Intrinsic oscillations in measuring the fractal dimension

Year: 1984

Authors: Badii R., Politi A.

Autors Affiliation: Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, italy

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.

Journal/Review: PHYSICS LETTERS A

Volume: 104 (6/7)      Pages from: 303  to: 305

KeyWords: fractals; oscillations;
DOI: 10.1016/0375-9601(84)90801-6

Citations: 59
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