Generative designs created using the equation for a Hypotrochoid curve.

Hypotrochoid

//Hypotrochoid(a,b,h,da,db)
//a is the radius of the fixed circle
//b is the radius of the circle rotating inside the fixed circle
//h is the distance between the drawing and the centre
//on the rotating circle

Hypotrochoid h;

void setup() {
  size(800, 800);
  h = new Hypotrochoid(random(50,150),random(10,30),random(20,40),random(0.001,0.005),random(0.004,0.012));
  background(50);
    pushMatrix();
  
  translate(width/2,height/2);
  
  for (int i = 0; i < 20000; i++){
    h.update();
    h.display();
  }
  //h.drawTail();
  popMatrix();
}

void draw() {
  rotate(0.01);

pause();
}

void save(){
  float a = random(0,1000);
  int b = int(a);
  save("images/generative_" + str(b) + ".jpg");
}

void keyPressed(){
  if (key == 's'){
    println("file saved");
    save();
  }
}

//a is the radius of the fixed circle
//b is the radius of the circle rotating inside the fixed circle
//h is the distance between the drawing and the centre
//on the rotating circle

//in a hypocloid, h = b;


class Hypotrochoid {

  PVector loc;
  float a, b, h;
  float theta, dtheta;
  float da, db;
  float prevX, prevY;
  color c;
  //ArrayList<PVector> history;

  Hypotrochoid(float _a, float _b, float _h, float _da, float _db) {
    loc = new PVector( ( (a-b)*cos(theta) + h*cos( ((a-b)/b)*theta) ), ( ((a-b)*sin(theta) - h*sin(((a-b)/b)*theta)) ) );
    a = _a;
    b = _b;
    h = _h;
    theta = 0;
    dtheta = 0.01;
    da += _da;
    db += _da;
    prevX = 0;
    prevY = 0;
    c = color(random(0,255),random(0,255),random(0,255),random(0,255));
    // history = new ArrayList<PVector>();
  }

  void display() {
    stroke(c);
    strokeWeight(1);
    // history.add(loc.get());
    line(prevX, prevY, loc.x, loc.y);
  }

  void update() {
    prevX = loc.x;
    prevY = loc.y;
    loc.x = (a-b)*cos(theta) + h*cos( ((a-b)/b)*theta);
    loc.y = (a-b)*sin(theta) - h*sin(((a-b)/b)*theta);
    theta += dtheta;
    h += 0.01;
    // println ("prevX: " + prevX + " " + "prevY: " + prevY);
    // println ("loc.x: " + loc.x + " " + "loc.y: " + loc.y);
  }

  // void drawTail() {
  //   beginShape();
  //   noFill();
  //   stroke(0);
  //   for (PVector v : history) {
  //     vertex(v.x, v.y);
  //   }
  //   endShape();
  // }
}