What the Old Masters Knew About Fractals

The geometry of fractals may be relatively new, but humans—especially artists—have perceived them in nature for ages.
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TRANSCRIPT

Question: Why do people find fractals beautiful?

Benoit Mandelbrot: Well, first of all, one explanation of that is that the feeling for fractality is not new.  It is one very surprising and extraordinary discovery I made gradually, very slowly by looking again at the paintings of the past.  Many painters had a clear idea of what fractals are.  Take a French classic painter named Poussin.  Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes.  And how did he choose them?  Well, he had the balance of trees, of lawns, of houses in the distance.  He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling. 

Take Hokusai, a famous Chinese painter of 1800.  He did not have any mathematical training; he left no followers because his way of painting or drawing was too special to him.  But it was quite clear by looking at how Hokusai, the eye, which had been trained from the fractals, that Hokusai understood fractal structure.  And again, had this balance of big, small, and intermediate details, and you come close to these marvelous drawings, you find that he understood perfectly fractality.  But he never expressed it.  Nobody ever expressed it, and then the next stage of Japanese image experts did some other things. 

So humanity has known for a long time what fractals are.  It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.  Never got together until I started playing with the computer and playing with topics which nobody was touching because they were just desperate and hopeless.

Recorded on February 17, 2010
Interviewed by Austin Allen