CN[] rts = new CN[5];
color[] colA = new color[5];

void setup() { 
  size(400, 500); 
 BFont metaBold; 
metaBold = loadFont("Meta.vlw.gz"); 
textFont(metaBold, 40); 
textMode(ALIGN_LEFT); 
stroke(0,0,255);
text("Fractal", 150, 430);
textFont(metaBold, 30); 

text("Basin of attraction, 5th roots of unity", 20, 460);
textFont(metaBold, 24); 

textMode(ALIGN_LEFT); 

text("Click me to start/clear", 0, 495); 

for (int m =0; m<5; m++)
   rts[m] = new CN(cos(TWO_PI*m/5), sin(TWO_PI*m/5));
    
colA[0] = color(255,0,0);
colA[1] = color(0,255,0);
colA[2] = color(0,0,255);
colA[3] = color(255,255,0);
colA[4] = color(0,255,255);
  } 
 
CN z1 = new CN(3.0,5.0);
CN z2 = new CN(5.0,6.0);

boolean b1;
int kmax = 20;
float sc = 100.0;

void loop() { 
 doit(b1);
} 
 
void doit(boolean b2){
if (b2){
noStroke(); 
colorMode(RGB, 255); 
for(int i=0; i<400; i++)  
  for(int j=0; j<400; j++){  
      z1.r = (i-200)/sc;
      z1.i = (j-200)/sc;
      stroke(255, 255, 255);
      for (int k=0; k<kmax; k++)
      {for (int m=0; m<5; m++)
        {if (z1.subt(rts[m]).modsqr()<1e-12)
           {stroke(colA[m]);
            k = kmax;}
            else{z2 = newt5(z1);
         z1 = z2;}
        }}
       point(i,j);  
         } 
    } 
 else{
 noStroke();
 fill(80);
 rect(0,0,400,400);}
 }
   
 void mouseReleased() 
{ 
  b1 = !b1;
} 

CN newt5(CN z){
   return (z.multC(0.8).add(z.sqr().sqr().inv().multC(0.2)));
  } 
 
class CN { 
  float r, i; 
  CN (float re, float im) {  
    r = re; 
    i = im; 
  } 
  
  CN add(CN z) { 
    CN res = new CN(0.0,0.0);
    res.r = r+z.r;
    res.i = i+z.i; 
    return res;
  } 
  CN subt(CN z) { 
    CN res = new CN(0.0,0.0);
    res.r = r-z.r;
    res.i = i-z.i; 
    return res;
  } 
  CN mult(CN z) { 
    CN res = new CN(0.0,0.0);
    res.r = r*z.r - i*z.i;
    res.i = r*z.i+i*z.r; 
    return res;
  } 
  CN div(CN z) { 
    CN res = new CN(0.0,0.0);
    CN cnj = new CN(z.r, -z.i);
    float msqr = z.modsqr();
    if (msqr == 0) {msqr =1e-20;}
    res = this.mult(cnj);
    res.r /= msqr;
    res.i /= msqr; 
    return res;
  } 
  
  float modsqr(){
    return (r*r + i*i);
    }
    
  CN conj() { 
    CN res = new CN(0.0,0.0);
    res.r = r;
    res.i = -i; 
    return res;
  } 
 
  CN multC(float c) { 
    CN res = new CN(0.0,0.0);
    res.r = r*c;
    res.i = i*c; 
    return res;
  } 
  CN inv() { 
    CN res = new CN(0.0,0.0);
    float msqr = this.modsqr();
    if (msqr == 0) {msqr =1e-20;}
    res = this.conj();
    return res.multC(1/msqr);
  } 
  CN sqr() { 
    CN res = new CN(0.0,0.0);
     res.r =r*r-i*i;
     res.i = 2*r*i;
    return res;
  } 
  float mod(){
  return sqrt(r*r+i*i);      
  } 
  float arg(){
  return atan2(i, r);      
  } 
  CN powC(float c) { 
    CN res = new CN(0.0,0.0);
    float m = this.mod();
    float t = this.arg();
    res.r = pow(m,c)*cos(t*c);
    res.i = pow(m,c)*sin(t*c);
    return res;
  } 

}