Department of Mathematics, Faculty of Science, Kyoto University
Keywords: fractals, self-similarity, Hausdorff dimension
Abstract. The following excerpt elaborates the mathematical theory on Fractals introduced by B. B. Mandelbrot (1982). The notion of the Fractals attracts many researchers in various fields, such as physics and the natural sciences. The Fractals with self-similarity are dealt here. With this formulation, one can easily create and handle such Fractals. In mathematics the Fractals are closely related to the well-known pathological examples, e.g. Weierstrass nowhere differentiable functions, Koch curves and Peano curves.