The astonishing evolutionary dynamics of a class of nonlinear discrete 2D pattern formation and growth models

A family of 2D pattern formation and growth nonlinear discrete binary models with feedback are introduced and their evolutionary dynamics is experimentally studied. The models are inspired by the famous mathematical “Game of Life” and act on rectangular arrays (“living space”) of cells, which assume binary states 0 (“dead”) and 1 (“alive”). At each evolutionary step, each cell keeps or inverts its state depending on weighted sum of states of its spatial neighbors at the previous step and on a random binary control signal, which activates or de-activates, with a certain probability, the change of the cell state. The summation weight coefficients specify particular models of the family. A number of new and astonishing phenomena discovered in the evolutionary collective behavior of patterns the models generate is described.