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Hi I just made some JIT formulas for Mandelbulb3D.

The best one I think is NOTHING. Becouse if you want to take something off the hybrid. Throught 1 iteration of nothing interferes with fractal and DE.

I would upload few pics here:
http://www.fractalforums.com/gallery/em-formulas-for-mandelbulb3d-pictures/

There are some question about programming too. But later.

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EDIT
Updated formulas with another one package with 9 new formulas and one small update. This one should be better.

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EDIT:
+ 1 new formula, generating buildings.

UPDATE of all other formulas: improved math - faster generation, correction of found errors say of spherefold, expansion of FLD's variable Addition into Julia like multi value addition.
To handle them all is marked with "Formula version 1.1" in commentary.

Everything is in the single zip file including explanation of all the values of building generator.


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EDIT:
UPDATE v1.2:
+ 3 new formulas. FLD mandelbrot set versions and one FLD.
6 formulas - updated and improved, including techna transform completely remade so that it now actualy works and not destroys DE, and  chudobox now is less boring.



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UPDATE: Version 1.3:
Added formulas:
+ JIT_EM_N_ElazoBulb.m3f
+ JIT_EM_N_KalezoBox.m3f
+ JIT_EM_U_Superseed_Lp.m3f
Chudobox, Domofractal, FLD_Boxbulb - added internal conditionals to speed up calculation with the default values

I alsou included in formula readmy article about mathematics of  most of the transformations used and the Lp spaces.

In searching I just found, it was a Newtonian Triples by jehovajah
 http://www.fractalforums.com/new-theories-and-research/newtonian-triples/
They would be a good start for a hybrid.

Here I did another bunch of formulas. This time with more of algebraic (and artistic) approach and understanding of process. So I think these formulas are better or at least more symmetric. The most intricate folding multiplications don't produces mandelbrot sets at all.
Realy this was more like an artistic inspiration.


I used this. throught I realy don't know what this does. But it's the main spin around for the Saturn:
x1:= ( x-w + y+z )*0.5;
y1:= ( x+w + y-z )*0.5;
z1:= ( x+w - y+z )*0.5;
w1:= ( y+z - x+w )*0.5;

I got it from hypercomplex 4D sinh when I delated all the trig.

In this compiler you can type sqr(x) or x*x. But the x*x is way faster. Probably becouse sqr(x) is turned into intPower(x,2) or even Power(x,2) what is not calculated by multiplication.

As a side I did tricorn conj(z*z)+c out of hypercomplex numbers. It looks just like mandelbulb tricorn. It seems that in 3D tricorn is somewhat universal like mandelbrot in 2D.

Thanks - will include those formulas in the next release and also push them to the repo at github

Cheers!

Update 1.3.
This could be a lucky number. I added two more formulas and then internal conditionals to some old to speed up calculation with default values, so not to calculate certain things witch then is not used.

All of them is based on Lp spaces and alsou on http://gannjondal.deviantart.com/ formula tutorials. In that tutorial there were just one formula I found very good and one abox version. It was good example on conditionals. The more later formulas is if not better then more elaborate and these are the most elaborate.

Elazobulb - Lp spaces distorts mandelbulb to Lp shapes. And two power in paralel creates very elaborate bulbs with lots of holes.
Kalezobox - boxfold fractal with Lp space sphere inversion between two radiuses. Spherefold was decunctructed in parts and then reconstructed. It is like Amazing Box but more different than most of it's versions.
They are kind of "smart formulas". Lp spaces is computationaly hard so I added conditionals to pick more lightweight equations when it is possible.

Superseed - I used to explore Lp spaces. It woun't do mutch more.

I alsou included in formula readmy mathematics of  most of transformations used. Becouse it's often the transformations witch constitute formula matters not a formulas itself. I often can decipher transformations present.

Compiler is weird. With conditionals it in certain formulas increases speed when I added conditional witch does nothing.
//=================================
// this useless conditional speed up the next one
// At least on my AMD PC.  
// Maybe becouse of weak compiler, some code optimisation or something like that, I have no idea why.
if Thickness = 4 then
   begin
   end;










Edit:
My mistake. It was https://en.wikipedia.org/wiki/Sigmoid_function  not sigma function I mentioned in readme about functions.

And the benessi Mag angle is
https://en.wikipedia.org/wiki/Magic_angle