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Fractals and chaos theory


Fractals and rules
Benoît Mandelbrot Mathematician
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There's a phrase, "Fractals are everywhere" it is the title of a book. The book was not written by me; the phrase was not coined by me. I think that the phrase is correct, to the extent that if you go around and look at phenomena of every kind, you probably will find somewhere in a corner an aspect which is fractal. I think it is probably correct. In this sense there are fractals everywhere. Now, I don't think that those fractal parts are necessarily important. In many phenomena they're not important, sometimes because those phenomena are simple and very often because they're even more complicated than any fractal. But this fractality is not complication without rules. Fractality is a form of geometric complication with very specific rules, very strong rules; and disorder, chaos, complexity, call it as you wish, and is present in many places in a way which does not have any clear rules. So if there are fractals everywhere, it doesn't mean that fractals are important everywhere. And it is not only my caution that tells me that, but also my experience.

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.

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, 28 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008