  A theoretical approach to computing the Hausdorff dimension of the
topological boundary of attractors of iterated function systems is developed.
The curve known as the L\'evy Dragon is then studied in detail and the
Hausdorff dimension of its boundary is computed using the theory developed. The
actual computation is a complicated procedure. It involves a great deal of
combinatorial topology as well as determining the structure and certain
eigenvalues of a $752 \times 752$ matrix. Perron-Frobenius theory plays an
important role in analyzing this matrix.

Dynamical Systems