Fractals: A Sense of Scale
 By Peter Tyson
 Posted 10.01.08
 NOVA
So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em,
And so proceed ad infinitum.
—Jonathan Swift, from "On Poetry: A Rhapsody"
The satirist and author of Gulliver's Travels might have been talking about fractals when he made this oftquoted observation—if he hadn't lived two centuries before fractals were discovered. (In fact, Swift was complaining about lesser poets criticizing better ones, like pestering fleas.) As it happens, these four lines can serve as a perfect metaphor for the infinitely detailed, "selfsimilar" nature of fractals. In this interactive, zoom deep into a Mandelbrot set, the most famous of fractals, to the mindbending magnification of 250,000,000x. Along the way, you'll see what is meant by selfsimilarity, how the iconic Mandelbrotset shape keeps turning up at smaller scales like one of Swift's evertinier fleas, and why the 18thcentury wit's metaphor suits fractals to a tee.
Explore the infinite detail of a Mandelbrot set as you zoom to a magnification of 250,000,000x.
Note: NOVA Online's Rachel VanCott used the program Ultra Fractal 5 to generate these images of the Mandelbrot set.
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 © WGBH Educational Foundation
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