Diffusion on Penrose tilings

The animations below are examples of diffusion on a family of P3 Penrose tilings constructed using Robinson subdivisions. For a given tiling, we solve the semi-discrete differential equation $\dot{u} = L u$, where $L$ is the graph Laplacian of the tiling, with Neumann (zero-flux) boundary conditions. The solution is given by $u(t) = \exp\{ t L \} u_0$, where $u_0$ is the initial condition (uniformly concentrated on the 5-pointed star at the center) and the time step length is $\Delta t = 10^{-2}$. The wavefront is represented in black.