Wrinkling and fractalization of curves in an interface model of diffusionally unstable flames Original Research Article

An equation of interface evolution modeling flame fronts and solid-liquid interfaces is studied numerically. The solutions exhibit two distinct types of behavior. In the first scenario, the curves develop chaotic cellular pattern and accelerate while embedding is sustained. In the second, self-intersections occur and equation gives birth to fractal-like structures with exponentially increasing length and only linearly increasing diameter, which results in dense covering of the plane.