zbMATH — the first resource for mathematics

Ulam’s cellular automaton and Rule 150. (English) Zbl 1308.37008
Ulam introduced a non-linear almost equicontinuous two-dimensional cellular automaton as a cell model of crystalline growth in 1962 [S. M. Ulam, in: Essays cellular Automata 219–231 (1970; Zbl 0241.94048)]. Here it is shown that this model contains as a subsystem a linear chaotic elementary cellular automaton. The inverse process to ultradiscretization is studied on the system, and it is shown that the resulting partial differential equation preserves the self-organising properties of Ulam’s cellular automaton.

37B15 Dynamical aspects of cellular automata
37B10 Symbolic dynamics
35Q92 PDEs in connection with biology, chemistry and other natural sciences
Full Text: DOI Euclid