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Fractals, Computer Science and Beyond
Abstract
In the modelling of the natural shapes (clouds, ferns, trees, shells, rivers, mountains), the limits imposed by Euclidean geometry can be exceeded by the fractals. Fractal geometry is relatively young (the first studies are the works by the French mathematicians Pierre Fatou (1878-1929) and Gaston Julia (1893-1978) at the beginning of the 20th century), but only with the mathematical power of computers has it become possible to realize connections between fractal geometry and the other disciplines. It is applied in various fields now, from the biology to the architecture. Important applications also appear in computer science, because the fractal geometry permits to compress the images; to reproduce, in the virtual reality environments, the complex patterns and the irregular forms present in nature using simple iterative algorithms execute by computers. Recent studies apply this geometry for controlling the traffic in the computer networks (LANs, MANs, WANs, and the Internet) and in the realization of virtual worlds based on World Wide Web. The aim of this chapter is to present fractal geometry, its properties (e.g., the self similarity), and their applications in computer science (starting from the computer graphics, to the virtual reality).
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