Lenia and Expanded Universe (2005.03742v1)

Abstract: 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.

Overview of "Lenia and Expanded Universe"

This paper presents an exploration of Lenia, a family of continuous cellular automata (CAs) known for producing lifelike self-organizing patterns called solitons. The authors have extended Lenia into higher dimensions and incorporated multiple kernels and channels, evolving it into an architecture akin to a recurrent convolutional neural network. These extensions fostered the emergence of novel phenomena and behaviors, expanding Lenia's capabilities beyond its original framework.

Key Extensions and Methodological Advancements

The research extends the Lenia model in three primary dimensions: higher dimensions, multiple kernels, and multiple channels. Each extension significantly broadens the scope of emergent behaviors.

1. Higher Dimensions: Transitioning from 2D arrays to multi-dimensional arrays (3D or beyond) proved challenging in identifying stable solitons. Yet, it resulted in solitons that exhibit high stability and complex symmetrical internal structures.
2. Multiple Kernels: This extension introduces dynamics by employing multiple kernels, each contributing differently to the emergence of solitons. This approach echoes concepts found in Multiple Neighborhood Cellular Automata (MNCA) and has facilitated the observation of advanced forms of self-organization like polyhedral symmetries and self-replication.
3. Multiple Channels: Implementing multiple interaction channels fosters diversity in soliton behaviors, mimicking complex biological phenomena such as division of labor and differentiation. Patterns developed in different channels interact, yielding self-organizing units with unique internal cooperation properties—termed "virtual eukaryotes."

Observations and Emergent Phenomena

The extended Lenia model demonstrates a variety of emergent structures and behaviors:

• Self-replication: New lifeforms capable of self-replication were discovered, providing insights into potential mechanisms in artificial systems resembling biological replication.
• Pattern Emission and Growth: The paper revealed solitons capable of structural growth via ingestion and pattern emission, akin to biological processes.
• Division of Labor and Differentiation: Through multi-channel setups, structures exhibit specialized functions reminiscent of cellular differentiation and organ functionality.

These findings underscore the model's capability to simulate biological-like processes and provide a platform for exploring complex systems' behavior.

Implications and Future Directions

The implications of these findings are manifold, affecting both theoretical and applied domains. Theoretically, Lenia's extension offers a unique testbed for studying complex systems' self-organization and evolution. Practically, it may inspire innovations in fields intersecting artificial life and AI, particularly through advanced neural network architectures resembling CAs.

Future research could focus on automating soliton identification and monitoring to enhance the robustness of evolutionary algorithms in pattern discovery. Further, leveraging the interplay between Lenia's architecture and neural networks might yield hybrid models with innovative capabilities in pattern generation.

In conclusion, "Lenia and Expanded Universe" advances the understanding of cellular automata's potential for simulating lifelike behaviors and complex system dynamics. Through methodical extension and experimentation, it lays the groundwork for subsequent exploration into synthetic life forms and their applications in AI and beyond.