Long-term evolutionary dynamics in heterogeneous cellular automata

Abstract

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.

Evolution of Heterogeneous Cellular Automata in Fluctuating Environments

“…As in the previous version of HetCA (Medernach et al, 2013), the genotype of an individual consists of its transition rules encoded in a custom CA-LGP program using the function set listed in Table 1. Such a program maps the space of neighborhood states to a new cell state, while providing an evolvable representation framework based on an alphabet of elementary functions.…”

“…HetCA (Medernach et al, 2013) is based on classical twodimensional CA with several additional features: cells follow a heterogeneous transition function, i.e. one which depends on their location, inspired by linear genetic programming (LGP); they can also fall into special decay and quiescent states; and there is a notion of genetic transfer of transition functions (i.e.…”

“…Living cells always automatically turn into decay after 7 consecutive iterations spent in any one or several living states (tracked by an "age" counter). Further details about the HetCA model can be found in (Medernach et al, 2013).…”

Comparison of Evolutionary Development of Cellular Automata Using Various Representations

“…In addition, various advanced concepts and modifications of cellular automata were investigated. For instance, Medernach studied a heterogeneous concept of cellular automata whose cells utilise some advanced items like age, decay or genetic transfer using open-ended evolution to create an evolving ecosystem of competing cell colonies [22]. Bandini et al dealt with effects in cellular automata that may be observed by introducing asynchronous update schemes [3].…”

Analysing Emergent Dynamics of Evolving Computation in 2D Cellular Automata

“…We then enhance these CAs by including genetic information, with the aim of understanding how complex information may emerge from this simple spatial version of evolution. The coupling of GoL to genetic information has already been attempted in various ways (precursors: immigration, quadlife; with genetics: Sprout Life [13], HetCA [14,15], evolife [16][17][18][19]), but a systematic investigation of evolving dynamics is still outstanding. We add genetics to GoL-like binary CAs by associating a genome with each live cell.…”