Category: Statistics

Summary: Using adaptive bisection and iterative deepening to bracket the spanning threshold of a large 2D percolation grid more efficiently than uniform parameter sweeps.

Percolation thresholds are usually estimated by scanning many occupation probabilities, but most of that work is spent far from the transition. This experiment asks how tightly the critical window can be localized by repeatedly bisecting only the still-uncertain part of the parameter range.

The script runs spanning tests on a large 2D grid, uses breadth-first-style dilation to detect connectivity, and prunes parameter regions that are already settled. Iterative deepening then concentrates additional compute near the apparent threshold instead of revisiting values that are clearly subcritical or supercritical.

That makes the project as much about experimental design as about percolation itself. It tests whether an adaptive search strategy can produce a sharper threshold bracket with the same compute budget.

Method: Adaptive spanning tests on a 2D lattice using iterative bisection, pruning, and BFS-style dilation near the critical occupation probability.

What is measured: Critical-threshold bracket, number of spanning tests completed, pruning efficiency, and grid-spanning outcomes near the transition.