Theσ-Game and Cellular Automata
作者:
SutnerKlaus,
期刊:
The American Mathematical Monthly
(Taylor Available online 1990)
卷期:
Volume 97,
issue 1
页码: 24-34
ISSN:0002-9890
年代: 1990
DOI:10.1080/00029890.1990.11995540
出版商: Taylor&Francis
数据来源: Taylor
摘要:
1. SummaryIn an article in this journal Don Pelletier discussed the mathematics involved in a little battery operated toy called Merlin (see [3], and also the“Addenda”in this Monthly, Dec. 1987, page 994). Several years ago Stephen Wolfram, in another article that appeared in the Monthly, analyzed a number of simple cellular automata and the fractal patterns generated by some of these automata (see [6]). In this article we point out the close connection between MERLIN-type games and a class of cellular automata related to the ones described by Wolfram. We introduce a game played on directed graphs and give a detailed analysis of the special case where the graph is a rectangular grid. Our analysis uses linear algebra as well as ideas from the theory of cellular automata.
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