Stacey

“Examined in color through the adjustable window of a computer screen, the Mandelbrot set seems more fractal than fractals, so rich is its complication across scales. A cataloguing of the different images within it or a numerical description of the set's outline would require an infinity of information. But here is a paradox: to send a full description of the set over a transmission line requires just a few dozen characters of code. A terse computer program contains enough information to reproduce the entire set. Those who were first to understand the way the set commingles complexity and simplicity were caught unprepared—even Mandelbrot.”
― James Gleick, Chaos: Making a New Science

“Mandelbrot saw a seemingly smooth boundary resolve itself into a chain of spirals like the tails of sea horses. The irrational fertilized the rational.”
― James Gleick, Chaos: Making a New Science

“The word “fractal” was coined in 1975 by the Polish/French/American mathematician, Benoît Mandelbrot (b. 1924), to describe shapes which are detailed at all scales.”
― Nigel Lesmoir-Gordon, Introducing Fractals: A Graphic Guide

“Fractals are a kind of geometry, associated with a man named Mandelbrot. Unlike ordinary Euclidean geometry that everybody learns in school—squares and cubes and spheres—fractal geometry appears to describe real objects in the natural world. Mountains and clouds are fractal shapes. So fractals are probably related to reality. Somehow. “Well, Mandelbrot found a remarkable thing with his geometric tools. He found that things looked almost identical at different scales.” “At different scales?” Grant said. “For example,” Malcolm said, “a big mountain, seen from far away, has a certain rugged mountain shape. If you get closer, and examine a small peak of the big mountain, it will have the same mountain shape. In fact, you can go all the way down the scale to a tiny speck of rock, seen under a microscope—it will have the same basic fractal shape as the big mountain.”
― Michael Crichton, Jurassic Park