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🔁 Prediction Error Field (Game of Life)

This model implements a 2D Game of Life world where each cell is also a local learner that tries to predict its own next state based only on its 8 neighbours.

Over time, the field of learners collectively approximates the underlying Game-of-Life rule. The prediction error becomes a spatial "surprise field".

🧠 Idea

  • The world is a binary grid (0/1) updated by Conway's Game of Life (B3/S23).
  • Each cell:
  • observes its 8 neighbours,
  • forms an input vector x = [1, N1..N8],
  • predicts its own next state with a small weight vector w and a sigmoid,
  • sees the true next state from the Game-of-Life rule,
  • updates its weights using a simple local error rule.

This creates a prediction error field on top of a classic cellular automaton: a layer of learning dynamics embedded in a layer of physical dynamics.

đŸ–ŧ Visualisation

The script shows a live animation with two panels:

  • Left: current world state (Conway's Game of Life, black/white)
  • Right: prediction error per cell (|prediction − reality|, heatmap)

Bright regions in the error field indicate where the local models are still "surprised" by the world's behaviour.

Press ESC in the window at any time to stop the simulation.

â–ļ Run

From the repository root:

```bash cd simulation-models/prediction-error-field python3 prediction_error_field.py