Development of Chaos and Fractals
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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 small fluctuations in terms of similarity in the stock market in 1961, the phenomena of non-standard scaling was determined. A paper published in 1967, used irregular shorelines as fractals when determining the length of the English coast, where as the degree of measurable detail increased the length of the shoreline also increased. Mandlebrot and his collaborators through the use of new fractal types like trees and mountains then looked into many complex models.
Mandlebrot and others made fractal geometry accessible to a wider audience through having work published, including the development of a theory of fractals by Mandlebrot in 1975. The subject importance was developed in the world of science. Investigations carried out by Mandlebrot included how from one length to another shapes are distorted. As the relationship between the fractals and their parts change, they are now referred to as non-linear. The Mandelbrot set is the most fascinating