This is the code that produced this Tumblr post: http://jtoprocessing.tumblr.com/post/42811336056/

NestedCircles2.java

PVector center;
float x1, y1, theta, r1, r2, x2, y2;
float bigTheta;

void setup() {
  size(500, 500);
  background(255);
  smooth();
  stroke(0,0,0,255);
  fill(0);
  
  center = new PVector(100, 0);
  r1 = 100;
  r2 = -100;
  theta = 1;
  bigTheta = 0;
}

void draw() {
  //this is for fading out
  fill(255,255,255,20);
  rect(-20,-20,width+20,height+20);
  fill(0);
  
  //move to the middle
  translate(width / 2, height / 2);
  
  //rotate the whole thing
  rotate(bigTheta);
  
  //calculate the next point for the two circles.
  //NOTE: there's an error in here, the y's are being
  //updated using center.x instead of center.y
  //i'm leaving it in so it matches what I posted.
  x1 = center.x + r1 * cos(theta);
  y1 = center.x + r1 * sin(theta);

  x2 = center.x + r2 * cos(theta);
  y2 = center.x + r2 * sin(theta);
  
  //draw the circles
  ellipse(x1, y1, 20, 20);
  ellipse(x2, y2, 20, 20);

  //update the angles.
  theta -= 2 * PI / 32;
  bigTheta += 2 * PI / 128;

  //this was used to capture frames for the animation.
  if(bigTheta >= 2 * PI && bigTheta <= 4 * PI) {
    //noLoop();
    //saveFrame("nestedAnimation######.png");
  }
}