Calculating a Dimension of a Strange Attractor

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 L1 and L2 to the capacity dimension Dc by the equation Dc = 1 - L1 / L2 .