Why do prime numbers make these spirals?

I guess in such examples Math shows us how close the universe is tied up.

Prime numbers are indeed interesting by their property of non-dividedness by anything except for 1, and a number itself. Spirals, zigzags, sinusoids, cosinusoids, etc are figures that have their "own style" (if this word is allowed to be used here). And, perhaps, the style of figures, and its essence (in Math) is tied up somehow in a mysterious way.