  We propose a flat-histogram Monte Carlo method to efficiently sample fractal
landscapes such as escape time functions of open chaotic systems. This is
achieved by using a random-walk step which depends on the height of the
landscape via the largest Lyapunov exponent of the associated chaotic system.
By generalizing the Wang-Landau algorithm, we obtain a method which
simultaneously constructs the density of states (escape time distribution) and
the correct step-length distribution. As a result, averages are obtained in
polynomial computational time, a dramatic improvement over the exponential
scaling of traditional uniform sampling. Our results are not limited by the
dimensionality of the phase space and are confirmed numerically for dimensions
as large as 30.
