Some times passed since I last posted something about a mathematician and today is the day I start writing about them again. Today 20th November for Benoit Mandelbrot. He is mostly known for fractal geometry. He was a Polish-born, French and American scientist-mathematician.
He started with fractals from studying the Julia sets, that were invariant under certain transformations of the complex plane. While studying these, he also looked at the Mandelbrot set fractal (now named after him). In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as “program artifacts”.
In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension. According to mathematics scientist Stephen Wolfram, the book was a “breakthrough” for Mandelbrot, who until then would typically “apply fairly straightforward mathematics … to areas that had barely seen the light of serious mathematics before.”Wolfram adds that as a result of this new research, he was no longer a “wandering scientist”, and later called him “the father of fractals”:
Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called “fractals”, that are equally “rough” at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.
Wolfram briefly describes fractals as a form of geometric repetition, “in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesco broccoli are two examples from nature.” He points out an unexpected conclusion:
One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.
Mandelbrot used the term “fractal” as it derived from the Latin word “fractus”, defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphic computer code.
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