Capturing Emerging Complexity in Lenia

Abstract

This work investigates the emergent complexity in Lenia, an artificial life platform that simulates ecosystems of digital creatures. Lenia’s ecosystem consists of a continuous cellular automaton where simple artificial organisms can move, grow, and reproduce. Measuring long-term complex emerging behavior in Lenia is an open problem. Here we utilize evolutionary computation where Lenia kernels are used as genotypes while keeping other Lenia parameters, such as the growth function, fixed. First, we use Variation over Time as a fitness function where higher variance between the frames is rewarded. Second, we use Auto-encoder based fitness where variation of the list of reconstruction loss for the frames is rewarded. Third, we perform a combined fitness where higher variation of the pixel density of reconstructed frames is rewarded. Finally, after performing several experiments for each fitness function for 500 generations, we select interesting runs for an extended evolutionary time of 2500 generations. Results indicate that the kernel’s center of mass increases with a specific set of pixels and the overall complexity measures also increase. We also utilize our evolutionary method initialized from known handcrafted kernels. Overall, this project aims at investigating the potential of Lenia as ecosystem for emergent complexity in open-ended artificial intelligence systems.