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The design of complex self-organising systems producing life-like phenomena,such as the open-ended evolution of virtual creatures, is one of the main goalsof artificial life. Lenia, a family of cellular automata (CA) generalizingConway's Game of Life to continuous space, time and states, has attracted a lotof attention because of the wide diversity of self-organizing patterns it cangenerate. Among those, some spatially localized patterns (SLPs) resemblelife-like artificial creatures and display complex behaviors. However, thosecreatures are found in only a small subspace of the Lenia parameter space andare not trivial to discover, necessitating advanced search algorithms.Furthermore, each of these creatures exist only in worlds governed by specificupdate rules and thus cannot interact in the same one. This paper proposes asmass-conservative extension of Lenia, called Flow Lenia, that solve both ofthese issues. We present experiments demonstrating its effectiveness ingenerating SLPs with complex behaviors and show that the update rule parameterscan be optimized to generate SLPs showing behaviors of interest. Finally, weshow that Flow Lenia enables the integration of the parameters of the CA updaterules within the CA dynamics, making them dynamic and localized, allowing formulti-species simulations, with locally coherent update rules that defineproperties of the emerging creatures, and that can be mixed with neighbouringrules. We argue that this paves the way for the intrinsic evolution ofself-organized artificial life forms within continuous CAs.

Flow-Lenia: Towards open-ended evolution in cellular automata through mass conservation and parameter localization