ABSTRACT
Sets, sequences, series, and functions occur in every area of applied mathematics. One of the common ways to form topological space is through the use of a distance function, also called a metric. Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. On the scale of a map, the deep fjords on seacoasts are clearly shown. The triadic Koch curve is one of the standard examples used to demonstrate that a curve has a fractal dimension. Feder gave an excellent description of the construction of the Koch curve as follows. The triadic Cantor set is one of the best known and most easily constructed fractal; nevertheless, it illustrates well many of the important, typical features of fractals. Gefen et al. reported the first systematic study of critical phenomenon that occurs near phase transitions in spin systems carried by self-similar fractal lattices. Mandelbrot and Feder introduced an interesting problem for measuring an area.
