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Alan Turing developed a precise machine model of effective computation in On Computable Numbers, with an Application to the Entscheidungsproblem by Alan Turing. A Turing machine combines a finite set of control states with an unbounded tape and local read/write moves; this permits mathematical questions about what an algorithm can compute, rather than tying computation to one physical device. His universal-machine construction is foundational to computability theory.^[ref] His later The chemical basis of morphogenesis by Alan Turing connects reaction–diffusion systems with the formation of spatial patterns.

A Turing machine is a model of computation with finite control, a tape of cells and a head scanning one cell at a time. An instruction of a Turing machine uses the current state and scanned symbol to determine a new state, a written symbol and a head movement. The finite transition rules form the machine's description; the tape supplies storage without a fixed global bound.

In a standard input convention, a finite word occupies part of an otherwise blank tape. A Turing machine configuration records the state, head position and tape contents, so the next-configuration relation determines each computation step. A machine can accept, reject or continue indefinitely. Recognizing a formal language permits nontermination on some nonmembers; deciding it requires an answer on every input.

The separation between a finite rule table and unbounded reusable storage makes the model useful for proving general statements about algorithms. Alan Turing's 1936 paper introduced this style of machine to analyze effective calculation; its original examples produce successive digits of numbers.^[ref] Multitape Turing machines change the storage organization and possible step counts while retaining the same computability power.