Cellular Automata are simple mathematical/computational models that have many applications. Essentially they are models for individuals interacting in very simple ways with their environment. The class of linear cellular automata is a particularly nice class since one can use the tools of linear algebra to study the long-term behaviour of these automata. This project is a brief overview of the topic of cellular automata, with particular attention paid to the class of linear CA and algebraic methods of characterizing Wolframâ€™s Rule 90 using the minimal annihilating polynomial. Some previous results for Wolframâ€™s Rule 90 are expanded to apply to the case where the update rule is acting on a ring instead of a field.

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