Bert Wang-Chak Chan

Erwan Plantec, Gautier Hamon, Mayalen Etcheverry et al.

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 goals of artificial life. Lenia, a family of cellular automata (CA) generalizing Conway's Game of Life to continuous space, time and states, has attracted a lot of attention because of the wide diversity of self-organizing patterns it can generate. Among those, some spatially localized patterns (SLPs) resemble life-like artificial creatures and display complex behaviors. However, those creatures are found in only a small subspace of the Lenia parameter space and are not trivial to discover, necessitating advanced search algorithms. Furthermore, each of these creatures exist only in worlds governed by specific update rules and thus cannot interact in the same one. This paper proposes as mass-conservative extension of Lenia, called Flow Lenia, that solve both of these issues. We present experiments demonstrating its effectiveness in generating SLPs with complex behaviors and show that the update rule parameters can be optimized to generate SLPs showing behaviors of interest. Finally, we show that Flow Lenia enables the integration of the parameters of the CA update rules within the CA dynamics, making them dynamic and localized, allowing for multi-species simulations, with locally coherent update rules that define properties of the emerging creatures, and that can be mixed with neighbouring rules. We argue that this paves the way for the intrinsic evolution of self-organized artificial life forms within continuous CAs.

Gautier Hamon, Mayalen Etcheverry, Bert Wang-Chak Chan et al.

The research field of Artificial Life studies how life-like phenomena such as autopoiesis, agency, or self-regulation can self-organize in computer simulations. In cellular automata (CA), a key open-question has been whether it it is possible to find environment rules that self-organize robust "individuals" from an initial state with no prior existence of things like "bodies", "brain", "perception" or "action". In this paper, we leverage recent advances in machine learning, combining algorithms for diversity search, curriculum learning and gradient descent, to automate the search of such "individuals", i.e. localized structures that move around with the ability to react in a coherent manner to external obstacles and maintain their integrity, hence primitive forms of sensorimotor agency. We show that this approach enables to find systematically environmental conditions in CA leading to self-organization of such basic forms of agency. Through multiple experiments, we show that the discovered agents have surprisingly robust capabilities to move, maintain their body integrity and navigate among various obstacles. They also show strong generalization abilities, with robustness to changes of scale, random updates or perturbations from the environment not seen during training. We discuss how this approach opens new perspectives in AI and synthetic bioengineering.

Erwan Plantec, Gautier Hamon, Mayalen Etcheverry et al.

Central to the artificial life endeavour is the creation of artificial systems spontaneously generating properties found in the living world such as autopoiesis, self-replication, evolution and open-endedness. While numerous models and paradigms have been proposed, cellular automata (CA) have taken a very important place in the field notably as they enable the study of phenomenons like self-reproduction and autopoiesis. Continuous CA like Lenia have been showed to produce life-like patterns reminiscent, on an aesthetic and ontological point of view, of biological organisms we call creatures. We propose in this paper Flow-Lenia, a mass conservative extension of Lenia. We present experiments demonstrating its effectiveness in generating spatially-localized patters (SLPs) with complex behaviors and show that the update rule parameters can be optimized to generate complex creatures showing behaviors of interest. Furthermore, we show that Flow-Lenia allows us to embed the parameters of the model, defining the properties of the emerging patterns, within its own dynamics thus allowing for multispecies simulations. By using the evolutionary activity framework as well as other metrics, we shed light on the emergent evolutionary dynamics taking place in this system.

Bert Wang-Chak Chan

We report experimental extensions of Lenia, a continuous cellular automata family capable of producing lifelike self-organizing autonomous patterns. The rule of Lenia was generalized into higher dimensions, multiple kernels, and multiple channels. The final architecture approaches what can be seen as a recurrent convolutional neural network. Using semi-automatic search e.g. genetic algorithm, we discovered new phenomena like polyhedral symmetries, individuality, self-replication, emission, growth by ingestion, and saw the emergence of "virtual eukaryotes" that possess internal division of labor and type differentiation. We discuss the results in the contexts of biology, artificial life, and artificial intelligence.

Bert Wang-Chak Chan

We report a new system of artificial life called Lenia (from Latin lenis "smooth"), a two-dimensional cellular automaton with continuous space-time-state and generalized local rule. Computer simulations show that Lenia supports a great diversity of complex autonomous patterns or "lifeforms" bearing resemblance to real-world microscopic organisms. More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation. They differ from other cellular automata patterns in being geometric, metameric, fuzzy, resilient, adaptive, and rule-generic. We present basic observations of the system regarding the properties of space-time and basic settings. We provide a broad survey of the lifeforms, categorize them into a hierarchical taxonomy, and map their distribution in the parameter hyperspace. We describe their morphological structures and behavioral dynamics, propose possible mechanisms of their self-propulsion, self-organization and plasticity. Finally, we discuss how the study of Lenia would be related to biology, artificial life, and artificial intelligence.