The Pythagoras tree is a fractal generated by squares. For each square, two new smaller squares are constructed and connected by their corners to the original square. The angle of the triangle formed can be varied.
The problem is finding the size of the bounding box (to a certain precision) for this fractal. The graph is essentially a rooted tree. Each node represents a square with a certain size and orientation. The tree is infinitely deep. For a certain precision, the problem is easily solved with a computer using branch and bound. I want to know if there are any estimates or hard limits on the size. Any bounds on the area of the fractal are also appreciated.
The isosceles right triangle case gives a nice bounding box of $6 \times 4$, which can be calculated easily with a geometric series. Other cases are more difficult for me (the maximal tree paths follow a zigzag pattern - for a while).