It isn’t difficult to spot natural fractals all around you, if you know what you’re looking for. It’s quite probable that you just don’t recognize them because you haven’t looked at enough computer generated fractals, at enough scales, to realize that even if something in nature doesn’t look like a whole fractal, i.e., you don’t really see the repetition of a pattern on smaller and smaller scales, it will look like part of one.
Before Benoit Mandelbrot came along, nature was regarded as a rather chaotically influenced version of Euclidian geometry. The artist Paul Cezanne said as instruction to young painters: “Everything in Nature can be viewed in terms of cones, cylinders, and spheres.” But Mandelbrot’s famous quote “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line” contradicts this, and rings very true.
Some mathematical experts are able to generate entire landscapes, or, small parts of nature like a fern leaf, just using fractal formulas. Benoit Mandelbrot gave a few examples of these in his book, The Fractal Geometry of Nature. Indeed, the generation of natural looking landscapes, textures, etc. using fractals is quite common, in video games. Ever wondered how the game manages to keep up the appearance of the surrounding landscape the character is travelling through? That’s how. They are also used in movies, creating alien landscapes.
Some examples of fractals in nature are depicted in the photographs that were part of my exhibit this summer. The patterns of ice crystal formation, mountain ranges, clouds, branching patterns of trees, growth patterns of mosses and lichens, flower structure, butterfly wings and their coloration, fur growth and patterning… on every scale you can recognize fractals, not just on earth but in the entire solar system and universe. (More about that later). For now, have a look at these, and look at the world in a new way the next time you go outside.