feigenbaum.pde

// F E  I   G    E     N      B       A        U         M
// G R  O   W    T     H
float f = 3; // we have to start with some kind of seed, and ~3.4 is where things get interesting
float x = -2; // start it a little off screen
float y = 0.85; // again, a seed value is needed to actually see anything

void setup() {
  size(800,800);
  pixelDensity(displayDensity());
  smooth();
  background(255);
}

void draw() {
  for(int i = 0; i < 10; i++) { // draw 10 points at once so that it doesn't take forever
    pushMatrix();
    translate(0, height*0.1);
    stroke(#E05362);
    
    // the formula is expressed as:
    // b = f * a * (1-a)
    // where 'b' is the next generation, 'a' is the current generation, and 'f' is the growth rate/fertility
    y = f * y * (1-y);
    point(x, y*(height*0.7));
    f += 0.000009;
    x+=0.0075;
    popMatrix();
    
    if(Double.isInfinite(y)) { // end the loop if we reach infinity
      noLoop();
      println("infinity reached");
      break;
    }
    
    if(x == width) {
      noLoop();
      break;
    }
  }
}

void mousePressed() {
  saveFrame("export-####.png");
}