  Scaling behaviour of dynamically driven vortex avalanches in superconducting
YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films deposited on tilted crystalline
substrates has been observed using quantitative magneto-optical imaging. Two
films with different tilt angles are characterized by the probability
distributions of avalanche size in terms of the number of moving vortices. It
is found in both samples that these distributions follow power-laws over up to
three decades, and have exponents ranging between 1.0 and 1.4. The
distributions also show clear finite-size scaling, when the system size is
defined by the depth of the flux penetration front -- a signature of
self-organized criticality. A scaling relation between the avalanche size
exponent and the fractal dimension, previously derived theoretically from
conservation of the number of magnetic vortices in the stationary state and
shown in numerical simulations, is here shown to be satisfied also
experimentally.
