POV Ray 3.7 code
//=======================================================
// Julia 3D set ($c = -0.7454294$) generated randomly
// (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 <00,0.0,0.0> }    // set black background

camera {							// set view point (camera) location
    location <-20, 20, -150>
    look_at  <-5, 0,  0>
}

light_source {						// set point light sources location
	< -3.0, 10, -5>
	rgb <1.000000, 1.000000, 1.000000> * 1.0     // set white light color and intensity
}

light_source {
	< 5.0, 10, -10>
	rgb <1.000000, 1.000000, 1.000000> * 2.0
}

#declare R = .1;     // set radius value
#declare L = 2;  // set square area side
#declare X = 0;  // set co-ordinate x initial value
#declare Y = 0;  // set co-ordinate y initial value
#declare Z = 0;  // set co-ordinate z initial value

#declare n = 200;    // set number of pixels per area side
#declare N = 30;   // set number of cycles
#declare Nr = 100;   // se number of sections
#declare Th = -35;
#declare Ph = 30;

#declare Cx  = -0.7454294;    // set parameter c values
#declare Cy = 0;

#declare P = array[2*n+1][2*n+1];    //  P matrix
#declare Q = array[2*n+1][2*n+1];    //  Q matrix

union{ #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;
      #declare P[p+n][q+n] = 0;
       #declare Q[p+n][q+n] = 0;

       #for (i,0,N)
       #declare XX = X*X - Y*Y  + Cx;
       #declare YY = 2*X*Y + Cy;
       #declare X = XX;
       #declare Y = YY;
       #if (X*X+Y*Y > R)
       	#if (X*X+Y*Y < R+.01)
        #declare P[p+n][q+n] = p+n;
       	#declare Q[p+n][q+n] = q;
#end  // end if
#end  // end if
#end  // end for i
#end  // end for q
#end  // end for p

#declare Rnd_1 = seed (1153);
#declare Rnd_2 = seed (553);
#declare Rnd_3 = seed (758);

//  replace Nr by Nr*clock for animation
#for(j,0,n*n*Nr)    // partial values n*n/64, n*n/16, n*n/4
#declare p = int(2*n*rand(Rnd_1));
#declare q = int(2*n*rand(Rnd_2));
#declare k = int(2*Nr*rand(Rnd_3));
 	 	sphere {
  		  < P[p][q], Q[p][q]*cos(6.28*k/Nr), Q[p][q]*sin(6.28*k/Nr) >, 1
  			 texture {
  			  pigment { color Col_Glass_Old }
      		 }
      		 finish { ambient rgb <0.3,0.1,0.1>
     			 diffuse .3
     			 reflection .3
     			 specular 1 }
   		}

#end  // end for j
rotate < 0, Th, Ph >
translate < -110, - 80, 0 >}