In my studies in computability I have come across the notion of the "machine", an abstract representation of a device that essentially computes. I have read about Turing Machines and Wolfram's binary cellular automata and I understand them.ie. the rules, states, colours, etc. and how they work. What I really don't get however is how they are viewed as an abstraction of computing. Why are automata even used to represent computers??
They begin in some state and run forever(unless a terminating state is specified). The critical point I'm trying to make here is that they receive no external input and are essentially functions of themselves:their current state is some function of its starting state.