Lines in image; are they significant to prime numbers if so how? Amateur math question. I was playing around generating some 2D images, and wondered what it would look like if placed $P_{i}$ dots on a circle with diameter of $i$ for increasing values of $i$, where $P_{i}$ is the $(i + 1)$-th prime - with $P_{0}$ being 1. One interesting thing about the image is that there appear to be contours emanating from the center of the image. In particular there appear to be 3 distinguishable meta axes running though the center of the image. One top to bottom, the other two at about 30 degrees to the horizontal. I can explain the one running top to bottom easily, and also the general left to right symmetry. But I can't explain the other two. Why are they there?
Note the first image has had some pre-processing and a threshold to show the contours more clearly.
Note code used to generate points is like:
primes = [];
radius = 75;
get_primes( primes, radius + 1 );
for( i = 0; i <= radius; i++ )
    prime = primes[i];

    for( j = 1; j <= prime; j++ )
      y = i * cos( 2 * M_PI * ( j /prime ) );
      x = i * sin( 2 * M_PI * ( j/prime ) );
      printf( "%5f\t%5f\n", x, y );
    end;
end;


Appendix 1: Original image, and one with 0 <= i < = 1000:


Appendix 2: I used PHP script to generate the dots, then gnuplot to generate image, and then GIMP for further processing. See http://pastebin.com/0Hfb6Kdq for the simple PHP and gnuplot code.
 A: The vertical line going up comes from when $j=prime$, so $x=0$, $y=i$. The vertical line going down comes from the fact that $prime/2$ is always fairly far ($1/2$) away from an integer, so $x=0$, $y=-i$, is white for $i$ sufficiently small.
There are also repeating patterns that occur nearby and approximately parallel to the axis. These correspond to formulas like $j=prime/2+1/2$, $j=primes/2+1$, etc.
The other axes are explained in a similar way. They correspond to $ prime/6$, $prime/3$, $2prime/3$, $5prime/6$, which are always $1/3$ away from an integer. $1/3<1/2$ so this is a less powerful pattern that lasts a shorter amount of time. Also, you see an oscillation based on which integer is closer, which depends on whether $p\equiv 1$ or $p \equiv 2$ modulo $3$.
If you shrunk the radius of the dots, then more primes would appear, and I believe you would start to see a more distinct pattern on the horizontal axis corresponding to $prime/4$. As the dots get smaller more and more patterns would appear. It might be interesting to make the radius of the dots vary proportionally to $i/prime$ so they always cover the same proportion of the circle.
