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yes I remember reading that, and now I am getting to the stage that I can understand some of it. There is so much for me to explore. I havent finished with the trig mandelbuld family, nor tried M.Benesi pinetree modifications. I found my original pinetree code was a  Pinetree just flipped, tried another combination and got  just the mirror image.  Another three  combinations gave me a fractal that crashed the software,  Then I got the three pointer, but have since got distracted.

 Once I thought there was just a small world of standard fractals, now there is an ever expanding universe of fractals.


Cheers

Lol I probably need to rename the whole topic (done!)... sorry Matthew (Benesi)
Another great formula author is msltoe - search all his post to find some great formulas lol....

Here I posted many formulas that I consider great... so take also a look!
http://www.fractalforums.com/releases-b233/mandelbulber-v2-2-03/

Good luckkkkk

About Mandelbulber Extended Formulas

Viewing the iteration loop as a Knight in a 3D chess game. At each iteration loop the Knight moves following a series of transforms (mathematical rules.)  The Knight moves until it either reaches a termination condition i.e. the maximum  number of moves allowed (maxiter) or moves out of the 3D chess board (bail out.)

Some standard fractals are made from two or more transforms.
The Mandelbulb and Quaternion comprise of two transforms. Their Base Formula function produces a sphere, that is modified by another transform ( a type of addition constant)
Mandelbox is simply four transforms:  boxFold, sphericaFold, scale and a type of addition constant.

The fractal formula_extended iteration loop is made up of transforms that can be either :

- single functions, example z = (z + const.A);  where z is changed by a single function, or,

- multiple functions , example z = (z – const.A) - (fabs(z)) + (z * const.B) + (const.C); where the change in z is the sum of a group of single and/or multiple functions.

After each transform the mathematics to create the next new z can be varied by changing parameter variables, including “start/stop at iteration” parameters and even the order of the transforms inside the loop. The possibilities are infinite , but because of render time considerations we have to restrict the number of options.

Example :Transform – Main Rotation.
In this transform we currently have  four  non-integer variables: weight,  alpha, beta and gamma. But weight could be  expanded to weight.x, weight.y, weight.z And each variable could be further modified at each new iteration (by various methods) and can also have a sequence of independent “start/stop at iteration” parameters, constructed to run until termination conditions are met.
Example: run transform for two iterations at five iteration intervals.

Running the fractal formula provides plenty of places to sample the data. With the extended formulas we have many z values:
Initial z,
Final z,
z0, z1, z2 etc; at the end of each iteration until Final z,
And there is a new z after each transform within the loop.

Manipulations of all preceding data can be fed back into the formula at any stage of the calculation. Some of all this data may be also useful with colouring methods,  audio interaction and DE calculations.

To date the extended formulas allow for the construction of only a  few of the infinite possible combinations of transforms, and generally using only the  low overhead functions. 

You can find the formulas all on https://github.com/buddhi1980/mandelbulber2/blob/master/mandelbulber2/src/fractal_formulas.cpp.
The generalized transforms for the New extended formulas are in .../src/fractal_transforms.CPP

The code is quite self explaining. And tightly bound to the interface.
If you compile the current code base, make settings in the ui and keep an eye in the source code it should be easy to follow the flow
If you have any specific questions i am sure Graeme can help you, Since he wrote most of the fresh extended formulas