Learning and Adaptation in Particle Lenia

Cellular automata exhibit a range of pattern formation behaviors from oscillations and seemingly chaotic patterns to extremely complex ones. Conway's game of life, with its three simple rules of birth, death, and survival, is one of the most known cellular automata, and is Turing complete. Lenia is a powerful artificial life simulation tool, initially introduced as an extension of Conway's game of life for continuous space, time, and states and is, therefore, based on fields. Particle Lenia repurposes the Lenia field into particles with the system accurately reflecting physical laws, such as mass conservation and collision dynamics. We aim to investigate the potential of Particle Lenia for understanding the physics of learning and adaptive behavior in complex, dynamic environments. We achieve this aim through modifying particle interaction rules and incorporating multiple species that serve as the particle's environment. We search for learning transitions as a function of the complexity of the environment to determine the conditions for agency and adaptivity. This work lays the ground for connecting concepts from physical learning and biological adaptation, using the tools from Artificial Life, to contribute to a deeper understanding of learning emerging from simple algorithms.