Stability index α
1.50
Walkers
20
Steps per frame
5
Lévy flights
For stability index α ∈ (0,2), step sizes follow power-law tails P(|x|>r) ~ r⁻α. Variance is infinite.
MSD grows as t^(2/α) — superdiffusion when α < 2.
α = 2: Gaussian (normal diffusion)
α = 1: Cauchy (ballistic!)
Lévy flights model animal foraging, stock prices, earthquake fault lengths.
For stability index α ∈ (0,2), step sizes follow power-law tails P(|x|>r) ~ r⁻α. Variance is infinite.
MSD grows as t^(2/α) — superdiffusion when α < 2.
α = 2: Gaussian (normal diffusion)
α = 1: Cauchy (ballistic!)
Lévy flights model animal foraging, stock prices, earthquake fault lengths.