1. A Turing machine based on an oscillatory chemical reaction comprising: a reactor comprising a reactant solution comprising a reactant; a first chemical species source to provide a selected amount of a first chemical species; a second chemical species source to provide a selected amount of a second chemical species; one or more controllers coupled to control the addition of the first and second chemical species from the first and second chemical species sources responsive to an input; and one or more sensors positioned to sense changes in the reactant as the controller controls the first and second chemical species sources to add selected amounts of the respective first and second chemical species to the reactor, wherein the controller receives signals corresponding to the state of the reactant and correlates the states of the reactant to a result that is computed as a function of the input.