  In this paper, we investigate parameter families of iterated function systems
and continuity. Specifically, if we have a set of iterated function systems
that depend continuously on a parameter, which properties of the invariant sets
will vary continuously? We show here that the invariant sets will vary
continuously as a function of the parameter. Furthermore, we give some
sufficient conditions under which the Hausdorff dimension will depend
continuously on the parameter. Lastly, we give a counter-example where the
dimension is not a continuous function of the parameter.
