// The Mandelbrot Set 
// Daniel Shiffman <http://www.shiffman.net> 

// Establish a range of values on the complex plane 
double xmin = -2.5; double ymin = -2; double wh = 4; 
// A different range will allow us to "zoom" in or out on the fractal 
// double xmin = -1.5; double ymin = -.1; double wh = 0.15; 
 
void setup() { 
  size(200,200,P2D); 
} 
 
void draw() { 
 
  loadPixels(); 
  
  // Maximum number of iterations for each point on the complex plane 
  int maxiterations = 200; 
 
  // x goes from xmin to xmax 
  double xmax = xmin + wh; 
  // y goes from ymin to ymax 
  double ymax = ymin + wh; 
  
  // Calculate amount we increment x,y for each pixel 
  double dx = (xmax - xmin) / (width); 
  double dy = (ymax - ymin) / (height); 
 
  // Start y 
  double y = ymin; 
  for(int j = 0; j < height; j++) { 
    // Start x 
    double x = xmin; 
    for(int i = 0;  i < width; i++) { 
      
      // Now we test, as we iterate z = z^2 + cm does z tend towards infinity? 
      double a = x; 
      double b = y; 
      int n = 0; 
      while (n < maxiterations) { 
        double aa = a * a; 
        double bb = b * b; 
        double twoab = 2.0 * a * b; 
        a = aa - bb + x; 
        b = twoab + y; 
        // Infinty in our finite world is simple, let's just consider it 16 
        if(aa + bb > 16.0f) { 
          break;  // Bail 
        } 
        n++; 
      } 
      
      // We color each pixel based on how long it takes to get to infinity 
      // If we never got there, let's pick the color black 
      if (n == maxiterations) pixels[i+j*width] = 0; 
      else pixels[i+j*width] = color(n*16 % 255);  // Gosh, we could make fancy colors here if we wanted 
      x += dx; 
    } 
    y += dy; 
  } 
  updatePixels(); 
  noLoop(); 
}