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Generalized a specific question I had which is:

Would it still be called Cellular Automata if the state of the cell depended on the state of all the other cells in the grid?

Rohit
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Yes. Expand the grid size to n-dimensional neighborhood:

http://en.wikibooks.org/wiki/Cellular_Automata/Neighborhood

  • There is also toroidal cellular automata: http://demonstrations.wolfram.com/CellularAutomatonLikeNeuralNetworkInAToroidalVectorField/ this results in grid wrapping which makes all states dependent on others as state wraps. –  Dec 28 '13 at 22:16
  • What n-dimensional CA has to do with the proposed definition of a transition function? – Jean-Baptiste Yunès May 23 '16 at 07:36