Maximum Individual Complexity is Indefinitely Scalable in Geb

Abstract

Geb was the first artificial life system to be classified as exhibiting open-ended evolutionary dynamics according to Bedau and Packard's evolutionary activity measures and is the only one to have been classified as such according to the enhanced version of that classification scheme. Its evolution is driven by biotic selection, that is (approximately), by natural selection rather than artificial selection. Whether or not Geb can generate an indefinite increase in maximum individual complexity is evaluated here by scaling two parameters: world length (which bounds population size) and the maximum number of neurons per individual. Maximum individual complexity is found to be asymptotically bounded when scaling either parameter alone. However, maximum individual complexity is found to be indefinitely scalable, to the extent evaluated so far (with run times in years and billions of reproductions per run), when scaling both world length and the maximum number of neurons per individual together. Further, maximum individual complexity is shown to scale logarithmically with (the lower of) maximum population size and maximum number of neurons per individual. This raises interesting questions and lines of thought about the feasibility of achieving complex results within open-ended evolutionary systems and how to improve on this order of complexity growth.