ABSTRACT
Mandelbrot introduced a new geometry fractal geometry to describe irregular and nonsmooth phenomena in nature, and it appears that this new field of investigation will be more applicable to the study of natural phenomena than regular and smooth curves and surfaces of classical geometry. A sponge cube looks three-dimensional in classical geometry, but it may be stressed in a plane because of a highly ordered structure of holes in it; thus, it also seems to be two-dimensional. In fact, the dimension of the sponge cube may be in the range between 2 and 3 because of existence of a highly ordered structure of holes in it; that is, fractional dimension. However, they are mostly independent of other parts of the book, so the reader interested only in the applications of fractals can neglect these chapters and sections. Fractal geometry is a new attractive discipline.
