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Calculating a Dimension of a Strange Attractor

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Bryan Robert Johnson

Based directly on the geometrical definitions of the capacity dimension adn the Lyapunov exponent, two computer algorithms were designed to find the fractal dimension of a stranger attractor describing the motion of a bouncing ball on an oscillating table. The algorithms were implemented on a Macintosh II microcomputer. The results of the two calculations are consistent and support the Kaplan-Yorke conjecture which relates the Lyapunov exponents *L*_{1} and *L*_{2} to the capacity dimension *D*_{c} by the equation *D*_{c} = 1 - *L*_{1} / *L*_{2} .