Anomalous Diffusion: Fractional Brownian Motion

Normal, sub-, and superdiffusion — MSD ∝ t^α with Lévy flights and waiting time distributions

α = 1.00 Type: Normal MSD slope: 1.00
About: Normal diffusion has mean-squared displacement ⟨x²⟩ ∝ t (α=1, Gaussian steps). Subdiffusion (α<1) arises from power-law waiting times (CTRW model) — found in crowded cells, glassy materials. Superdiffusion (α>1) arises from Lévy flights with heavy-tailed step distributions — found in animal foraging, turbulent transport. The MSD log-log slope directly reveals α. Fractional Brownian motion generalizes Brownian motion with long-range correlations.