dimensional case and to Bethe lattices,
where two new corresponding integer sequences [3,4]
arise.

[1] J Nagler and J. C. Claussen, Phys. Rev. E 71, 067103 (2005)

[2]
Jens Christian Claussen,
Rule 150 cellular automata on 2D and Bethe lattices, Journal of Mathematical Physics 49, 062701 (2008)

[3] Jens Christian Claussen, Total activity of the Rule 150 cellular automaton on a Bethe lattice with coordination number 3, Online Encyclopedia of Integer sequences A138276

[4] Jens Christian Claussen, Total activity of the Rule 150 cellular automaton on a Bethe lattice with coordination number 4, Online Encyclopedia of Integer sequences A138277