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Coupled Dynamics: Lenia ↔ Boids

This directory contains a simulation demonstrating multi-model coupling, specifically illustrating bidirectional causality across fundamentally different substrate models.

The Models

  1. Continuous Cellular Automaton (Lenia): Represents the "environment" or "caloric mass". It has its own intrinsic dynamics of growth, propagation, and decay based on a continuous convolution kernel.
  2. Agent-Based Swarm (Boids): Represents foraging agents traversing the continuous environment.

Bidirectional Causality

The experiment explores what happens when two separate chaotic/complex systems become mutually dependent:

  • Upward Causation (Environment \(\to\) Agents):

    • Attraction: The Boids' acceleration vector is modified by a "Foraging Force" that points up the gradient of the Lenia density. They actively hunt high-density zones.
    • Survival: Boids must consume Lenia mass to maintain energy. If they fail to find dense Lenia patches, they stave and die.

  • Downward Causation (Agents \(\to\) Environment):

    • Consumption: When a Boid feeds, it reduces the Lenia mass in that specific grid cell, suppressing the continuous CA's growth at that node.
    • Fertilization: When Boids migrate, they leave a trace amount of "fertilizer" (waste) that minimally boosts Lenia. More importantly, when a Boid dies, its body undergoes catastrophic decay, massively boosting the localized Lenia density and triggering a new "bloom" of CA growth.

Emergent Dynamics

Observing this coupled system, you can see patterns reminiscent of macroscopic ecology: - Boom and Bust Cycles: If the Boid population explodes due to high Lenia density, they rapidly overgraze the environment, causing mass starvation. The resultant die-off fertilizes the ground, allowing Lenia to recover and restart the cycle. - Herding: The swarm follows moving Lenia blobs (gliders). - Substrate Symbiosis: Without the Boids dying and fertilizing the ground, the Lenia simulation might collapse to zero due to its volatile growth parameters. Without Lenia, the Boids starve.