POV Ray 3.7 code
//=========================================================
// Quaternion 3D Mand-Mand-Mand set generated sequentially
// (POV-Ray point by point generation)
//=========================================================

#include "colors.inc"    // Standard Color definitions
#include "glass.inc"    // Glass pigment effect
#include "metals.inc"   // Metal pigment effect

global_settings {assumed_gamma 1.0}   // set display gamma
background { color rgb <00,0.0,0.0> }      // set black background

 camera {							// set view point (camera) location
    location <-20, 20, -300>
    look_at  <-5, 0,  0>
  }

   light_source {						// set point light sources location
	< -20, 20, -10>
	rgb <1.000000, 1.000000, 1.000000> * 2.0
 }

 light_source {
	< 20, 20, -10>
	rgb <1.000000, 1.000000, 1.000000> * 3.0
 }

#declare R =  .1;   // set radius value
#declare L = 2;     // set square area side
#declare n = 200;     // set number of pixels per area side
#declare ns = 200;  // partial values ns = 50, 75, 100
#declare st = 1;
#declare N = 40;  // N = 40
#declare Th = -45;
#declare Ph = 30;

//  replace  ns by ns*clock for animation
 union{ #for (p, -ns, ns, st)
     #declare IncX = p*L/n;   // Mand1 X increment

    #for (q, -ns, ns, st)
       #declare IncY = q*L/n;    // Mand1 Y1 increment

    #for (r, -ns, ns, st) // alternative #for (r, 0, ns, st) [open sets]
      #declare IncZ = r*L/n;  // Mand2 Y2 increment

      #declare X = 0;   // start MandX
      #declare Y = 0;   // start MandY
      #declare Z = 0;   // start MandZ

     #for (k,1,N)
       #declare XX = X*X - Y*Y - Z*Z + IncX;  // cycle MandX
       #declare YY = 2*X*Y + IncY;  // cycle MandY
       #declare ZZ = 2*X*Z + IncZ;   // cycle MandZ
       #declare X = XX;
       #declare Y = YY;
       #declare Z = ZZ;
       #declare W = X*X +Y*Y + Z*Z;

   #if ( W > R)    		  // escape if
     	#if (W < R + 0.0015)     // escape if
 	 	sphere {
  		  < p, q, r >, 1   //  adding 3d axis
     			 texture {
    			  pigment { color Col_Glass_Yellow }
      		 }
      		 finish { ambient rgb <0.3,0.1,0.1>
     			  diffuse .3
     			 reflection .3
     			 specular 1 }   // plot sphere
   		}
#end  // end if
#end  // end if
#end  // end for k
#end  // end for q
#end  // end for p
#end  // end for r
translate < 30, 15, 0 >
rotate < 0, Th, Ph > }