This PhD is a practice-based study of how the computer functions in art practice, which takes on the notion of a fine art computing “medium”. Current research, while sometimes referencing the computer as a potential art medium, mostly defines it non-explicitly as a type of “hybrid” media device or some sort of “multimedia” machine. These terms leave the existence of a specific computing medium in art practice undefined and have historically led the analysis of artworks that employ computers to rely on critical frameworks that were either developed for earlier physical media, or have no structural similarities to computers. Such approaches can fail to examine unique ontological issues that arise - especially at a structural level - when using a computer to produce art. To achieve a formal description of a hitherto loosely defined (or non-defined) art medium, the research employs a range of critical and theoretical material from fields outside art practice, chiefly among them Alan Turing’s definition of a "a(utomatic)-machine", (nowadays called a “Turing machine”) from his 1936 paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Turing described a machine which can “simulate” any other computing machine including all modern computers. His machine is here used to propose a ‘Turing-complete medium’ of art, of which every computer is a computationally equivalent member. Using this perspective/definition, the research undertook an investigation of a ‘Turing-complete medium’ by developing creative practice in the form of individual works that explored specific aspects of computing systems. The research then engaged in a written analysis of the practice, again employing the concept of a ‘Turing-complete medium’, working towards the development of medium-specific critique of any art made with any computer. In foregrounding the nature and functions of computing machines, the research explores how these elements can be made intrinsic to our interpretations of computer-based art while also being aware of the limitations of medium-specific critique as exposed within the modernist tradition.