zeichneBaum(A,B,tiefe):
  berechne die beiden eckpunkte C,D des quadrats ABCD
  berechne zufälligen winkel a
  berechne eckpunkt E des dreiecks mit winkel a
  zeichne quadrat und dreieck
  wenn tiefe < 0, fertig
  zeichneBaum(C,E, tiefe-1)
  zeichneBaum(C,B, tiefe-1)

import java.util.Random;
import java.lang.Math;
import java.util.ArrayList;
import java.util.LinkedList;
 
public class PythagoreanTree {
 
    private static Random rand = new Random();
 
    static class Point{
        double x,y;
 
        Point(double x, double y){
            this.x = x;
            this.y = y;
        }
 
        @Override
        public String toString(){
            return String.format("(%.3f,%.3f)", x, y);
        }
    }
 
    static class Rectangle{
 
        Point A,B,C,D,E;
        int depth;
 
        Rectangle(Point A, Point B, int depth){
            this.depth = depth;
            this.A = A;
            this.B = B;
            this.C = null; // TODO
            this.D = null; // TODO
            double alpha = Math.PI/6 * (1+rand.nextDouble());
            this.E = null; // TODO
        }
 
        Rectangle getLeftChild(){
            return new Rectangle(D,E,depth+1);
        }
 
        Rectangle getRightChild(){
            return new Rectangle(E,C,depth+1);
        }
 
        @Override
        public String toString(){
            StringBuilder str = new StringBuilder();
            str.append("[")
            .append(A + ", ")
            .append(B + ", ")
            .append(C + ", ")
            .append(D + "]");
            return str.toString();
        }
 
        String toTikz(){
            StringBuilder str = new StringBuilder();
            str.append(String.format("\\draw[fill=black!%.0f] ",300.0/(2.0+depth)))
            .append(A + " -- ")
            .append(B + " -- ")
            .append(C + " -- ")
            .append(D + " -- cycle;\n");
            return str.toString();
        }
    }
 
    static ArrayList<Rectangle> pythagoreanTreeList(int depth){
        ArrayList<Rectangle> tree = new ArrayList<>();
        LinkedList<Rectangle> stack = new LinkedList<>();
        Rectangle rect = new Rectangle(new Point(0,0),new Point(1,0),1);
        stack.add(rect);
        while (!stack.isEmpty()){
            rect = stack.pop();
            tree.add(rect);
            if (rect.depth < depth){
                stack.add(rect.getLeftChild());
                stack.add(rect.getRightChild());
            }
        }
        return tree;
    }
 
    static String treeToTikz(ArrayList<Rectangle> tree){
        StringBuilder str = new StringBuilder();
        str.append("\\begin{tikzpicture}\n");
        for (Rectangle rect : tree){
            str.append(rect.toTikz());
        }
        str.append("\\end{tikzpicture}\n");
        return str.toString();        
    }
 
    public static void main(String args[]) {
        System.out.print(treeToTikz(pythagoreanTreeList(7)));
    }
}