Macroscopic Spatial Complexity of the Game of Life Cellular Automaton: A Simple Data Analysis

In this chapter we present a simple data analysis of an ensemble of 20 time series, generated by averaging the spatial positions of the living cells for each state of the Game of Life Cellular Automaton (GoL). We show that at the macroscopic level described by these time series, complexity properties of GoL are also presented and the following emergent properties, typical of data extracted complex systems such as financial or economical come out: variations of the generated time series following an asymptotic power law distribution, large fluctuations tending to be followed by large fluctuations, and small fluctuations tending to be followed by small ones, and fast decay of linear correlations, however, the correlations associated to their absolute variations exhibit a long range memory. Finally, a Detrended Fluctuation Analysis (DFA) of the generated time series, indicates that the GoL spatial macro states described by the time series are not either completely ordered or random, in a measurable and very interesting way.