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Image kernels generalize very naturally to real values (so naturally that it hardly constitutes a generalization). CAs can be generalized but it seems less nat
by jpfed 10y ago
Image kernels generalize very naturally to real values (so naturally that it hardly constitutes a generalization). CAs can be generalized but it seems less natural.
The common element you are picking up on, I think, is [comonadic computation](http://blog.sigfpe.com/2006/12/evaluating-cellular-automata-is.html http://blog.sigfpe.com/2006/12/evaluating-cellular-automata-...).
- Isamu 10y agoCAs are already highly generalized, we are just conditioned to only think of the famous ones like the Game of Life. All you need for a CA is a space in which to map your cells (in an arbitrary number of dimensions, with an arbitrary mapping), some state for each cell (maybe a real, this is arbitrary) and some transition function to compute the next state of each cell from its current state and that of its "neighborhood" (which again is arbitrarily defined.)
- contravariant 10y agoThe problem is that CAs are too generalized. They don't have the kind of structure image kernels have (in particular, they aren't linear transformations).
- obashut0 10y agoJust wanted to add this is quoting the definition of CA as instances of dynamical systems. It is interesting to think about how a large number of filter passes would affect an image. Makes me wonder if there are very simple filters that create absolute chaos after a while (could an edge detector be one?).