The figure shows the M-set of a Mandelbox with negative scale and rotated folding planes (negscale rotbox) – with (l) and without (r) grid-Mandelbox.
The grid-Mandelbox means: scale=1 (neutral) minRadius=0, the rest default and this 12-20 times – this depends on other parameters – and without adding c. For further info see attached parameters.
>> the parameters were replaced due to an error (10/06)

We see a Mandelbox that is deformed but unchanged in overall size. At this point, I was not sure, whether this is a simple overlay or a completely new object. It turned out to be an overlay. What do I mean?
You can implant a particular Mandelbox J-set parameter with all the trimmings (including the global constant c) and the result shows this Mandelbox in many precise details, woven in a PseudoKleinian grid. The grid Mandelbox has no influence on detail development

the harvest – more or less a classic from 2011. I used this as input parameter. Clear shapes. Suitable for that quest.

The parameters ar included in the gallery The Mandelbox, an artistic and geometric journey | IMAGINARY

an early, plain implementation already shows many parts of the original parameter.

This is a two formula cycle. Mandelbox + Mandelbox in different configurations. Global c is added after the second one.

one step further. Adding a linear offset between the two slots, makes it possible, to move the second Mandelbox within the PseudoKleinian grid. Yes, it is that simple.

A sphere inversion as pre transform (slot 1) completes the elaboration. With the resulting four slot system you can almost sculpt freely with the input parameter. 

Same overall environment as the previous one, only altering shere inversion and add constant parameters.

And a third one with “the harvest” as input parameter. Also here only sphere inversion and add constant parameters are edited. Finding apt parameters is quite a quest. I “find” them by creating large random fields for the three dimensional vectors involved. This seems the most effective method to me. Mandelbulber has built in opportunities to exchange data of animations with spread sheets via csv-files. Here I simply generate random fields of any size.

A Mandelbox as shown in PIP in PseudoKleinian. The difference between a plain PseudoKleinian, which is Mandelbox+Mandelbox and this four slot cycle is sphere inversion and add constant, both executed one time. A non-linear and a linear transformation. I can imagine, that this combination is resposible for this “spiraling off”, for which I have no other explanation.

This is an example of a randomly created result. Done with a basic, unrotated Mandelbox

Annoter one from a similar unrotated Mandelbox.

Parameter is a to do