Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton

Javier E. Contreras-Reyes

Chaos, Solitons & Fractals, 2021, vol. 151, issue C

Abstract: 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.

Keywords: Conway’s game of life; Cellular automata; Maximum nonsymmetric entropy; Hurwitz–Lerch Zeta function; Lerch distribution; Golden number (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077921006263
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006263

DOI: 10.1016/j.chaos.2021.111272

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().