Diffusion on the Sierpiński Gasket

Anomalous subdiffusion: ⟨r²⟩ ~ t^(2/d_w) with d_w = log5/log2 ≈ 2.32

Parameters

MSD Exponent

⟨r²⟩:
Step count:0
Fitted α:
Theory (2/d_w):0.862

Anomalous Diffusion

Normal diffusion on Euclidean space: ⟨r²⟩ ∝ t (random walk, d_w=2). On the Sierpiński gasket, the fractal structure creates "dead ends" that slow transport:

⟨r²⟩ ∝ t^(2/d_w), d_w = log5/log2 ≈ 2.32

giving α ≈ 0.862 < 1 — subdiffusion. The walk dimension d_w encodes how tortuous paths through the fractal are. Measured via log-log slope of MSD vs time.