Screenshots of some new "arena" (made by tweaking old one, but looks cooler IMO):
Screenshot from the 'arena' editor:
The table specifies parameters to the attractor. Attractor is given by polynomials like dx=x*x*a+x*y+b+x*z*c+x*d+y*y*e+... same for dy and dz, and cells in table specify coefficients a,b,c...
On top, you can see the factors (xx, xy, xz, x, ...) that are multiplied by cells in table.
Looks intimidating? I myself have no clue what particular set of parameters will look like until I try it! Which, by the way, means that you could tweak it as well as I can even if you don't know how it works. Results depend to tastes, not to technical knowledge.
I rarely enter parameters by hand, though - the "next fractal" button tries a lot of different random parameters until it finds something that seems interesting. Sort of artist AI. Like any today's AI, it is somewhat stupid, but gives good starting point for tweaking parameters by hand.