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So this does not need large training data sets like traditional models?

The lizard and the Game of life example seem to illustate that you only need one data points to create or "reverse" engineer a an algorithm that "generates" something Equal to the data point.

How is this different from using a neural network and then over fitting it?

Maybe that instead learning trained weights, the Cellular Automata learns a combination of logic (a circuit).

So the underlying, problems with over fitting an neural network (a model being un able to generalise) still hold for this "logic cellular automata"?