Repressilator with diffusion / periodic boundary conditions
Reference:
Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature. 403:335-338.
http://www.nature.com/nature/journal/v403/n6767/full/403335a0.html
Generate a random square grid tissue, and show the vertices on the boundary.
Convert the tissue to a torus for periodic boundary condition, and then display the matching vertices on the boundary
Draw a picture to demonstrate how the points on the boundary match up with edges on the opposite boundary
Define a network in a single cell
Define random initial conditions
Run the simulation
Plot species PX in all cells
Generate each frame in the movie
Repeat the simulation on the original tissue, but not as a torus, so there are no boundary conditions.