Flow-Lenia: Towards open-ended evolution in cellular automata through mass conservation and parameter localization (2212.07906v2)

Abstract: 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.

• The paper introduces a novel CA model, Flow-Lenia, that conserves mass and localizes parameters to facilitate the emergence of spatially localized patterns.
• It demonstrates multi-species simulations by evolving update rules, enabling heterogeneous creatures to exhibit directed and angular motion.
• The methodology leverages evolutionary strategies to optimize CA dynamics, paving the way for scalable, adaptable research in artificial life.

An Analysis of "Flow-Lenia: Towards Open-ended Evolution in Cellular Automata through Mass Conservation and Parameter Localization"

The paper "Flow-Lenia: Towards Open-ended Evolution in Cellular Automata through Mass Conservation and Parameter Localization" introduces Flow Lenia, an innovative extension to the Lenia family of cellular automata. The primary objective is to facilitate the open-ended evolution of spatially localized patterns (SLPs) by introducing mass conservation and parameter localization. This exploration of cellular automata (CAs) is rooted in the broader pursuit of artificial life, where evolving systems simulate life-like behaviors without predefined outcomes.

Key Contributions

1. Mass Conservation in Cellular Automata: The introduction of mass conservation in Flow Lenia addresses two significant challenges observed in Lenia models: the difficulty in discovering life-like SLPs and the isolation of creatures governed by different update rules. By conserving mass in the system, Flow Lenia inherently constrains emerging patterns to remain spatially localized, simplifying the discovery of complex SLPs.
2. Parameter Localization and Multi-species Simulations: Flow Lenia enables localized parameter dynamics, allowing heterogeneous creatures with diverse behaviors to coexist and interact within the same simulation. This breakthrough facilitates multi-species simulations, providing a platform for intrinsic evolutionary processes to unfold akin to natural ecosystems.
3. Optimization of CA Update Rules: The system effectively utilizes evolutionary strategies to optimize CA update rule parameters, leading to the emergence of patterns exhibiting specific behaviors like directed motion and angular movement. The capability to evolve creatures without complex, fine-tuned search algorithms marks a substantial improvement in ease and efficacy compared to existing Lenia systems.

Detailed Findings

• Emergence of Complex Patterns: Flow Lenia's mass-conservative nature results in a higher prevalence of spatially localized patterns during random parameter searches. The paper demonstrates the emergence of both static and dynamic patterns with intricate behaviors, such as gyrating motions and self-replicating patterns resembling reaction-diffusion systems.
• Behavioral Specification through Optimization: By employing evolutionary strategies, Flow Lenia can derive update rules that yield desired behaviors. This facilitates targeted exploration in the CA parameter space for applications where specific life-like phenomena are sought.
• Parameter Embedding: The paper innovates by embedding update rule parameters within the CA dynamics, thereby introducing adaptability and interaction among differing simulated life forms. This flexibility advances the potential for simulating complex life-like interactions and evolutionary dynamics.

Implications and Future Directions

The introduction of Flow Lenia represents a significant stride in simulating open-ended evolution within CAs. It paves the way for richer ecological simulations where diverse artificial life forms interact, evolve, and potentially display increased complexity. The mass conservation principle, in particular, coupled with the adaptability afforded by parameter localization, creates new avenues for exploring life-like phenomena in computational environments.

In the field of artificial intelligence, Flow Lenia could significantly influence the development and paper of emergent intelligence and adaptation. Future research might focus on quantifying evolutionary processes within such systems to better understand the intrinsic mechanisms driving complexity and diversity. Moreover, studying the ecological interactions and potential emergence of agency within these simulations could illuminate theories of cognition and complexity.

Flow Lenia stands as a promising model, promising intriguing developments in both the theoretical exploration of artificial life and practical applications where self-organization and adaptability are paramount. The advancement of such systems could be pivotal in the broader aim of understanding and replicating life-like properties in digital domains.