It's a fractal. You can imagine like this: Take a math function and feed in the x,y, and z coordinate. The function puts out x,y,z again. Take the result and feed it again. Run this as often as you like and do this for all x,y,z that you can see. Now the visible shape is all the x,y,z coordinates where the result does not exceed a certain value. And the colors e.g. can be defined according the amount of loops you need to exceed that value. Mandelbulb 3D might make this a wee bit different but that's basically how it works in 2D at least.
I haven't done fractals in a while, this one here is so cool because of the way it came out, and it can go well on a possible video game background scene say in a scene similar to Earthworm Jim's. Nice!!