Models of fractal cracks

We present theoretical ideas which allow us to understand part of the scaling laws recently observed on branched cracks. We argue that some features are common to all critical branched structures, which barely survive when propagating. These ideas are illustrated by the directed percolation problem, which serves as an excellent toy model. Finally, we propose a Langevin equation for unbranched cracks in three dimensions, which naturally leads to self-affine structures.