Reaction-diffusion waves interacting with fractals, spirals, and concave & soft obstacles*

We simulate the recovery and delay of reaction-diffusion wave fronts colliding with various obstacles in narrow two-dimensional channels by numerically integrating the two-variable Tyson-Fife reduction of the three-variable Oregonator model of the chemical Belousov-Zhabotinsky reaction. We investigate the influence of obstacles on the wave front's shape and its recovery after passing around/through fractals (e.g. Hilbert curve, Peano curve, inverse Sierpinsky carpet), Archimedian spirals, and convex & concave polygons by plotting the wave front's left most point and delay versus time. We find that wave fronts behave the same when propagating through symmetric obstacles (e.g., Hilbert curve and Sierpinski carpet) at specific angles, which is in contrast to non-symmetric obstacles such as the Peano curve. At long times, wave fronts follow the same power-law recovery behavior as previously observed for convex obstacles.
We also construct two types of chemical clocks, using illumination gradients with the light-sensitive reaction term or using space-dependent diffusion constants in the diffusion term.