Pattern Generation by Cellular Automata (Invited Talk)




Kari Jarkko

Femke van Raamsdonk

2013

24th International Conference on Rewriting Techniques and Applications (RTA 2013)

LIPIcs

1

3

3

978-3-939897-53-8

1868-8969

DOIhttps://doi.org/10.4230/LIPIcs.RTA.2013.1

http://drops.dagstuhl.de/opus/volltexte/2013/4049/



A one-dimensional cellular automaton is a discrete dynamical system where a sequence of symbols evolves synchronously according to a local update rule. We discuss simple update rules that make the automaton perform multiplications of numbers by a constant. If the constant and the number base are selected suitably the automaton becomes a universal pattern generator: all finite strings over its state alphabet appear from a finite seed. In particular we consider the automata that multiply by constants 3 and 3/2 in base 6. We discuss the connections of these automata to some difficult open questions in number theory, and we pose several further questions concerning pattern generation in cellular automata.

Last updated on 2024-26-11 at 12:56