Document Zbl 1498.37019

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(2021)</a>. </div> <div class="abstract">Summary: Conway’s Game of Life (GoL) is a biologically inspired computational model which can approach the behavior of complex natural phenomena such as the evolution of ecological communities and populations. The GoL frequency distribution of events on log-log scale has been proved to satisfy the power-law scaling. In this work, GoL is connected to the entropy concept through the maximum nonsymmetric entropy (MaxNSEnt) principle. In particular, the nonsymmetric entropy is maximized to lead to a general Zipf’s law under the special auxiliary information parameters based on Hurwitz-Lerch Zeta function. The Lerch distribution is then generated, where the Zipf, Zipf-Mandelbrot, Good and Zeta distributions are analyzed as particular cases. In addition, the Zeta distribution is linked to the famous golden number. For GoL simulations, the Good distribution presented the best performance in log-log linear regression models for individual cell population, whose exponents were far from the golden number. This result suggests that individual cell population decays slower than a hypothetical slope equal to a (fast decaying) negative golden number.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7568957">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A37B15" title="MSC2020">37B15</a> </td> <td class="space"> Dynamical aspects of cellular automata </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A11M35" title="MSC2020">11M35</a> </td> <td class="space"> Hurwitz and Lerch zeta functions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AConway%27s+game+of+life">Conway’s game of life</a>; <a href="/?q=ut%3Acellular+automata">cellular automata</a>; <a href="/?q=ut%3Amaximum+nonsymmetric+entropy">maximum nonsymmetric entropy</a>; <a href="/?q=ut%3AHurwitz-Lerch+zeta+function">Hurwitz-Lerch zeta function</a>; <a href="/?q=ut%3ALerch+distribution">Lerch distribution</a>; <a href="/?q=ut%3Agolden+number">golden number</a></div> <div class="software"> <h3>Software:</h3><a href="/software/771">R</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1498.37019" data-ciurl="/ci/07568957" data-biburl="/bibtex/07568957.bib" data-amsurl="/amsrefs/07568957.bib" data-xmlurl="/xml/07568957.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07568957.pdf" title="Zbl 1498.37019 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.chaos.2021.111272" aria-label="DOI for “Lerch distribution based on maximum nonsymmetric entropy principle: application to Conway's game of life cellular automaton”" title="10.1016/j.chaos.2021.111272">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Conway, J., The game of life, Sci Amer, 223, 4 (1970)</td> </tr><tr> <td>[2]</td> <td class="space">September 2013</td> </tr><tr> <td>[3]</td> <td class="space">Murugan, B.; Nanjappa Gounder, A. 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