Fractals and Chaos Theory

With the advancement to computer graphics, new forms of geometry have evolved, this is known as Fractal Geometry which is composed of special types of irregular shapes. These shapes, however are self similar, meaning they are a subset within a subset which is equivalent to the whole system. Fractals are particularly simple but highly complex. The reason for their complexity is due to the infinite detail and unique properties of mathematical contained within. As the fractals are simple, this is due to the particular operations attached to them.

Fractals was discovered by Benoit Mandelbrot (1924), a French mathematician, used this as a way of describing in seeing infinity. Fractals are used to used to study complex phenomena, such as distribution of earthquakes, and the evolution of cities. Fractals offers unlimited ways of describing, measuring and predicting natural phenomena (Fractal Org, n.d).  This led to the new theme of "Chaos Theory".

Chaos Theory describes phenomena which are not random, due to a slight change in the initial conditions can produce large changes in behavior of the solutions. Such chaotic behavior is closely connected with the fractal property of an area, known as the self similar. For example, by changing the scale on which the behavior is depicted, the same variability will be visible. A benefit of chaos theory is that the 'ignorance' aspect is taken into account and is incorporated into what is being perceived.

References:

• Fractal Org. (n.d). Fractals: Useful Beauty - (General Introduction to Fractal Geometry). [Online]. Available: http://www.fractal.org/Bewustzijns-Besturings-Model/Fractals-Useful-Beauty.htm [2013, 07/02/2013].