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//There are three types of formulas:
//1) which uses analytic distance estimation: trig_DE, trig_optim (default)
//2) IFS formulas and Mandelbox: menger_sponge, tglad, smoothMandelbox, kaleidoscopic, mandelboxVaryScale4D
//3) rest of formulas, which uses "delta DE" algorithm for distance estimation.

Hi Buddhi, following is the basic code I now use for quarternions, set up with 7 parameters to tweek. (I sometimes also add in box fold and mandelbox  3D rotation and fabs.)


Code:

// This file has all commands which are executed once before iteration loop.
// It can be used to initialize all variables and do some preliminary calculations
// all available variables are defined in mandelbulber_cl_data.h

// quart Jc4 addition like Julia, c4 = c4 * point


   float4 newz = 0.0f;
   float4 zp = (float4){1.0f, 0.0f, 0.0f, 0.0f};
   float4 z4 = (float4){z.x, z.y, z.z, 0.0f};
   //float4 c4 = (float4){c.x, c.y, c.z, 0.0f};
   
//contant addition   
float4 Jc4  = (float4){consts->fractal.custom[3], consts->fractal.custom[4], consts->fractal.custom[5], consts->fractal.custom[6]};   

// constant point multiplier
float4 c4  = (float4){consts->fractal.custom[9] * point.x, consts->fractal.custom[10] * point.y, consts->fractal.custom[11] * point.z, 0.0f};   






Code:

// QU+c4+Jc4

// This file has all commands which are executed inside iteration loop
//    for(i = 0; i < N; i++)
// example is based on Quarternion formula
// z is a main 3-dimentional iterated vector
// c4 and Jc4 are constant variables like in Mandelbrot set: z(n+1) = z(n)^2 + c
// r is a length of z vector

// basic quarternion

   zp = 2.0 * quaternionMul(z4, zp);
         newz = quaternionSqr(z4);
         z4 = newz + c4 + Jc4;
         r = length(z4);
            
         if (r < colourMin) colourMin = r;
         if(r>40.0f || any(isinf(z4)))

         {
         float rp = length(zp);
         dist = 0.5f * r * native_log(r) / rp;
         out.colourIndex = colourMin * 5000.0f;
               
         break;
            }






I have been experimenting with adding a C constant (which can be a Julia coordinate) and adding also a  point multiplier constant .

i.e   z = z * m + Jc3 + c3     for mandelbox,   z+=( Jc3 + c3)    for mandelbulb

This approach gives more parameters to tweek, and you can morph/animate between normal and Julia.

So maybe consider this approach for formulas .


As always, thanks so much for this software, I have fun and have also learnt a bit about programming.