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The results show that the fractal characteristics of the patterned surface quantitatively mirror the physical process that created the pattern, as characterized by its Lyapunov exponent. Relevant tests employed include neural networks, correlation dimensions, Lyapunov exponents, fractional integration and rescaled range. A deeper question concerns the meaning of the ever-increasing divergence of nearby orbits -- as measured by a number known as the Lyapunov exponent -- in a chaotic system. |
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