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<h2 id="generalized-cellular-automata">Generalized cellular automata</h2> <p>The number of possible rules, <i>R</i>, for a generalized cellular automaton in which each cell may assume one of <i>S</i> states as determined by a neighborhood size of <i>n</i>, in a <i>D</i>-dimensional space is given by: <i>R=SS(2n+1)D</i> </p><p>The most common example has <i>S = 2</i>, <i>n = 1</i> and <i>D = 1</i>, giving <i>R = 256</i>. The number of possible rules has an extreme dependence on the dimensionality of the system. For example, increasing the number of dimensions (<i>D</i>) from 1 to 2 increases the number of possible rules from 256 to <i>2512</i> (which is <i>~1.341×10154</i>). </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Ceccherini-Silberstein, Tullio; Coornaert, Michel (2010). Cellular Automata and Groups. Springer. p. 28. doi:10.1007/978-3-642-14034-1. ISBN 978-3-642-14034-1. Retrieved 22 October 2022. <a href="978-3-642-14034-1" target="_blank">978-3-642-14034-1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Wolfram, Stephen (July 1983). "Statistical Mechanics of Cellular Automata". Reviews of Modern Physics. 55 (3): 601–644. Bibcode:1983RvMP...55..601W. doi:10.1103/RevModPhys.55.601. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Wolfram, Stephen (May 14, 2002). A New Kind of Science. Wolfram Media, Inc. ISBN 1-57955-008-8. <a href="1-57955-008-8" target="_blank">1-57955-008-8</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> </ol>