Tuesday, 1 May 2007
The posts start at the top and go down in this section.
It's Fractal Day 1 on the blog!
(Oh noooooo, he's discovered fractals...
Wot's a fractal?
From the Latin fractus, meaning broken, coined by the champion of the science, Benoit B Mandelbrot in 1975. Forms - in nature and mathematics - which display self-similarity on many scales. The best examples in nature are clouds. But fractals also occur in many other places, such as the human body's maximally packed venous, arterial and respiratory systems, and anyplace where branching forms are called for. The most widely explored example in mathematics is the Mandelbrot Set, pieces of which have been rendered on computers such that if the entire Set were at such a scale, it would be larger than the entire universe. Literally.
The seminal book on the subject has to be Mandelbrot's own The Fractal Geometry of Nature, which has had several editions.
I was delving into fractals in the mid-1980s: instantly fascinated with their forms (lavishly illustrated in the scientific literature), which must have spoken to my personality as an artist. Fractals are nature's structures. My own simplest definition of the word fractal is "made of itself". Mathematical fractals have the addictive quality of being calculable as large as your computing power and patience allows. I will describe several types on these pages, with some examples. And someday maybe I'll get to photographing some real-world ones as well...
(Now is perhaps a good time to point out that ALL of the pictures I post in the main part of my blog will reopen in a larger size (usually 1000 pixels on the long side) when you click on them once. They can then be saved to your computer as wallpaper or whatever. Enjoy.)
The aforementioned Mandelbrot Set, most famous fractal of them all, calculated from z->z^2+c on the complex plane. Enough of formulae: enjoy the pretty pictures. The complete critter in white (top), and 2 small details of the infinity to be found along its border (below). Made in Fractint.