Pythagoras Tree (Trivia # 2)

The Pythagoras tree is a plane fractal constructed from squares. It is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem. From the left each image is an iteration of this function growing exponentially more complex. The top is a 45,45,90 triangle and the bottom is a 30, 60, 90 triangle resulting in a lopsided tree.

Pythagoras tree

If we add a third dimension by making the squares into cubes and exploring the geometry in 3 dimensional space we get a Dragon Curve. The cubes were rendered 95% transparent so you can see the geometry inside of it.

Pythagoras Dragon Curve