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The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
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Flow-Lenia: Emergent Evolutionary Dynamics in Mass Conservative Continuous Cellular Automata.

Erwan Plantec1, Gautier Hamon2, Mayalen Etcheverry2

  • 1IT University of Copenhagen Robotics, Evolution and Artificial Life Laboratory erpl@itu.dk.

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|April 29, 2025
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Summary

Flow-Lenia, a new model extending Lenia, creates complex artificial life "creatures" with emergent behaviors. This mass-conservative system allows for multispecies simulations and studies evolutionary dynamics in artificial systems.

Keywords:
Cellular automataLeniaartificial evolutionevolutionary activityopen-ended evolutionorigins of life

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Area of Science:

  • Artificial Life research exploring emergent properties of living systems.
  • Computational modeling and simulation of complex adaptive systems.

Background:

  • Artificial Life (ALife) aims to create artificial systems exhibiting life-like properties such as self-replication and evolution.
  • Cellular Automata (CA), including continuous models like Lenia, are powerful tools for studying these phenomena, generating complex patterns resembling biological organisms.

Purpose of the Study:

  • To introduce Flow-Lenia, a novel mass-conservative extension of the Lenia model.
  • To demonstrate Flow-Lenia's capability in generating complex, spatially localized patterns with emergent behaviors.
  • To explore multispecies simulations and emergent evolutionary dynamics within the Flow-Lenia system.

Main Methods:

  • Development and implementation of Flow-Lenia, a mass-conservative extension of continuous cellular automata.
  • Experimental parameter optimization to generate specific complex behaviors in emergent patterns ('creatures').
  • Utilizing the evolutionary activity framework and other metrics to analyze emergent evolutionary dynamics.

Main Results:

  • Flow-Lenia effectively generates complex, spatially localized patterns exhibiting sophisticated behaviors.
  • Optimization of update rule parameters allows for the creation of diverse 'creatures' with targeted behaviors.
  • The system supports multispecies simulations by embedding model parameters within its dynamics, revealing emergent evolutionary processes.

Conclusions:

  • Flow-Lenia represents a significant advancement in continuous cellular automata for Artificial Life research.
  • The model successfully generates complex emergent behaviors and facilitates the study of multispecies interactions and evolution.
  • Flow-Lenia offers a promising platform for exploring open-ended evolution and the fundamental principles of life-like systems.