  Conductance fluctuations have been studied in a soft wall stadium and a Sinai
billiard defined by electrostatic gates on a high mobility semiconductor
heterojunction. These reproducible magnetoconductance fluctuations are found to
be fractal confirming recent theoretical predictions of quantum signatures in
classically mixed (regular and chaotic) systems. The fractal character of the
fluctuations provides direct evidence for a hierarchical phase space structure
at the boundary between regular and chaotic motion.
