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Advanced Mathematical Case Studies 3 Cellular Automata 1) A discrete dynamical system forms a cellular automaton. [1] They first appeared in the specifications of digital computers and are processors of information. They are a self generation computer universe that has been designed by ourselves in which space is represented by the grid. [2] This grid contains a number of cells each contains data and discrete steps in time advances while the laws of the fictional universe are stated in a reference table, these form the rules of life. A cell or automaton may change state only at fixed or regular intervals and only in accordance with fixed rules that depend on cells owns values of neighbours within certain proximity. [3] Each cell has it's own state which can vary as the generations occur. They have several main components which are: 1. The array dimension 2. The neighbourhood structure 3. The transition rules 4. Time 5. Cell states The transition...

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