ABSTRACT
This chapter dercibes complex patterns that resemble complicated terrain, clouds, turbulent liquid flows can be constructed by methods. One such method is the use of self-similar structures. Self-similar structures are objects that when observed on any scale look the same. Most people are familiar with objects having integer dimensions. For example, lines are one dimensional, areas are two dimensional, and special relativity deals with four dimensions. The fractal dimension d can be used to characterize various types of terrain in aerial photographs. For example, aerial photographs of mountains, forests, and cities have different fractal dimensions. The simplest way of interpreting a difference equation is that every value of the subscript n corresponds to an increment of time. The kinetic energy, though quantized, has a form similar to the classical mechanical kinetic energy of a particle.
