Percolation Duel

Race on a 21×11 lattice. Start anywhere on the left edge (x = 0). First token to reach the target (20, 5) wins. Now with Bernoulli site percolation obstacles and a start‑position win‑rate heatmap.

Coords: x from 0→20 (left→right), y from 0→10 (bottom→top). Top edge y=10; bottom edge y=0; middle 1–9. Dark squares are blocked (closed sites); tokens cannot enter them.

Percolation & Simulation

Math behind the game (very short & friendly)

Percolation studies how things spread through a grid — like water in a sponge or a signal in a network. Here we use a simple version: each cell is independently either open with probability p (you may step on it) or blocked with probability 1−p. As p increases, there is often a critical probability where long‑range connections suddenly become likely.

In Percolation Duel, movement is random but biased to the right. Obstacles make some paths impossible, so choosing a smart start matters. The heatmap shows, for each left‑edge starting height, how often a random walker reaches (20,5) under the current field and rules.

Curious to go further? Try exploring percolation on rectangles and wedges, crossing probabilities, and phase transitions in modern research.