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Also in the beta formula the non-linear bits can be applied as modifiers mixed with the affine transforms, so you can get escape-time renders that are as "rich" as using the purely convergent methods - it just takes judicious use of the modifier mixing.

Here's an example:

"Undersea Illuminations"



Full-size:
http://www.deviantart.com/deviation/44737262/

If you use the plain inverse of the convergent version of say z^2+c then you end up computing (-z)^2+c and (+z)^2+c which makes the inverse IFS method simply a very slow way of calculating the inside of a standard escape-time fractal - the beauty is that you can change it so that (for example) the two transforms are z^2+c1 and z^2+c2 which results in attractors that wouldn't be possible any other way - obviously you could use any polynomial instead of z^2+c. Alternatively you could use the two transforms as two different polynomials say z^2+c and z^3+c for example - obviously the possibilities are endless as with anyything fractal related !