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October 2014 Ulam's cellular automaton and Rule 150
Akane KAWAHARADA
Hokkaido Math. J. 43(3): 361-383 (October 2014). DOI: 10.14492/hokmj/1416837570

Abstract

In this paper we study Ulam's cellular automaton, a nonlinear almost equicontinuous two-dimensional cell-model of crystalline growths. We prove that Ulam's automaton contains a linear chaotic elementary cellular automaton (Rule 150) as a subsystem. We also study the application of the inverse ultradiscretization, a method for deriving partial differential equations from a given cellular automaton, to Ulam's automaton. It is shown that the partial differential equation obtained by the inverse ultradiscretization preserves the self-organizing pattern of Ulam's automaton.

Citation

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Akane KAWAHARADA. "Ulam's cellular automaton and Rule 150." Hokkaido Math. J. 43 (3) 361 - 383, October 2014. https://doi.org/10.14492/hokmj/1416837570

Information

Published: October 2014
First available in Project Euclid: 24 November 2014

zbMATH: 1308.37008
MathSciNet: MR3282639
Digital Object Identifier: 10.14492/hokmj/1416837570

Subjects:
Primary: 35Q92, 37B10, 37B15

Rights: Copyright © 2014 Hokkaido University, Department of Mathematics

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Vol.43 • No. 3 • October 2014
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