Abstract: Since Mandelbrot coined the term fractals in 1977, fractal analysis dominated the scientific literature for over two decades. Fractal geometry was derived mainly because of the inefficiency of classical geometry in describing complex shapes and phenomena. In fractal geometry, a curve can have noninteger dimension value ranging from 1.0 to 2.0, and a surface from 2.0 to 3.0. The more complex a curve or surface is, the higher the fractal dimension. Fractal applications in geography mainly fall in two groups. The first utilizes the fractal dimension for characterizing the complexity of spatial forms and patterns such as coastlines, river networks, city growth, and landscapes. The second type of applications focuses on simulating artificial images for testing a variety of geographic models. Despite its extensive applications, there are major issues and limitations in fractal analysis, including the unrealistic assumption of self-similarity for natural phenomena, discrepancies in fractal calculation from using different algorithms, and oversimplifying the representation of complex systems by a single index. Recent studies center on developing robust algorithms for fractal measurement and expanding new applications on relating fractal patterns with underlying processes.
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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