March 14th is Pi Day (3.14) and it is also Einstein’s birthday. In celebration of Pi I give you this… (And yes, I know what day it is, this is posted a day early so I can forward it to select folks.)
The most inefficient way to estimate Pi, by using the Mandelbrot set.
For those of you who don’t remember what the Mandelbrot set is, here is a straightforward (if long-winded) description of the set, and a video of what the set looks like when you zoom in to examine a very small portion of the set.
(The colors in the rendition of the Mandelbrot set indicate if a given point is inside or outside the set. Points rendered in black are IN the set. Other colors are assigned to the points outside the set, and the various colors indicate how quickly the function for that point diverges under iteration. All that is explained in the video describing the set.)
OK, you’ve learned something. Now go plan to eat some pie with your lunch tomorrow.
If you want the proof that this is really pi, see this companion video. (Well, sort of… there is a little bit of hand waving, but then how much do you really remember about the complex plane?)