  We use a spatially resolved cavity ring-down technique to show that the 2D
eigenmode of an unstable optical cavity has a fractal pattern, i.e. it looks
the same at different length scales. In agreement with theory, we find that
this pattern has the maximum conceivable roughness, i.e., its fractal dimension
is 3.01 plus\minus 0.04. This insight in the nature of unstable cavity
eigenmodes may lead to better understanding of wave dynamics in open systems,
for both light and matter waves.
