# Problem 395: Pythagorean tree
The Pythagorean tree is a fractal generated by the following procedure:
Start with a unit square. Then, calling one of the sides its base (in
the animation, the bottom side is the base): Attach a right triangle to
the side opposite the base, with the hypotenuse coinciding with that
side and with the sides in a 3-4-5 ratio. Note that the smaller side of
the triangle must be on the 'right' side with respect to the base (see
animation). Attach a square to each leg of the right triangle, with one
of its sides coinciding with that leg. Repeat this procedure for both
squares, considering as their bases the sides touching the triangle. The
resulting figure, after an infinite number of iterations, is the
Pythagorean tree. It can be shown that there exists at least one
rectangle, whose sides are parallel to the largest square of the
Pythagorean tree, which encloses the Pythagorean tree completely. Find
the smallest area possible for such a bounding rectangle, and give your
answer rounded to 10 decimal places.