Automatic generation of iterated function systems

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Sprott, J.: Automatic generation of iterated function systems. Computers & Graphics 18(3), 417–425 (1994)



A set of affine mappings with randomly chosen coefficients is repeatedly iterated numerically using the random iteration algorithm to produce an attractor with fractal characteristics. The attractor is tested for boundedness, sensitivity to initial conditions, and correlation dimension. In this way, a computer can generate a large collection of fractal patterns that are all different and most of which have considerable aesthetic appeal. A simple computer program and examples of its output are provided. Many of the attractors have been systematically evaluated for visual appeal, and a correlation is found with the Lyapunov exponent and correlation dimension.

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