Co-evolutionary Cellular Automata

Turing-complete gladiators in the Game of Life.

Explore a computational universe where two fields evolve together, shaping each other’s behavior in Conway’s Game of Life - a Turing-complete system capable of producing anything from logic gates to glider-based processors or even neural-like structures. This project uses a genetic algorithm to evolve the initial states of two fields, creating patterns that emerge not by design, but through co-evolutionary pressure.

🧬 Genetic Search in a Turing-Complete Universe

Conway’s Game of Life is more than a simulation - it’s a Turing-complete substrate where any computable process can theoretically emerge, given the right initial conditions. Finding those conditions in an infinite space of possibilities is the challenge. Here, we let a genetic algorithm navigate this space, evolving two fields that influence each other to produce dynamic, computational patterns. The result is an experiment in emergent complexity, where simple rules and co-evolution can lead to surprising outcomes.

🧠 How It Works

• The Grid: Two fields (A and B) form a combined toroidal grid, with A’s top edge adjacent to B’s bottom, and B’s top edge wrapping to A’s bottom, creating seamless boundary interactions.
• The Rule: A cellular automaton (default: Conway’s Game of Life, customizable) runs for a set number of steps.
• Fitness: Field A’s fitness is the number of cells in Field B that change (“flicker”) between the last two steps. Field B’s fitness is A’s flickering. This mutual dependency drives co-evolution.
• Co-Evolution: Two populations evolve in parallel. Each epoch, pairs of individuals (A[i], B[i]) are combined, evolved under the automaton, and scored based on their effect on each other.
• Genetics:
  • Selection: The top 50% of each population survives, preserving high-fitness patterns.
  • Crossover: Random cell mixing, with half the population kept as parents for stability.
  • Mutation: A low mutation rate (e.g., 1%, 1 cell flip) ensures gradual co-evolution, allowing fields to adapt to each other’s patterns slowly.
• Visualization: The test100and101steps function generates a PNG heat map showing flickering (white for changes, black for stable cells), highlighting boundary interactions.

⚔️ Co-evolution, Not Competition

Unlike traditional competition, this system has no fixed roles. Fields A and B co-evolve, each striving to maximize the other’s computational activity (flickering). They might:

• Develop patterns that destabilize the other, like glider streams crossing boundaries.
• Form symbiotic structures, such as oscillators that sustain mutual activity.
• Evolve computational systems, from logic gates to complex processors, as the Turing-complete substrate allows.

The toroidal boundaries ensure constant interaction, while the low mutation rate fosters a slow, adaptive “dance” where fields refine their influence over thousands of epochs.

📚 Related Project

This project is a follow-up to Evolving Cellular Automata, where the focus was on evolving the rules of cellular automata. In that earlier project, the 512-bit rule space defined the genotype, and fitness was tied to patterns produced after N iterations.

Here, we fix the rule (Conway’s Game of Life) and evolve the initial field state instead - flipping the genetic axis from rule evolution to field evolution.

📈 Observations

Experiments reveal diverse behaviors:

• Smaller grids (e.g., 55x55) may show fitness fluctuations after several hundred epochs, indicating dynamic shifts in co-evolution.
• Larger grids support more complex patterns but may stabilize without fluctuations, as patterns take longer to propagate.
• The number of iterations affects pattern reach—fewer iterations limit propagation in large grids, while more iterations allow deeper interactions.
• These outcomes depend on grid size, iterations, and mutation rate, making experimentation key.

📁 Repo Structure

📁 initial-state-evolution/
├── automata.html            # Single Conway's Game of Life automata for example
├── automata.js              # Logic for Conway's Game of Life (used in automata.html)
├── draw_node.js             # Main project file (entry point)
├── repl.js                  # Command-line REPL to launch cell functions
├── style.css                # Styles for testpop_from_file.html
├── testpop_from_file.html   # Client-side visualizer for 5 random automata
├── testpop_from_file.js     # JavaScript logic for client visualizer
├── visualize.html           # Heatmap viewer
├── storage/                 # Directory for saved .json population/fitness data
├── README.md                # Project overview and theory

🚀 Running the Simulation

node repl.js

Use this functions:

module.exports = { evil, recreate, mutate, printBestGrid, restoreBestPopulations };

cell.recreate(); // New population
cell.evil(1000); // Run 1000 epochs

📜 License

MIT License. See LICENSE for details.

📬 Contact

Serhii Herasymov
📧 [email protected]
🌐 https://github.com/xcontcom

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Built not to model life as it is, but to search for what life could be - in Conway’s strange, silent universe.