Pioneering work by Wolfram illustrated the complexity in cellular automata where dimension or topological entropy gives a generalized measure of the density of possible configurations generated by cellular automaton evolution. More recently, concluded that GoL reproduces power-law asymptotic behavior of wealth distribution corresponding to the richest sector of the population.ĭespite the extensive literature on the power-law scaling to describe the living cell population of GoL, a connection between GoL and ’s maximum entropy (Ma圎nt) principle to describe scaling behavior of frequency distribution of events was not evidenced. considered natural self-organized systems of living creatures, showing that the spatial living expectations of different phenotypes may also satisfy the power-law scaling. considered a probabilistic cellular automaton to determine the local transition rules based on the number of living cells in the neighborhood of each cell. Monetti and Albano introduced stochastic rules in the GoL in the context of the dynamic of evolution of a society in the presence of random noise. used a statistical analysis to study the number of clusters of a group of living cells, founding a scaling region characterized by a power-law. The GoL frequency distribution of events on log-log scale has been proved to satisfy the power-law scaling, ,. More recently, reproduced the wealth distribution observed in real economic data using the statistical properties of GoL. Examples include the development of an automatic generation of chess variants in a computer game, image encryption algorithms based on the combination of chaos and cellular automata, and development of application specific future electronic systems such as memristor devices. It has also been considered in several scientific fields and applications. 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. This result suggests that individual cell population decays slower than a hypothetical slope equal to a (fast decaying) negative golden number.Ĭonway’s Game of Life (GoL) is a cellular automaton created by Conway.
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. In addition, the Zeta distribution is linked to the famous golden number. The Lerch distribution is then generated, where the Zipf, Zipf–Mandelbrot, Good and Zeta distributions are analyzed as particular cases. 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. In this work, GoL is connected to the entropy concept through the maximum nonsymmetric entropy (MaxNSEnt) principle. The GoL frequency distribution of events on log-log scale has been proved to satisfy the power-law scaling.
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.
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