Computing The Dimension Of Dynamically Defined Sets I: E2 and Bounded . . .

We present a powerful approach to computing the Hausdorff dimension of certain conformally self-similar sets. We illustrate this method for the dimension dim H (E 2 ) of the set E 2 , consisting of those real numbers whose continued fraction expansions contain only the digits 1 or 2. A very striking feature of this method is that the successive approximations converge to dim(E 2 ) at a super-exponential rate