One field per cell, updated as
new x = tanh(J·(neighbour mix) + region bias + input field − fatigue·a) + noise.
When the coupling J exceeds ~1.15, agreement between neighbours becomes
self-reinforcing and whole regions lock into the same sign: the grid stops
acting like independent cells and starts acting like a material. The
grid is cut into vertical stripes (regions) with no neighbour links across
boundaries — each stripe is its own quasi-independent magnet. Higher worlds
add per-region response speeds (some react in ~20 ticks, some 25× slower) and
a slow fatigue variable that integrates recent activation and pushes
back — hold a region "up" too long and it rebounds, even oscillates, after
release. The discoverable laws are collective: switching thresholds,
hysteresis, relaxation schedules, fatigue rebound.
Clean senses, one collective mode. 6 inputs, 24 well-behaved sensors, low noise. The tutorial world: find polarities, find the switch, map the loop.
Same law, murky senses: 4 dead channels, 35% inverted sensors, gain spread 0.6–1.6×, more noise. Tests sensor calibration before science.
Three semi-independent regions (modules) with their own switches + murky senses. Local inputs matter: which port drives which region?
Six modules, weak global coupling, tighter budget. Requires targeted per-region experiments and bookkeeping.
Frontier: 8 modules, per-module response speeds (25× spread), and a slow fatigue variable (~200-tick memory) that turns the world into a slow relaxation oscillator. Duration of drive matters; states drift for hundreds of ticks after release. Best current agents: ~0.2–0.4.
