Random Walk on the Sierpiński Gasket

On a fractal lattice, diffusion is anomalous: ⟨r²⟩ ~ t^(2/d_w) where d_w > 2 (spectral dimension d_s = 2 ln3/ln5 ≈ 1.365). The random walk explores the fractal topology, getting trapped in sub-triangles. Contrast with flat 2D: ⟨r²⟩ ~ t. The diffusion exponent d_w = log5/log2 ≈ 2.322 for the Sierpiński gasket, making diffusion subdiffusive.

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