[This is a back-issue of one of this site’s newsletters]
The ancient Greeks told a story about Icarus, who wanted to fly. He glued feathers to his arms with wax, and flew – but flew too close to the sun. The wax melted, the feathers dropped, and Icarus fell to his death.
Six months ago, we were told about a coming “Comet of the Century”, comet ISON. If things had played out differently, it might have been brighter than the full moon in the dawn skies around now.
Alas, like Icarus, ISON has flown too close to the sun, and melted away. Perhaps this is unsurprising – it got close enough to be torn apart by the sun’s tidal forces, while being baked to a toast 2700 degrees celsius (4900 fahrenheit). That’s hot enough to melt iron. Far too warm for a dirty snowball.
So, since we can’t play with comets, let’s play with fractals! If you haven’t played with the famouse Mandelbrot set, download Xaos and start exploring. Xaos is the best free fractal exploration software, available for Windows, Mac and Linux.
You may have known already how the mandelbrot set is defined: Choose a number c.Then repeat: square your number and add the original c. For some c, this process “converges”, that is, your numbers settle down, getting closer and closer to some answer. Other c’s lead you to a cycle of numbers that repeats, or chaotically jump around. For other values of c, the numbers quickly get larger and larger. If you let c range over the complex numbers, and color the complex plane according to how your numbers jump around, you get beautiful Mandelbrot fractals.
Here’s two facts you might not have known about the Mandelbrot set
- Germans call the shape the “Apple Man”. You can see why.
- The Mandelbrot Set is not just about that one specific formula, it appears in all sorts of places. At the link above, I show a video of a fractal related to solving cubic ploynomials. You can clearly see the Apple Man shapes as the video zooms in.