Prime Number Spiral Clusters

Question

I've written a program in Python that uses Turtle to draw out Prime Spirals. Essentially, it starts with a line of length 2, turns $\theta$ degrees then draws a line of length 3 and so on.

If I choose $\theta$ as the prime number itself (eg. I draw a line of length 2, then turn 2 degrees etc.), I get this interesting pattern of clusters:

Prime Spiral Clusters

Is there a simple explanation for what these clusters represent?

Thanks!

Edit - Here are some new results from various tests:

This is running through the same program, except with the Naturals rather than Primes.

This is the result of it running through the even Natural numbers.

And the same with odd Natural numbers.

This is every third Natural number.

Finally (and most interestingly) this is every third Prime number. Notice how chaotic it is compared to the rest!