Did you like geometry in school or did you find it dry and out of this world subject? There is another kind of geometry that has emerged in the 70’s. It is called “Fractal geometry”.
Mandelbrot discovered the so-called "geometry of nature" that goes away from the Euclidean geometry where everything is smooth and simple but feels inadequate to model the world around us. Mandelbrot describes himself as a deeply visual person and explained how he solved complicated mathematical algebra by visualising the result and describing it afterwards.
Mandelbrot discovered the so-called "geometry of nature" that goes away from the Euclidean geometry where everything is smooth and simple but feels inadequate to model the world around us. Mandelbrot describes himself as a deeply visual person and explained how he solved complicated mathematical algebra by visualising the result and describing it afterwards.
If you are curious to learn more about fractal geometry, you should watch “Clouds Are Not Spheres” , a 51 minutes documentary on fractal geometry and its creator, Benoît Mandelbrot available on the Teacher TV website.
Mandelbrot's famous quote gives a good idea of the underlying principle of his theory:
"Clouds are not spheres, mountains are not cones, coastlines are not circles, bark is not smooth, nor does lightning travel in a straight line." (B. Mandelbrot, introduction to "The Fractal Geometry of Nature")
Now, stop and read again the quote above with your artist’s hat on: can you see texture and patterns of the convoluted reality? Fractals are everywhere: animal, vegetal, mineral.
One of the scientists interviewed in the program said that, after reading Mandelbrot’s book on fractal geometry, you can’t look at a cloud in the same way again.
Fractals break the barrier between figurative and abstract geometrical art in the sense that, when you start to look at nature closely, you find geometrical patterns that repeat themselves on decreasing scales. In other words, abstract and geometrical patterns are everywhere in the natural world.
Fractal designs are not only intriguing but really beautiful. You can see some examples in the articles provided below.
Related articles and resources
- Wikipedia entry on Mendelbrot
- Wikipedia article on Fractal with many photographs and illustrations of different fractal sets.
- Introducing Fractal Geometry (Introducing...)
by Nigel Lesmior-Gordon
- The Fractal Geometry of Nature
by Benoit Mandelbrot
- Fractals Everywhere
by Michael F. Barnsley
Fractal geometry Fractals Benoit Mandelbrot Geometry of Nature Art and science Teacher TV
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