int windowsize=300;
int n;
float arcsize;

void setup(){
  size(windowsize, windowsize);
  background(255);
  PFont fontA = loadFont("CourierNew36.vlw");
  textFont(fontA, 14);
  textAlign(CENTER);
  smooth();
  noStroke();
  int margin = 6;
  translate(margin*1.5, margin*2);
}




void draw()
{   
    fill(255);
    rect(0,0, windowsize,windowsize);    
    n=mouseY*48/windowsize+2;
    float arcsize=0.8*windowsize;
    fill(255);
    ellipse(windowsize/2, windowsize/2, 0.92*arcsize, 0.92*arcsize);        
    stroke(0,0,0);
    strokeWeight(1);
    line(windowsize/2, windowsize/2, windowsize, windowsize/2);
    drawCircle(n, 0.92*arcsize, 255);
    fill(255);
    ellipse(windowsize/2,windowsize/2, 0.7*arcsize, 0.7*arcsize);
    fill(0);
    text("U("+n+")",windowsize/2,windowsize/2);  
}




void drawCircle(int n, float arcsize, float opacity)
{   
  int groupOrder= order(n);   
  for(int i=1; i<n+1; i++)
  {  
    if (gcd(i,n)==1)
    {
      primitive(i, n, groupOrder, opacity);
    }
    // if the slice does not represent an element of U(n) color it white
    else
    { 
       fill(255);
    } 
    arc(windowsize/2,windowsize/2, arcsize, arcsize, -PI/n-2*(i)*PI/n, -PI/n-2*(i-1)*PI/n);
  }    
}




public static int gcd(int n, int d)
   {
   if ( d == 0 )
      {
      return 1;
      }
   int r = n % d;
   return( r == 0 ) ? d : gcd( d , r );
   }




int order(int n)
{
  // calculate the order ofU(n)
  int order=0;
  for(int i=1;i<n+1; i++)
  { 
    if (gcd(i,n)==1)
    order=order+1; 
  }
  return order;
}  




void primitive(int element, int group, int groupOrder, float opacity)
{
  int power = element;
  int counter=1;
  while(power != 1)
    {  
      power = (element * power) % group; 
      counter=counter+1;
    }
  // color the element a shade of gray depending upon the order  
  fill(235-235*counter/groupOrder, 235-235*counter/groupOrder, 235-235*counter/groupOrder, opacity);
  // if the element is primitive, make it red
  if(counter==(groupOrder))
  {
    fill(150,0,0,opacity);
  }  
}