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Fractals in education


The origin of fractals
Benoît Mandelbrot Mathematician
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And finally, there is the question of the origin of fractals, which has raised a new fashion by this aesthetic aspect. After I began writing about using the 'monsters' of 1900 vintage - all kinds of discoveries made around 1900 for the purposes of either being mathematical pathologies or perhaps exotic observations in economics - when I had described the use of these structures to create shapes that are beautiful, readers of my books started writing that I was completely wrong in believing that these shapes originated in 1900. One form, which I called the Sierpinski triangle, Sierpinski gasket, which is made of several parts identical to itself, turns out to be very common in decoration in Italian churches, either on the pavement or in paintings, on the roof and on the ceiling. Other structures were found in Persian art or in Indian art of different periods, and very surprising to me, very moving for me, a loop seems to be established between structures that first were identified for the purposes of mere decoration; then much later, probably unconsciously, they were introduced by mathematicians for the purposes of, again, pathology. Again, much later, they were used by me for the purpose of science. Then unwittingly, as a free bonus, for the purpose of creating beauty; that a loop is from decoration to decoration, from beauty to beauty via mathematics and physics, which I think, if confirmed would be a very strong element of unity between different human enterprises.

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, 1 second

Date story recorded: May 1998

Date story went live: 29 September 2010