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Wednesday, August 15, 2018

Benoit Mandelbrot and fractals


Photo source: Wikimedia Commons, Rama

Photo license: CC BY-SA 2.0 FR


Benoit Mandelbrot (1924-2010) was a Polish-French mathematician best known for his work on fractals. Physicist John Barrow said,


"Benoit Mandelbrot has pioneered the study of natural and computer-generated patterns that are scale-free. He calls them fractals..." (The Artful Universe, 1995)


Below is a photo of a Mandelbrot set.

Photo source: Wikimedia Commons, Fedi, CC BY-SA 3.0



The rest of this post is a some quotes from Mandelbrot.




"A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales..." (Quotes in a review of The Fractal Geometry of Nature by J. W. Cannon, 1984)


"A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that." (A Theory of Roughness, 2004)


"There is nothing more to this than a simple iterative formula. It is so simple that most children can program their home computers to produce the Mandelbrot set." (The Fractal Geometry of Nature, 1982)


Philosophy of mathematics


"...nobody will deny that there is at least some roughness everywhere." (A Theory of Roughness, 2004)


"Contrary to popular opinion, mathematics is about simplifying life, not complicating it." (The Mis-Behavior of Markets, 2004)


"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." (The Fractal Geometry of Nature, 1982)


Computer graphics


"That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to present." (Wikiquote)