  We study the magnetic flux landscape in YBa$_2$Cu$_3$O$_{7-x}$ thin films as
a two dimensional rough surface. The vortex density in the superconductor forms
a self-affine structure in both space and time. This is characterized by a
roughness exponent $\alpha = 0.76(3)$ and a growth exponent $\beta = 0.57(6)$.
This is due to the structure and distribution of flux avalanches in the
self-organized critical state, which is formed in the superconductor. We also
discuss our results in the context of other roughening systems in the presence
of quenched disorder.

Statistical Mechanics;Superconductivity