POV Ray 3.7 code
//=====================================
// Newton's method 3D set as a whole
// (POV-Ray cylindrical symmetry)
//=====================================

#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 <0.0,0.0,0.0> }   // set black background

 camera {							// set view point (camera) location
    location <-20, 20, -400>
    look_at  <-35, 1,  0>
    angle 100
  }

  light_source  						// set area light sources location
{
  0*x // light's position (translated below)
  color Silver  // light's color
  // <widthVector> <heightVector> nLightsWide mLightsHigh
  area_light
  <8, 0, 0> <0, 0, 8> // lights spread out across this distance (x * z)
  4, 4                // total number of lights in grid (4x*4z = 16 lights)
  adaptive 0          // 0,1,2,3...
  jitter              // adds random softening of light
  translate <40, 80, -40>   // <x y z> position of light
}

#declare R = 0.9;     // set radius value
#declare L = 1.10;  // set square area side
#declare X = 0.01;  // set co-ordinate x initial value
#declare Y = 0.01;  // set co-ordinate y initial value

#declare n = 200;    // set number of pixels per area side
#declare N = 10;   // set number of cycles
 #declare Nr = 100;  // alternative  Nr = 25;   // set number of sections
 #declare Th = -45;
  #declare Ph = 30;

  #for (p, -n, n, 1)
    #declare IncX = p*L/n;
    #for (q, -n, n, 1)
    #declare IncY = q*L/n;
    #declare X = IncX;
    #declare Y = IncY;
       #for (i,1,N)
       #declare XX = 3*X/4 - X*(X*X - 3*Y*Y)/(X*X + Y*Y)/(X*X + Y*Y)/
       (X*X + Y*Y)/4;
       #declare YY = 3*Y/4 - Y*(Y*Y - 3*X*X)/(X*X + Y*Y)/(X*X + Y*Y)/
       (X*X + Y*Y)/4;
       #declare X = XX;
       #declare Y = YY;
  	#if (X*X+Y*Y > R)
	#if (X*X+Y*Y < R+.05)
	#for (k,0,Nr)   //  replace Nr by Nr*clock for animation
 		 sphere {
  	  	< p, q*cos(3.14*k/Nr), q*sin(3.14*k/Nr) >, 1
  	 	hollow
  		radiosity { importance 1.0 }
   		 texture {
    		  pigment { color Col_Glass_Yellow
    		}
      	     		  }
      	 finish { ambient rgb <0.3,0.1,0.1>
		 diffuse .3
     		 reflection .3
     		 specular 1
     		}
   	}

#end  // end if
#end  // end if
#end  // end for k
#end  // end for i
#end  // end for q
#end  // end for p
rotate < 0, Th, Ph >
translate <50,20,0> }