Another perhaps surprising aspect, to me at least, is the apparent uniformity of the density of prime numbers in the plane. It's my understanding that the density of the prime numbers decreases as you go higher [1], so why does the plane look so uniformly covered? [1] http://en.wikipedia.org/wiki/Prime_number_theorem
> why does the plane look so uniformly covered?
It's a purely perceptual effect. As you track away from the center of the spiral, your eyes are following lines, which are one-dimensional, but you're tracking the lines through a plane, which is two-dimensional. The area increases rapidly as you move away from the center of the figure, but the one-dimensional lines don't have area. This gives the lines an apparent weight that they don't actually have.