Another way to make my Riemann sphere "bulb" using a conformal transformation

[mclarekin]

Nice work and information 

[msltoe]

@gannjondal: Thanks for spreading the formula to the Mandelbulb3D crowd. Also, I like how all the ridges connect in the 2nd picture.

[M Benesi]

popped in to do a drive by <clap>.   

 

[ericr]

Sorry but i usé thé parm paste,copy and i don t have your fractal i have nothing
I usé your 2 formulas but no !!!!!!!!

[ericr]

sorry again but yet all goes very well 
it is find and wonderfull and I do the same !!!!!!!!!!
nice day

[gannjondal]

@msltoe + mclarekin:  Thank you very much for sharing your knowledge, and for explaining the details. That did help quite much

Regarding the second picture: 
I tried several ways to change the last step, i.e. the tiling, mainly with some remembrance to something what had been done in good old UF.
It's amazing what effects can come up if trying to use common 2D effects to 3D.
 
One combination proved to be particular fruitful. The connections come up more or less automatically through the usage of sin and cos:

Code:

// original tiling
  x := x_tmp - Round(x_tmp);
  z := z_tmp - Round(z_tmp);

-->

// changed tiling
 else if Type_Tiling = 2 then
   begin
     x_diff := sin(x_tmp);
     z_diff := cos(z_tmp);
   end
		   
   .....
		   
 else if Type_PostCalc = 6 then
   begin
     tmp1 := x_diff*x_diff;
     SinCos(z_diff, stmp2, ctmp2);
     x := tmp1 + (1-ctmp2)/2;
     z := tmp1 + (1+stmp2)/2;
   end

The effect is too strong to use it in the full formula.
But if using in hybrids like [n times full formula (almost unchanged) -> tile formula only with changed tiling] things like the second picture can come up.


@ericr:  Great to hear that it finally works