Fractal Geometry

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Fractal Geometry
How would you like to take a class called geometry of chaos? Probably doesn’t sound too thrilling. A man named Benoit Mandelbrot is responsible for creating the geometry of chaos. The geometry of chaos is considered to be the fourth-dimension. It is considered to be the world in which we live in, a world where there is constant change based on feedback, an open system where everything is related to everything else. It is now recognized as the true geometry of nature. The geometric system the can describe the simple shapes of the world (Lauwerier). Fractal geometry is a structure that provided a new key for the study of non-linear processes (Lauwerier). Benoit Mandelbrot explained that lines have a single dimension, plane figures have two dimensions and that we live in a three dimensional spatial world (Fractals Useful Beauty). In a paper published in 1967, Mandelbrot investigated the idea of measuring the length of a coastline. Mandelbrot explained that the shape of a coastline defies conventional Euclidean geometry and that rather than having a natural number dimension, it has a “fractional dimension.” The coastline is an example of a self-similar shape, which is a shape that repeats itself over and over on different scales (Fractals).

Benoit Mandelbrot was born in Warsaw in 1924 to a Lithuanian Jewish family and grew up there until they moved to Paris in 1936 (Fractals). Benoit had never received formal education and was never taught the alphabets; to this day he still doesn’t know them from memory. Benoit’s mind was a visual geometric mind, he had a tremendous gift in math in which he would take the problems from his work and translate them mentally into pictures. Benoit’s incredible mind took him all the way to the United State in 1958 to pursue his own way of doing math (Barnsley). Mandelbrot was offered a job at IBM’s research center in New York and was allowed free reign to pursue his mathematical interests as he wished. They proved to...
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