Development of Chaos and Fractals
Essay title: Development of Chaos and Fractals
In very simple terms, fractals are geometrical figures that are generated by starting with a very simple pattern that grows through the application of rules. In many cases, the rules to make the figure grow from one stage to the next involve taking the original figure and modifying it or adding to it. This process can be repeated recursively (the same way over and over again) an infinite number of times.
There is a complex, formal definition of a fractal, but there are some more informal definitions. One way is to define fractals as processes or images that exhibit self-similarity. In other words, reduced versions of the fractal appear throughout the fractal.
“Fractal Geometry is not just a chapter of mathematics, but one that
helps everyman to see the same old world differently”. – Benoit Mandelbrot
A fractal, short for “fractional dimension” determined by Dr. Benoit Mandlebrot was a way for coping in the real world the problems of scale. The definition of the fractal is a curve or surface that is scale independent. Self-similarity, the name given to the property means that the whole curve would be identical once blown up to scale to any portion of the curve. This change from one scale to the other is a simple scaling process.
Benoit Mandelbrot determined the geometry of the fractal in 1970s. The relationship between fractals and nature was considered. Through looking at the flow of large and