Discrete Heat flow

Olli Cellular Automated

A color picture can be identified as an element in S G , where S is the set of colors (in our case, a 256x256x256 color cube) and where the group G = Z n x Z m represents the set of pixels (if the picture has width n and height m). We think of a picture as a discrete analogue of a vector field because at each point is attached a 'rgb vector' (red(x,y),green(x,y),blue(x,y)). A discrete version of the heat flow e - L t with Laplacian L acting on vector fields is a special kind of cellular automata map. (In general cellular automata can be seen as discretisations of partial differential equations. Not only space and time are discrete but also the target space).
The 'heat flow cellular automaton' averages in each time step in each color coordinate the 5 color values of its 4 nearest neighbors and its own color. We have applied this cellular automaton on a picture. What you see is the movie, when time is reversed.

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