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1

As long appropriate initial constraints on the CA rule (and, in particular, on the neighborhood size) are provided, yes, this is possible. In fact, the basic algorithm is quite simple. It relies on the fact that the transition rule for a CA with a finite number of states and a finite neighborhood size has a finite number of possible inputs, and can thus be ...

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This problem is somewhat similar to programming by example https://en.wikipedia.org/wiki/Programming_by_example In this paradigm, a system is given a sequence of states (examples) and asked to synthesize a program that could generate that sequence. The system could be given many different examples and asked to synthesize a program that works with all ...

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Cellular automata can be defined on Cayley graphs of arbitrary groups. Intuitively, the states go on the nodes of the graph, and the neighborhood of a node is defined using the edges. The $d$-dimensional case corresponds to the group $\mathbb{Z}^d$ with edges $(\vec v, \vec v \pm \vec e_i)$ for all nodes $\vec v \in \mathbb{Z}^d$ and the standard basis ...

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