  It is shown that conductance fluctuations due to phase coherent ballistic
transport through a chaotic cavity generically are fractals. The graph of
conductance vs. externally changed parameter, e.g. magnetic field, is a fractal
with dimension D=2-b/2 between 1 and 2. It is governed by the exponent b (<2)
of the power law distribution P(t) ~ t^{-b} for a classically chaotic
trajectory to stay in the cavity up to time t, which is typical for chaotic
systems with a mixed (chaotic and regular) phase space. The phenomenon should
be observable in semiconductor nanostructures and microwave billiards.
