While the computer is a discrete device, it is often used to solve problems of a continuous nature. The field of Real Computation addresses the issues of computability in the continuous setting. As in the discrete case, we would like to define the notion of a computable subset of R^n. The definition we use has a computer graphics interpretation (in the case n=2), as well as a deeper mathematical meaning.

The Julia sets are particularly well studied sets arising from complex dynamics. In the talk we will discuss efficient computability of real sets, and describe some results about the computability of Julia sets. Our computability results come in contrast to the Julia sets noncomputability results presented by Blum/Cucker/Shub/Smale. This discrepancy follows from the fact that we are using a different computability model.