What branches of mathematics are used to create this pattern?

[jit2006]

This is my first post. Please pardon me if I am breaking any forum rules.
While going through Wikipedia I came across this image.
How is this image created?I mean what equations are generally used creating this charts?
What mathematics knowledge would I require to comprehend this pattern or the equations.?
Please Help.
Jit

 

[Demystifier]

I think the corresponding branch of mathematics is the theory of groups and their representations.