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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.

🖼 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.

▶ Run

From the repository root:

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