Long-term evolutionary dynamics in heterogeneous cellular automata

In this work we study open-ended evolution through the analysis of a new model, HetCA, for "heterogeneous cellular automata". Striving for simplicity, HetCA is based on classical two-dimensional CA, but differs from them in several key ways: cells include properties of "age", "decay", and "quiescence"; cells utilize a heterogeneous transition function, one inspired by genetic programming; and there exists a notion of genetic transfer between adjacent cells. The cumulative effect of these changes is the creation of an evolving ecosystem of competing cell colonies. To evaluate the results of our new model, we define a measure of phenotypic diversity on the space of cellular automata. Via this measure, we contrast HetCA to several controls known for their emergent behaviours- homogeneous CA and the Game of Life-and several variants of our model. This analysis demonstrates that HetCA has a capacity for long-term phenotypic dynamics not readily achieved in other models. Runs exceeding one million time steps do not exhibit stagnation or even cyclic behaviour. Further, we show that the design choices are well motivated, as the exclusion of any one of them disrupts the long-term dynamics.