Mandelbrot set and prime numbers

Question

I have written a simple program in C to generate Mandelbrot set. Wherever I zoom in, it seems to me that I see prime numbers, most often 11, 17, 19. For example the object on the attached image has 11 branches.

Is there some deeper explanation, or have I just been misled by some kind of numerology?

Answer 1

Apparently fractals are related to partition numbers, and Ramanujan found a way to relate some prime numbers to partition numbers (5, 7, 11), according to the following articles:

http://www.wired.com/wiredscience/2011/01/partition-numbers-fractals/

http://www.aimath.org/news/partition/

I see your primes are higher, but who knows, maybe you will find these ties in higher partition numbers or different fractals.