Here by "LRIFS" I mean "Language Restricted IFS" and the idea for the escape-time version is basically the logical extension of Tglad's Mandelbox and renders Buddhi has produced as well as methods like the alternation of formulas.

I'm thinking of writing another type of formula for my wip3D renderer for UF that allows user-selection of multiple transforms with user-definition of how/when these are applied.

So far I'm going to impliment it with the following options/controls for which transforms to apply on a given iteration/depth:

1. Location based choice (essentially as I've applied for the "Simple Sierps" option in my current formula) - based on IFS techniques.
2. Iteration depth based choice - a method used in IFS that also allows for the escape-time alternation method.
3. Order based choice - again a method taken from IFS, here transform x could be set so it cannot be followed by transform y on the next iteration (this also covers the reverse).
4. Consequetive/counted restrictions e.g. such that transform x cannot be repeated consequetively more than n times (maybe also so that transform x cannot be repeated more than n times overall).
5.

Anyone any further suggestions ?

I've no idea how that would look like or how it could be done but the Order based gave me an odd idea
Maybe, you could define the order in some way by a Cellular Automaton?

Am working on a full suite of classes for ray-tracing but I won't be working on it in earnest until I'm happy with the organisation of it - I mean my preliminary design, which is still changing too quickly at the moment as I find new ideas to include - the thing is I don't want to start seriously until I'm happy that it's not going to involve major re-writes at a later stage.
So currently I'm concentrating on trying every idea I can think of in the wip3D formula though I think I will add some simple class-based options for the ideas I suggested in this thread

The ordering method is fairly straightforward and all the methods can be implimented fairly simply, on each iteration:

  for i=0 to numtransforms-1
     if transform is allowed on this iteration based on applicable criteria
        get decision value for transform i (e.g. distance)
        if decision value is better than current best then set transformtouse to i
     endif
  next i
  apply transformtouse

For the "ordering" method we just use "lasttransformused=transformtouse" at the beginning of each iteration and check a bitwise flag table in the loop for transform i to see if it is allowed to follow lasttransformused and if not then that transform is not considered for the current iteration. (Note that on initial entry tranfsormtouse would be set to say -1).

My mmf4.ufm:3D IFS formula (for purely affine IFS) includes all the options I suggested except the location based restriction - in that formula because Hart's method of transforming the viewing ray is applied we can actually check the entire IFS tree per-pixel rather than having to restrict things to one transform per iteration depth - though the location-restriction method has given me some optimisation possibilities for the 3D IFS formula (for certain "regular" IFS types)
A truly generic and complete solution is to use the distance estimation method but applying the full IFS tree per-pixel but that's definitely going to be slower - hence my experimentations here http://www.fractalforums.com/3d-fractal-generation/tglad%27s-mandelbox-and-using-the-delta-de-methods-for-rifs/msg13259/#msg13259

Oh, wow, very nice image. I like the variation. Is the color based on the transforms applied or something else?

Ah, that makes sense. Excellent!