### Happy pi day!

Happy Pi Day!

I wanted to make a picture based on pi. Since I have been playing around with fractals recently I though I should try making one based on pi. After all, there are many beautiful formulas that generate pi, and some ought to be possible to turn into fractals.

One of the earliest and most impressive pi formulas is François Viète's formula:

Unfortunately the formula is a bit too nicely behaved to produce any fractals on its own. However, my first try to implement it was a mistake but it produced a neat fractal (with a bit of motion illusion):

In this case the recursion formula is z_{n+1} = z_{n} sqrt(0.5 + 0.5*z_{n}). In the above picture I plot the argument of the iterates. A nice hyperbolic tiling inside a brain-shaped fractal.

Posted by Anders3 at March 14, 2009 07:06 PM