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Fractals and the distribution of galaxies


The complicated nature of DLA
Benoît Mandelbrot Mathematician
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This branching structure, DLA, the diffusion limit aggregate, proves to be of extraordinary complication. It is perhaps like turbulence, a phenomenon that I think will be with us for a very long time. Now why are we so excited about this structure? Because first of all it represents in one form or another way many of the natural dendrites encountered in many different fields of geology and elsewhere. By a total shock, it seems, it turned out to be a structure that rules the growth of certain bacteria under certain conditions. One is used to thinking of a Petri dish in which one gives lots of food to bacteria. You start with a little spot, it will grow more or less as a circle, but if the bacteria are starved- not starved but very much undernourished - they change tactic completely, instead of growing like a frond, they grow like trees, and the trees happen to follow this very simple mechanism called DLA. The complication of DLA is also extraordinary because it turns out that it attains a steady state very slowly. When many articles were written about DLA's of a few thousand particles, then people could make a few tens of thousands and found different properties. There was a great deal of surprise: why is it that one man's paper contradicts the second man's paper, until a third one comes with even bigger DLA and finds different properties. It is an object that takes a very long time to settle down to a, how should I say, final behaviour. More generally, it is an object in which every level of carelessness is punished very rapidly.

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: 2 minutes, 15 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008