Reaction diffusion is a great system to develop intuitions about complexity and emergence. The above equations describe behavior at individual points (pixels here), and the complex dynamics you observe are the result of neighboring points interacting with each other. The Gray-Scott model considers a population of an organism eating a food source and replicating. It needs food (added at a constant rate specified by the "feed" parameter (denoted "F" in the equations) to sustain its population because the organism also dies off at a constant rate, specified by the kill parameter (denoted "k" in the equations).
Try to change the parameters to get emergent behaviors that resemble cell-division or traveling waves! Be careful, because certain combinations of feed and kill will lead to colony collapse (but you can always reset the simulation to a symmetric or a random initial state!).
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