Dryland Vegetation Patterns
Klausmeier model: Turing instability creates spots, stripes, labyrinths
Step: 0
⟨veg⟩: -
⟨water⟩: -
Pattern: initializing
The Klausmeier (1999) model: ∂w/∂t = a − w − wn² + d_w∇²w; ∂n/∂t = wn² − bn + d_n∇²n.
Water (w) diffuses fast, vegetation (n) diffuses slowly. Below a critical rainfall a_c,
the uniform state is Turing-unstable, spontaneously forming patterns.
Low rainfall → spots; intermediate → labyrinths; near transition → stripes.