Superstring theory goes a long way to answer this question; one of the reasons it was proposed was that it provides 'granularity' to the universe. In the Standard model version of physics, there is no such thing (in the theory) as a smallest bit of space/time. When you try and extend the theory to such distances, i.e. infinitely small, the theory breaks down, giving infinite answers.
With super-strings however, the smallest bit of space/time is the strings themselves, everything else is derived from them. If this theory is right; and many of the most intelligent people ever to have lived seem to think so (but equally smart people think not of course!), then who knows? Perhaps the strings are in fact cellula automata, and as cellular automata could be used to run computations, who knows maybe you're right!