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

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Generate a random square grid tissue, and show the vertices on the boundary.

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Convert the tissue to a torus for periodic boundary condition, and then display the matching vertices on the boundary

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Draw a picture to demonstrate how the points on the boundary match up with edges on the opposite boundary

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Define a network in a single cell

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Define random initial  conditions

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Run the simulation

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Plot species PX in all cells

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Graphics:PX

Generate each frame in the movie

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Created with the Wolfram Language