Chapter 1 Concept of Fractals and Fractals Geometry

FIG. 14 shows a typical fractal design showing three iterations of the initial base curve pattern to form a ring in a narrow spatial region for compression.

Fractal geometry is used in natural science - mathematics, physics, chemistry, biology - but it has been used recently in architecture and urban design. For example, Mit Media Lab's Neri Oxman calculates simulations from nature to the design and creation of new materials, and fractal shaped buildings (see below).

The latest development of geometry is fractal geometry. Fractal geometry was developed and promoted by Benoit Mandelbrot in his book "Natural Fractal Geometry" published in 1982. Fractal is a self-similar form (invariant to changes in scale) and is a geometric shape with fractional dimensions. As with chaos theory, this is a study of nonlinear systems, fractals are very sensitive to initial conditions, small changes in the initial conditions of the system may make the output of the system significantly different.

An interesting component of chaos theory is a complex image called fractal. There is a close relationship between chaos and fractal. For example, fractal geometry is the geometry that represents the chaotic system we find in nature. Fractal is a way to describe language and shape. Fractal geometry is described in an algorithm which is a series of instructions on how to create a fractal. The computer converts the instructions into patterns we see and calls fractal images. These same chaotic features also apply to mathematics. In order to create an image called a fractal, several equations can be repeated multiple times. Suppose that the two equations contain only one X and Y variable and some constants. When the equation is repeated multiple times, the result is drawn on the computer screen. Immediately, a very complex image (called a fractal) is magnified and the pattern repeats. Fractal shows all chaotic features