Labyrinthine structure emerging from (1) and (20) with parameters , and Heaviside threshold . The initial spot of radius has a mode four instability, cf. Figure 4. This is primed by perturbing R with . Rows A show u and the colorbar below indicates its values. Rows B illustrate the evolution of the interface (, golden outline) due to the normal velocity of the boundary (green arrows, to scale but enlarged by a factor 50). The Liapunov function of (2) is noted at all eight time steps. See also the video in Additional file 1.