Fractures are a critical process in how materials wear, weaken, and fail
whose unpredictable behavior can have dire consequences. While the behavior of
smooth cracks in ideal materials is well understood, it is assumed that for
real, heterogeneous systems, fracture propagation is complex, generating rough
fracture surfaces that are highly sensitive to specific details of the medium.
Here we show how fracture roughness and material heterogeneity are inextricably
connected via a simple framework. Studying hydraulic fractures in brittle
hydrogels that have been supplemented with microbeads or glycerol to create
controlled material heterogeneity, we show that the morphology of the crack
surface depends solely on one parameter: the probability to perturb the front
above a critical size to produce a step-like instability. This probability
scales linearly with the number density, and as heterogeneity size to the 5/2
power. The ensuing behavior is universal and is captured by the 1D ballistic
propagation and annihilation of steps along the singular fracture front