Ulam Spiral Demo

I am fascinated by the beauty of mathematics and especially emergent patterns. One of the best known examples of this is the mysterious 'Ulam Spiral', named after the Polish mathemitician who discovered it. Basically, using a rectangular grid of numbers, starting at 1 and spiraling out, the prime numbers tend to line up along diagonal lines. This makes sense considering all primes must be odd, but that does not explain the tendency of primes to tend towards some diagonals more than others. Of course there are infinitely many primes by Euclid's famous proof so the pattern will continue inifitely.

I'm not sure why exactly this happens but it was trivial to utilize the HTML5 canvas element and the Sieve of Eratosthenes to generate the pattern with javascript.

More info at Wikipedia

Demo Here

Javascript code here