Pythagoras trees

The Pythagoras tree is a plane fractal constructed from squares.The construction of the Pythagoras tree begins with a square. Upon this square are constructed two squares, each scaled down by a linear factor of $\frac12\sqrt{2}$, such that the corners of the squares coincide pairwise. The same procedure is then applied recursively to the two smaller squares, ad infinitum

GeoGebra Applet: