FIG. 15.

(Color online) Solutions of Eq. (63) with σ=1 at various rescaled times t given random initial conditions on the circle bounding the homeland, $H(0,\varphi )=\frac{1}{2}$. Time increases from the top curves to the bottom curves. Note that there is no observable difference between H(500,ϕ) and H(1000,ϕ) because H(t,φ) reaches a nontrivial limit shape as t→∞.