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Fractal Geometry: Mathematical Foundations and Applications main elements: the concept of fractal geometry by B. Mandelbrot first proposed in 1975, ten years, it has rapidly developed into a new branch of mathematics. This is a research and treatment projects in the irregular shapes of nature and a powerful theoretical tool, its applications involving almost all fields of natural science, even social sciences. And in fact, play to link the various fields of modern science role. They associate it with a total of dissipative structures and chaos theory as the mid-20th century, 70 the three most important scientific discovery.