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NEXT STORY

The birth of fractals (Part 1)

RELATED STORIES

The Hausdorff Dimension
Benoît Mandelbrot Mathematician
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In '64 I must say I returned to IBM and my feelings and my status and everything had changed radically. I was no longer, how should I say, dabbling in esoterica of various kinds, giving lectures which are amusing but nobody followed, but I had now done this work on prices which were at the very core of economics and this work on turbulence at the very core of fluid mechanics. Moreover very skilled, demanding and 'show me' individuals had become convinced that I had a path through the truth and I was able to go on. Each had to be enormously developed, because it was not a matter of picking up a book off the shelf that had a theory applicable to it, but in fact of doing it more or less from scratch. In particular, having listened to Paul Levy about the stable distribution and stable processes, I was aware of the Hausdorff dimension and realised that the Hausdorff dimension was something which was ready to move from esoterica to reality. I may add that I knew more about the Hausdorff dimension than just from Paul Levy. While I was a post-doc of Von Neumann I met a student at Princeton named H. J. McKean who later became a very famous mathematician, Henry had written a Ph.D. on the Hausdorff Besikovitch dimension of certain sets in probability theory. I was very surprised that a man as bright, as brilliant as Henry was worrying about this little esoteric exercise but this was my friend, I read his thesis, therefore I found out about this technique, which of course at that time I spurned very greatly. But again, for myself in '64, in the context of prices, the measurement of relativity was a Hausdorff dimension, or some other dimension like Hausdorff's. In the context of turbulence the measurement of roughness was again the Hausdorff dimension. Hausdorff dimension was coming into the centre of things.

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: Bernard Sapoval Daniel Zajdenweber

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.

Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.

Duration: 2 minutes, 42 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008