Invasion Percolation — Fractal Frontier

Invasion percolation models fluid displacing another in a porous medium. The invader always captures the boundary site with lowest random resistance. The resulting cluster is self-similar with fractal dimension d_f ≈ 1.89 in 2D — identical to standard percolation at p_c (Wilkinson & Willemsen 1983).

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Invaded: 1 Cluster size: 1 Fractal dimension ≈