float maxImaginary = 2;
void setup () {
  colorMode(HSB, 360, 100, 100);
  size(8000, 8000);
  fill(0);
  rect(0,0,width,height);
  mandelbrot();
}

void draw () {
}

void mandelbrot () {
  int maxIterations = 500;
  for (int x=0; x!=height/80; ++x) {
    for (int y=0; y!=width/80; ++y) {
      float real = map(x, 0, width/80, minReal, maxReal);
      float realConst = real;
      float imaginary = map(y, 0, height/80, minImaginary, maxImaginary);
      float imaginaryConst = imaginary;
      int iterations = 0;
            int x1 = int(x*80+map(real, 0, 4, 0, 80));
      int y1 = int(y*80+map(imaginary, 0, 4, 0, 80));
      int x2 = int(x*80+map(real, 0, 4, 0, 80));
      int y2 = int(y*80+map(imaginary, 0, 4, 0, 80));
      while ((real*real+imaginary*imaginary) < 4 && (iterations < maxIterations)) {
        float realTemp = real;
        real = (real*real) - (imaginary*imaginary) + realConst;
        imaginary = (2*realTemp*imaginary) + imaginaryConst;
        stroke(color(map(iterations, 0, maxIterations, 0, 360), 100, 100));
        int x3 = int(x*80+map(real, 0, 4, 0, 80));
        int y3 = int(y*80+map(imaginary, 0, 4, 0, 80));
        int x4 = int(x*80+map(nextReal(real, realConst, imaginary, imaginaryConst), 0, 4, 0, 80));
        int y4 = int(y*80+map(nextImaginary(real, realConst, imaginary, imaginaryConst), 0, 4, 0, 80));
        noFill();
        curve(x1,y1,x2,y2,x3,y3,x4,y4);
        //arc(float(x2), float(y2), float(x3), float(y3), angle(x2, y2, x3, y3), angle(x3,y3,x4,y4));
        //line(x2,y2,x3,y3);
        x1 = x2;
        y1 = y2;
        x2 = x3;
        y2 = y3;

        //set2(int(x*80+map(real,0,4,0,80)),int(y*80+map(imaginary, 0,4,0,80)), color(map(iterations, 0, maxIterations, 0, 360), 100, 100), 1);
        ++iterations;
      }
    }
  }
}
float nextReal (float real, float realConst, float imaginary, float imaginaryConst) {
  float realTemp = real;
  real = (real*real) - (imaginary*imaginary) + realConst;
  imaginary = (2*realTemp*imaginary) + imaginaryConst;
  return real;
}
float nextImaginary (float real, float realConst, float imaginary, float imaginaryConst) {
  float realTemp = real;
  real = (real*real) - (imaginary*imaginary) + realConst;
  imaginary = (2*realTemp*imaginary) + imaginaryConst;
  return imaginary;
}
float angle(int cx, int cy, int ex, int ey) {
  int dy = ey - cy;
  int dx = ex - cx;
  float theta = atan2(dy, dx); // range (-PI, PI]
  return theta + PI;
}

void set2 (int x, int y, color Color, int scale) {
  for (int i=0; i!=scale; ++i) {
    for (int i2=0; i2!=scale; ++i2) {
      set(x*scale+i, y*scale+i2, Color);
    };
  };
}