Pattern propagation driven by surface curvature

Pattern formation and dynamics on curved surfaces are abundant in biological systems. Although past studies have revealed that surface curvature affects pattern dynamics and plays biological roles, a comprehensive understanding is still lacking. In this presentation, we report a novel mechanism of pattern propagation driven by surface curvature. By employing reaction-diffusion systems exhibiting Turing pattern on curved surfaces, we show for the first time that static patterns on a flat plane can propagate on a curved surface. Numerical and theoretical analyses reveal that the symmetry of the surface and pattern are involved in conditions for the pattern propagation.