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Fractals and the importance of proper description
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Commonality of structure
Benoît Mandelbrot
Mathematician
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Views | Duration | |
|---|---|---|---|
| 61. Writing and publishing work on rivers | 310 | 05:20 | |
| 62. Self-affining and self-similar fractals | 311 | 02:43 | |
| 63. Geometry; coming home to pictures | 323 | 04:13 | |
| 64. Origins and publication of Fractal Objects | 308 | 04:32 | |
| 65. The printing of Fractal Objects | 267 | 04:12 | |
| 66. Commonality of structure | 249 | 01:11 | |
| 67. Fractals and the importance of proper description | 1088 | 03:13 | |
| 68. Setting conficting goals | 366 | 05:54 | |
| 69. Self-similarity | 313 | 03:53 | |
| 70. Cartoons | 344 | 02:15 |
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The main question again was at the time of this lecture in the Collège de France in '72 and the beginning operation of the book of '75, I became utterly convinced that this was not just a collection of miscellaneous titbits which were linked by my personality, by my desire to love this kind of esoterica married to other esoterica, but by a commonality of structure. The commonality of structure again is scale, scalessness, scaling, renormalisability, the use of fixed points as privileged models, and many other techniques that were developed at the same time, in an entirely different context, entirely different style, with much greater precision, but with a much narrower scope in physics. At that point, '72, '75, I became aware of this work and studied it and started working in physics very strongly. But that's a later stage of the story.
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: Commonality of structure
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, 11 seconds
Date story recorded: May 1998
Date story went live: 24 January 2008
