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Commonality of structure


Origins and publication of Fractal Objects (Part 2)
Benoît Mandelbrot Mathematician
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Well, I went to one of our sons' study. He had the Latin dictionary because oddly enough Latin was studied in that High School in America, and I looked up under fraction, under fractial, in French, in English to Latin. They all refer to the Latin word fractus. I looked it up in a bigger Latin dictionary from fractus and it said that it describes what a stone becomes after you hit it, it becomes broken into many pieces and the pieces are rough. Therefore the ideas of brokenness and of roughness were very present in that word fractus. I started playing with fractus, fractus, trying to get a word good in French and English at least, and hit upon fractal. Then my book of 1975 was being prepared, it was already on word-processing, it was edited - and the word 'fractal' was put all over where it belonged. The title was changed to Les Objets Fractal "Fractal Objects". Well, the book represented only a selection of my work, did not include the work on prices, because by then the work on prices had become less central to economics and I felt its limitations very strongly. And it was published. I may say how it was published. I have no shame at all in saying that for all practical purposes this was what's called "vanity publishing". The topic was totally esoteric. The readership was completely undefined. It had the virtue of being well written because my French teacher in high school had done her job very well. I knew how to write reasonably elegant French. It was published by your well-known publisher... Yes, who were quite, quite unrelated to this type of book- it was published by them because of relations, by and large. The book represented for them almost no risk because it was already presented in camera-ready copy. In fact it was the first book that Flammarion published in camera-ready form. When I brought it there they called the production manager, looked at it, and they said, "Well, so now we're going to send it to typography to print it." I said, "No, no, no, no, no, no. You don't." He said, "What do I do?" "You just take it and you photograph it. You make an offset." But he said, "But offset is for magazines, not for books." "Well," I said, "from now on offset is for books also." Of course now it's the routine situation, but in '75 the fact that IBM already had a word-processing system was just because IBM was manufacturing these kind of things. The book would not have been given a second look by anybody had it required external refereeing and seeing whether it would sell enough for its purposes. Well, I don't want to rush ahead but it now has had four editions and I think that it must sold fifty thousand copies in French, or something of this sort. The English book that came shortly afterwards sold well over a hundred thousand. The topic was timely; this effort to, how should I say, avoid resistance by side manoeuvre, by introducing pictures, was successful. And then in due time the scope of the whole work extended by iteration and of course became a very favourite object of play to many people thanks to the small computers. But that is going very fast ahead.

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: 4 minutes, 13 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008