The Beauty of Math

Incalculable beauty is the result when equations produce fractals

1 min read
Image: Daniel White
Image: Daniel White

Who said algebra isn’t fun? This ornately detailed figure, which brings to mind the craggy but beautiful contours of a coral reef, is actually a 3-D computer rendering of a mathematical equation. It’s an example of a fractal, which breaks the rules of traditional geometry because its area and perimeter are incalculable. The numbers behind these beasties can’t be crunched, because no matter how closely you zoom in, the features always look like ever-smaller copies of the entire figure. Widely available fractal-generating software allows anyone to plot simple designs. This highly intricate figure, produced by Daniel White, a Web developer and amateur mathematician based in Bedford, England, is one of many at his Web site, http://www.skytopia.com.

This article appears in the March 2010 print issue as “Painting by Numbers.”

The Conversation (0)

From WinZips to Cat GIFs, Jacob Ziv’s Algorithms Have Powered Decades of Compression

The lossless-compression pioneer received the 2021 IEEE Medal of Honor

11 min read
Horizontal
Photo: Rami Shlush
Yellow

Lossless data compression seems a bit like a magic trick. Its cousin, lossy compression, is easier to comprehend. Lossy algorithms are used to get music into the popular MP3 format and turn a digital image into a standard JPEG file. They do this by selectively removing bits, taking what scientists know about the way we see and hear to determine which bits we'd least miss. But no one can make the case that the resulting file is a perfect replica of the original.

Not so with lossless data compression. Bits do disappear, making the data file dramatically smaller and thus easier to store and transmit. The important difference is that the bits reappear on command. It's as if the bits are rabbits in a magician's act, disappearing and then reappearing from inside a hat at the wave of a wand.

Keep Reading ↓ Show less