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Thermal and Superthermal Income Classes in a Wealth Alike Distribution Generated by Conway’s Game of Life Cellular Automaton
H.A. Del Faro-Odi, R.R. López-Martínez, M.E. Rodríguez-Achach and A.R. Hernández-Montoya

By means of a data analysis, we study and confirm that the complexity of Conway’s Game of Life cellular automaton (GoL) is enough to reproduce the statistical universal properties of wealth distributions as they are observed in real economic data. In GoL’s Economy, we interpret each rebirth of a cell as the event of an agent gaining a “monetary unit”. We show that the GoL’s “wealth distribution” generated in this way is compatible with the exponential/gamma distribution observed in real economical complex systems for the low and medium classes of the population of a country or a society (thermal class). Furthermore, GoL also reproduces the power law asymptotic behavior of real wealth distribution corresponding to the richest sector of the population (superthermal class). Analyses of Gini index and of the stationarity of GoL generated wealth distribution were also performed.

Keywords: Game of life, econophysics, wealth distribution, gamma distribution, power law distribution

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