We present a new method to calculate the Hausdorff dimension of a certain
class of fractals: boundaries of self-affine tiles. Among the interesting
aspects are that even if the affine contraction underlying the iterated
function system is not conjugated to a similarity we obtain an upper- and
lower-bounds for its Hausdorff dimension. In fact, we obtain the exact value
for the dimension if the moduli of the eigenvalues of the underlying affine
contraction are all equal (this includes Jordan blocks). The tiles we discuss
play an important role in the theory of wavelets. We calculate the dimension
for a number of examples
