The motion of a crack in dynamic fracture has been shown to be governed by a dynamical instability causing oscillations in its velocity and structure on the fracture surface. We present experimental evidence indicating that the mechanism for instability is attempted local crack branching. At the instability onset, a crack will locally change its topology and sprout small, microscopic side branches. The trajectories of these local branches are independent of the crack velocity and exhibit scaling behavior. A connection between microscopic and macroscopic crack branching is established.