Mandelbrot, Knitting and Everything

Benoit Mandelbrot, the 'father of fractals,' is dead.

As good as he was at math and geometry, his true gift was for seeing. He saw connections between widely scattered ideas, and saw deeper meaning where others saw mere curiosities.

The nature of fractals, where the same formula applied over and over creates a greater whole, gives insight into many parts of nature, but I want to talk about a simple one: sea shells. Think of a clam shells, which has a simple curve and a simple widening as it grows. If you change the rate of curve, so it curves just a little more, you can end up with a snail shell. If you angle the curve just a bit, you get a conch.

sea shells

And yet, it's all variations on what is in fact a simple process. A curve is just slightly more cells on one side, or one part, than another, so all it is, is a selective speeding up a bit. Widening is making two where there was once one.

Knitting helped me understand this. Simple patterns can be made by changing just one element, but doing it over and over. Change one bit of the pattern, change where a yarnover is in relation to a decrease, and you can change waves into zigzags. Small changes can have large effects.

For example, these two types of scarves are knit exactly the same, except one is in garter and one is in ribbing.

The only difference is in whether one knits all the time, or knits and purls all the time. 

To round out the theme of math, art and nature, the following link is to a TED talk which has a presentation of the crocheted reef you may have seen around the web, as well as an explanation of how fiber arts can be excellent echoes of nature -- in this case, hyperbolic space.

 http://www.ted.com/talks/margaret_wertheim_crochets_the_coral_reef.html

Enjoy the show, and next time you see an equation, think of it as just another knitting pattern.