equivalence_percolation

Activated clusters found using depth-first (left) and breadth-first (right) searching using the WTM with a threshold of τ occurring with probability p(1−p)τ−1 (independently of d ) and p=0.51 for a 9×9 lattice. The number at each node is its threshold. The circled nodes are the initial nodes chosen for each cluster. The bottom left node is chosen first, and its cluster traced out. The next cluster is initialized by the bottommost of the leftmost remaining nodes. Thick colored edges formed the final interaction that caused activation. Nonexistent edges failed to cause activation (but moved the node closer to its threshold). Dashed black edges were not tested because both nodes were already active when the edge was considered. The clusters remain the same for both search orders (but edges change).