How do runners with no map and no memory still find the exit? The scent spreads from the green exit through corridors only. In the Labyrinth it reaches the entrance, 200 cells away along the corridors, about 30 ticks in.
Try this Set falloff to 80 and press Reset (falloff itself takes effect live). The visible scent now fades out within a few dozen cells of the exit and scent-coverage drops from 409 to 140, yet the runners arrive at about the same tick as before. They only compare neighboring values, and at the entrance the scent is still about 4 × 10⁻¹⁸, above zero.
About this model Where it ends up
A MathPets model in the Logo and NetLogo tradition of gradient followers. Runners find the exit of a maze with no map or memory by climbing a scent field kept up by the exit. The scent drops by a fixed factor per step along open corridors, so the field is a distance map of the maze and walking uphill follows a shortest path.
The grid is 35 × 25 patches. Each tick the scent is updated in four passes in which the goal patch is set to scent-strength, every open patch takes the largest scent among its four neighbors times falloff / 100, and walls hold 0. Patches update in random order within a pass, so the front advances at least four cells a tick. Then each seeking runner turns toward whichever of the four patches around it has the most scent (or turns randomly by up to 90° either way if it smells nothing) and steps forward 1; walls block it. population is read at setup, scent-strength and falloff every tick. The paintbrush toggles walls, and the presets stamp different layouts.
