ABSTRACT
Fractal geometry dates from 1975 when Benoit Mandelbrot introduced the notion of the fractal set and developed the basis of a new geometric language allowing one to describe complex objects that Euclidean geometry left aside as being formless “monsters.” Fractal geometry also has the ability to describe natural phenomena and finds use in a number of diverse fields including viscous flow through porous media, aggregation, chaos, and turbulence. Fractals can be also viewed as disordered systems whose disorder can be described in terms of nonintegral dimension. Self-similarity means that the dilations that leave the system invariant scale all coordinates by some factor. The procedure is continued to give a fractal that has self-similarity properties. One of the most important features of a fractal is its dimension. There is also a very useful spectral dimension used for physical quantities.
