//A complete binary tree has pow(2,k) nodes at every depth k < n and between pow(2,n) and pow(2,n+1)-1 nodes altogether
BTree btree;
void setup(){
  size(400, 400);
  btree = new BTree(5, height / 2, 8);
  smooth();
  ellipseMode(CENTER);
}
void draw(){
  background(255);
  btree.draw();
}
class BTree{
  int depth;
  Vec2 [] node;
  BTree(float x, float y, int depth){
    this.depth = depth;
    node = new Vec2[(int)pow(2,depth + 1)];
    node[1] = new Vec2(x, y);
    for(int i = 1; i < node.length - (int)pow(2, depth); i++){
      float xn = node[i].x + cos(random(1.0)) * (50.0);
      float yn = node[i].y + sin(random(1.0)) * (50.0);
      node[2 * i] = new Vec2(xn, yn);
      xn = node[i].x + cos(-random(1.0)) * (50.0);
      yn = node[i].y + sin(-random(1.0)) * (50.0);
      node[1 + 2 * i] = new Vec2(xn, yn);
    }
  }
  void draw(){
    for(int i = 1; i < node.length - (int)pow(2, depth); i++){
      line(node[i].x, node[i].y, node[2 * i].x, node[2 * i].y);
      line(node[i].x, node[i].y, node[1 + 2 * i].x, node[1 + 2 * i].y);
    }
    for(int i = 1; i < node.length; i++){
      ellipse(node[i].x, node[i].y, 10, 10);
      node[i].dither();
    }
  }
}

class Vec2{
  float x,y;
  Vec2(float x, float y){
    this.x = x;
    this.y = y;
  }
  void dither(){
    x += random(-1.0, 1.0);
    y += random(-1.0, 1.0);
  }
}