Calling all art-snivelers
I'm writing a couple of introductory paragraphs for this book I'm working on. It's ridiculously difficult to condense everything I want to say into a small, reasonable amount of text. The goal here is to provide just enough information that a non-mathematical, art-oriented person would be interested, but not so much that it would confuse them. At the same time, I don't want to be guilty of oversimplifying things so much that they become less than true.
Here's what I have so far:
In 1918, a young mathematician named Gaston Julia published a paper titled Mémoire sur l'itération des fonctions rationnelles. It made him briefly famous, but was then forgotten for decades, until it came to the attention of Benoît Mandelbrot, who was using non-Euclidean geometry to describe naturally-occurring patterns like the shapes of clouds and coastlines. Mandelbrot called this new geometry "fractal," from the Latin word fractus, meaning broken.
Fractals are the product of thousands of calculations. A simple process is repeated over and over again, with each result becoming the seed of the next iteration. Over time, complex and beautiful patterns are revealed. Complexity from a simple process? Think of the millions of individual water droplets that come together to make a cloud, or the cells that grow into a flower.
As the art of photography had to wait for the invention of the camera, the art of fractals has waited for the computer. Julia was unable to illustrate his award-winning paper. Mandelbrot's early images, made in the mid-70s, were crude and slow. Now, at the turn of the millennium, the technology is finally catching up to the vision.
Comments? Critiques? Complaints? I'd be especially interested in hearing from people who hate math, or who are unfamiliar with fractals.
Here's what I have so far:
In 1918, a young mathematician named Gaston Julia published a paper titled Mémoire sur l'itération des fonctions rationnelles. It made him briefly famous, but was then forgotten for decades, until it came to the attention of Benoît Mandelbrot, who was using non-Euclidean geometry to describe naturally-occurring patterns like the shapes of clouds and coastlines. Mandelbrot called this new geometry "fractal," from the Latin word fractus, meaning broken.
Fractals are the product of thousands of calculations. A simple process is repeated over and over again, with each result becoming the seed of the next iteration. Over time, complex and beautiful patterns are revealed. Complexity from a simple process? Think of the millions of individual water droplets that come together to make a cloud, or the cells that grow into a flower.
As the art of photography had to wait for the invention of the camera, the art of fractals has waited for the computer. Julia was unable to illustrate his award-winning paper. Mandelbrot's early images, made in the mid-70s, were crude and slow. Now, at the turn of the millennium, the technology is finally catching up to the vision.
Comments? Critiques? Complaints? I'd be especially interested in hearing from people who hate math, or who are unfamiliar with fractals.