Fractals based on prime numbers

[elphinstone]

Random idea:

Prime numbers have a caothic distribution and are more dense near 0. For thoose who have more Mathematical backgrounds than me: is it possible to define prime numbers in an interesting way w.r.t some 2D or 3D space? Maybe over Gaussian integers? This could lead to sets (of prime numbers) with interesting shapes. Someone already tried?

[Dinkydau]

I know there's Ulam's spiral that looks somewhat fractal, except it doesn't have infinite details when you zoom in.
http://en.wikipedia.org/wiki/Ulam_spiral

In this image, the idea of this spiral is expanded by adding composite numbers to it. The size of the dots indicates the number of factors that the composite numbers have, or, you could say, how not-prime they are. The small red dots are prime numbers.

[KRAFTWERK]

Interesting image Dinkydau... I see some patterns almost repeating...

...also looks like the roadmap of Barcelona, the roads "Diagonal" and "Parallell" is clearly visible! 

[elphinstone]

Never saw the Ulam's spiral before... very interesting!

Anyway what I was looking for is an "interesting" (in fractal sense) way to define prime numbers in 2/3D real/complex space. Will try in the next days, but I don't know if I have enough math knowledges.

Thank you guys!

[hgjf2]

I know there's Ulam's spiral that looks somewhat fractal, except it doesn't have infinite details when you zoom in.
http://en.wikipedia.org/wiki/Ulam_spiral

Wow! This "fractal" same as irregular kaleidoscope like in my topic "Polihedron many polihedrons" what contain a few examples of my unperiodic tilling
 

[hgjf2]

Let's compare!

[hgjf2]

It's a really cubical kaleidoscope same as into rectangular irregular polihedron made from mirrors