Diffusion on Fractal Lattices
Anomalous subdiffusion ⟨r²(t)⟩ ~ t^(2/d_w) on Sierpinski gasket and percolation cluster
Fractal Lattice
MSD vs Time (log-log)
Parameters
Fractal type:
Sierpinski Gasket
Percolation Cluster
Comb Lattice
Generation n:
4
Walkers:
50
Steps:
500
Run Simulation
Reset
Hausdorff d_f:
—
Walk dim d_w:
—
Spectral dim d_s:
—
Measured slope:
—
Status:
Ready
Spectral dimension: d_s = 2d_f/d_w
Sierpinski: d_f = log3/log2, d_w = log5/log2
Normal diffusion: d_w = 2, d_s = d_f
Alexander-Orbach conjecture: d_s ≈ 4/3