Fractal analyses of some natural systems

Wu, Shi-Ching

Abstract

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series.

Citation

Wu, S. (1999). Fractal analyses of some natural systems. (Thesis). University of Hull. Retrieved from https://hull-repository.worktribe.com/output/4224357

• Thesis Type: Thesis
• Deposit Date: Oct 12, 2022
• Publicly Available Date: Feb 24, 2023
• Keywords: Geography
• Public URL: https://hull-repository.worktribe.com/output/4224357
• Additional Information: Department of Geography, The University of Hull
• Award Date: Jan 1, 1999