archimedean spiral bluish noise

I noticed that if you make an archimedean spiral in polar coordinates starting at the origin that goes to [1,0] at theta = 2*pi, you can solve for the next point on the curve that is a distance 1 from the last point, and it has a sort of blue noise look to the pattern of the dots...

In fact it's easy to prove that every point is at least distance 1 apart so it has that quality that blue noise has...

The maple commands to solve for the next point...

If you add a couple more points at the very middle of the spiral and crop to an offset square it starts to look very blue noisy...

Maybe it would look even better if you vary randomly the length instead of just 1 apart around the curve a little more or equal to 1...