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The origin of fractals


Fractals and beauty
Benoît Mandelbrot Mathematician
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But from these very specific applications I would like to move on to two others, which are very different and, in a certain sense, perhaps far more surprising and to me very exciting. One of them is simply the beauty of fractals. The fact that they're beautiful and that they have inspired, for example, musicians to better understand their craft. Music consists in creating very complicated systems of sounds. Great musicians have confided to me that their schools never taught them how to distinguish music from noise. They had many rules, but the rules were not sufficient to characterise music. Upon learning of fractals they realised, as others have realised independently by more mundane techniques, that music of every culture, of every period, is invariably fractal, 1/f noise. Music that is not fractal is not perceived as beautiful. What does fractal mean in this case? That the structures on a large scale, in the middle scale, and the small scale are in balance with each other. It is not the case that there's a very large scale variation with nothing of small scale supported on it, or the converse. That is, an element of balance that is implied in beauty, which actually has been implied very strongly since the sixth century BC, which beauty consists in the harmony of the parts. This element is present completely in fractals and by people who are not themselves artists. It is perceived as an element of attractiveness in an aesthetic sense. This has led many of my friends to question, again, 'givens' about what is beauty, what is decoration, what is the share of the intent, what is the share of the personality of the artist and what is the share of simple structure rules in this problem? This applies also to architecture, to a large extent, but it would be too long to explain.

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, 22 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010