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The Mandelbrot set and fractals
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The Mandelbrot set and fractals
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Views | Duration | ||
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81. Beginning to work on the problems of Julia and Fatou | 196 | 03:42 | |
82. Julia sets | 208 | 02:33 | |
83. Development of the Mandelbrot set; 'dirt' in the picture | 294 | 03:57 | |
84. The first conjecture of the Mandelbrot set | 266 | 05:31 | |
85. The haunting beauty in both the Julia set and Mandelbrot set | 285 | 01:16 | |
86. The Mandelbrot set and fractals | 1 | 620 | 01:42 |
87. The branching structure of Mandelbrot sets | 238 | 02:53 | |
88. Brownian motion and the four-thirds conjecture | 352 | 06:06 | |
89. The four-thirds conjecture and proof that mathematics is still... | 244 | 03:26 | |
90. Multifractals | 246 | 05:35 |
I would like to continue with the matter of iteration before returning to other issues. The next thing which surprised us very much, is that both for Julia sets and even more so for the Mandelbrot set, the complication was not, how to say, arbitrary, and almost everybody found the impression that these shapes were hauntingly beautiful. These shapes resulted from the most ridiculous transformation, z2+c, taken seriously, respectfully and visually. And people thought at first that they were totally wild, totally 'extraterrestrial', but then after a very short time, they came back and said, "You know, I think they remind me of something. I think they're natural. I think they are like perhaps nightmares or dreams, but they're natural." And this combination of being so new, because literally when we saw them nobody had seen them before, and being the next day so familiar, is still to me extraordinarily baffling.
Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance during the Second World War, and is famous for his work on fractal geometry - the maths of the shapes found in nature.
Title: The haunting beauty in both the Julia set and Mandelbrot set
Listeners: Daniel Zajdenweber Bernard Sapoval
Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.
Bernard Sapoval is Research Director at C.N.R.S. Since 1983 his work has focused on the physics of fractals and irregular systems and structures and properties in general. The main themes are the fractal structure of diffusion fronts, the concept of percolation in a gradient, random walks in a probability gradient as a method to calculate the threshold of percolation in two dimensions, the concept of intercalation and invasion noise, observed, for example, in the absorbance of a liquid in a porous substance, prediction of the fractal dimension of certain corrosion figures, the possibility of increasing sharpness in fuzzy images by a numerical analysis using the concept of percolation in a gradient, calculation of the way a fractal model will respond to external stimulus and the correspondence between the electrochemical response of an irregular electrode and the absorbance of a membrane of the same geometry.
Duration: 1 minute, 17 seconds
Date story recorded: May 1998
Date story went live: 24 January 2008