Intrinsic oscillations in measuring the fractal dimension

Abstract

In measuring the fractal dimension of a strange attractor, the logarithmic slope of the mean nearest-neighbour distance among n points displays in general an oscillating component. It is shown that such an oscillation is an intrinsic effect, and that even strictly self-similar sets exhibit slope oscillations. The Zaslavsky attractor is studied as a representative example of this phenomenon. Finally, an analytic explanation in terms of the Lyapunov exponents is given for a simplified model. © 1984.