A chemically-operated Turing machine based on a non-linear oscillatory chemical reaction comprising: means for providing a sequence of data to feed a reactor comprising a reactant solution comprising a reactant capable of attaining multiple states; the sequence of data consisting of symbols from a two-symbol alphabet; a first chemical species source to provide a selected amount of a first chemical species to the reactor comprising the reactant solution comprising the reactant, the first chemical species corresponding to a first symbol in the two-symbol alphabet; a second chemical species source to provide a selected amount of a second chemical species to the reactor comprising the reactant solution comprising the reactant, the second chemical species corresponding to a second symbol in the two-symbol alphabet; one or more controllers coupled to control the addition of the first chemical species and the second chemical species from the first chemical species source and the second chemical species source responsive to said means for providing; and one or more sensors positioned to sense changes in the reactant as the controller controls the first chemical species source and the second chemical species source to add selected amounts of the respective first chemical species and the second chemical species to the reactor, wherein the controller receives signals representative of amplitude and frequency of oscillations of the non-linear oscillatory chemical reaction corresponding to the state of the reactant and correlates the states of the reactant in the reactor to a result that is a chemically computed function of the input; characterized in that the chemically-operated Turing machine uses chemical energy for all the chemical reaction state transitions and does not require any mechanical, electrical, electronic or any other form of external intervention for its operations. means for providing a sequence of data to feed a reactor comprising a reactant solution comprising a reactant capable of attaining multiple states; the sequence of data consisting of symbols from a two-symbol alphabet; a first chemical species source to provide a selected amount of a first chemical species to the reactor comprising the reactant solution comprising the reactant, the first chemical species corresponding to a first symbol in the two-symbol alphabet; a second chemical species source to provide a selected amount of a second chemical species to the reactor comprising the reactant solution comprising the reactant, the second chemical species corresponding to a second symbol in the two-symbol alphabet; one or more controllers coupled to control the addition of the first chemical species and the second chemical species from the first chemical species source and the second chemical species source responsive to said means for providing; and one or more sensors positioned to sense changes in the reactant as the controller controls the first chemical species source and the second chemical species source to add selected amounts of the respective first chemical species and the second chemical species to the reactor, wherein the controller receives signals representative of amplitude and frequency of oscillations of the non-linear oscillatory chemical reaction corresponding to the state of the reactant and correlates the states of the reactant in the reactor to a result that is a chemically computed function of the input; characterized in that the chemically-operated Turing machine uses chemical energy for all the chemical reaction state transitions and does not require any mechanical, electrical, electronic or any other form of external intervention for its operations.