Isolating individual parts of this shape to look at would reveal the same repeating pattern of similar triangles infinitely. This fractal starts with a triangle, and then as you “zoom in” on the shape, or look at it on different levels, it is composed of smaller similar triangles. One simple example of a fractal is the Sierpinski Gasket. In nature, we can see this occurring in snowflakes, trees, mountain ranges, hurricanes, seashells, human blood, etc. The recursive formula that creates the pattern of the structure we are observing remains consistent as you look closer. Remember that a fractal is a “never ending pattern that repeats itself at different scales” (Wolfe & Tyrrel). Using this idea of fractals that he was developing, Mandelbrot worked to popularize the concept and teach how it applied in mathematics as well as in nature.Įxplanation/Application of Mathematics Introduction to Fractals He is credited with developing the idea of the Mandelbrot Set, which is “a connected set of points in the complex plane” (O’Connor & Robertson, 1999) that can be found using recursive equations shown in the math section. Yet Mandelbrot was not only interested in these naturally occurring fractals he also focused largely on the abstract application of fractals in mathematics. These exist all over nature consider snowflakes as an example.
They are created by repeating a simple process over and over in an ongoing feedback loop” (Wolfe & Tyrrel). Fractals are infinitely complex patterns that are self-similar across different scales. According to the Fractal Foundation, “a fractal is a never-ending pattern. Mandelbrot becomes significant in our study of mathematics in nature because he is responsible for introducing and explaining the concept of fractals. He just passed away in 2010, so his contributions to mathematics are considerably recent. Benoit Mandelbrot is a much more modern mathematician than the likes of Euclid or Newton.
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