Lévy flights (α=1.5) vs Brownian motion for foraging in sparse environments
Viswanathan et al. (1999, Nature) showed Lévy flights with exponent μ≈2 (α≈1) minimize search time for sparse, randomly-distributed, revisitable targets. The step-length distribution P(ℓ)∝ℓ^(-μ) has infinite variance for μ≤3, enabling occasional long jumps that relocate the searcher efficiently. Observed in albatross foraging, shark movements, and human travel patterns.