Lévy Flight vs Brownian Motion (2D) — Random Walk Simulator

Parameters

Lévy exponent μ 2.0

Walk mode

Steps per second 40

Trail length 4000

Lévy Brownian

Live stats — Lévy

Steps0

Distance travelled0

Displacement from origin0

Live stats — Brownian

Steps0

Distance travelled0

Displacement from origin0

Lévy flight: step length l drawn from P(l) ∝ l^−μ, 1<μ≤3, via inverse-transform sampling l = l_min·U^{−1/(μ−1)}. Low μ ⇒ heavy tail ⇒ rare huge jumps and fractal clustering.
Brownian motion: each step's x/y offset drawn independently from a Gaussian (Box–Muller) — uniform, no long jumps.