Mark Townsend's Fractalia formulas in mt.ufm in essence is
xnew = quadratic in x and y ynew = quadratic in x and y znew = xnew + flip(ynew)
Since each quadratic has 6 free parameters, he made 6 versions, Fractalia-1 through Fractalia-6, so the user could switch among them to help find good parameters.
My version instead uses one or two steps of randomization of parameters to help find a good set. Each step either replaces each parameter with a random number in the range -scale to +scale, or adds to each parameter a random number in the range -scale to +scale.
An example fractal with parameters is in the Ultra-Fractal-Redux site on deviant art, at