What the Old Masters Knew About Fractals
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
The geometry of fractals may be relatively new, but humans—especially artists—have perceived them in nature for ages.
Is everyone's favorite Thanksgiving centerpiece really to blame for the post-dinner doldrums?
- Americans kill around 45 million turkeys every year in preparation for the Thanksgiving meal, only to blame our favorite centerpiece for the following food comas.
- Rumor has it our after-dinner sleepiness results from the tryptophan found in turkey.
- However, it is the meal's overall nutritional imbalance, not just the tryptophan, that make us want to leave the dishes for tomorrow. Or maybe the next day.
Pfizer's partnerships strengthen their ability to deliver vaccines in developing countries.
- Community healthcare workers face many challenges in their work, including often traveling far distances to see their clients
- Pfizer is helping to drive the UN's sustainable development goals through partnerships.
- Pfizer partnered with AMP and the World Health Organization to develop a training program for healthcare workers.
The famed author headed to the pond thanks to Indian philosophy.
- The famed author was heavily influenced by Indian literature, informing his decision to self-exile on Walden Pond.
- He was introduced to these texts by his good friend's father, William Emerson.
- Yoga philosophy was in America a century before any physical practices were introduced.
SMARTER FASTER trademarks owned by The Big Think, Inc. All rights reserved.