TRANSLATING THE CONWAY'S GAME OF LIFE AS A DISCRETE LOGISTIC CELLULAR AUTOMATA MODEL WITH DENSITY EFFECTS

John H. Conway (1937-2020) has introduced a series of cellular automata (CA) models to demonstrate that simple rules can lead to very complex phenomena. Game of Life (GoL) is one of the most renowned CA models invented by Conway in 1970's. In fact, GoL is a 'game' without players, by which the spread of artificial life on 2-dimensional plane under periodic boundary conditions is progressively simulated. The present study shows that GoL can be remodeled as a parameter-adjustable CA-based logistic model applicable for simulating the population dynamics of organisms, by emphasizing the intrinsic modes of density effects found in original GoL which are equivalent to the logistic and Allee effects observed in population dynamics in living organisms. The strategy taken was to design a novel Hill-type density-responsive algorithm functioning behind the actions of the logistic CA model extended from GoL. Lastly, the growth curves simulated by the modified GoL and logistic model were compared to clarify that the growth patterns in GoL obey the logistic growth prediction under strong influence of carrying capacity, but the harm by low density could be overcome by local configuration of live cells.