Monday, December 24, 2007

Fractal Christmas Tree

Merry Christmas!
This is a fractal generated by a program written by yours truly. I like to show off. It would take a while to explain how I created this, but suffice it to say that it involves using Newton's method of approximating roots, as applied to the function f(x) = log(x2) over the complex plane.

Actually, since this tree was created using a mathematical process invented by Isaac Newton, perhaps it would more appropriately be called a Newtonmas tree. See, Sir Isaac Newton, unlike Jesus, was actually born on December 25th under the Julian Calendar. As a result, some people with a bad case of hero worship like to talk about "Newtonmas". Of course, the Newtonmas tree is usually an apple tree.