  We study the geometrical characteristic of quasi-static fractures in
disordered media, using iterated conformal maps to determine the evolution of
the fracture pattern. This method allows an efficient and accurate solution of
the Lam\'e equations without resorting to lattice models. Typical fracture
patterns exhibit increased ramification due to the increase of the stress at
the tips. We find the roughness exponent of the experimentally relevant
backbone of the fracture pattern; it crosses over from about 0.5 for small
scales to about 0.75 for large scales, in excellent agreement with experiments.
We propose that this cross-over reflects the increased ramification of the
fracture pattern.
