Pythagoras tree (fractal)

Invented by the Dutch mathematics teacher Albert E. Bosman in 1942,[1] it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem.

However, some of the squares overlap starting at the order 5 iteration, and the tree actually has a finite area because it fits inside a 6×4 box.

[2] It can be shown easily that the area A of the Pythagoras tree must be in the range 5 < A < 18, which can be narrowed down further with extra effort.

An interesting set of variations can be constructed by maintaining an isosceles triangle but changing the base angle (90 degrees for the standard Pythagoras tree).

The general pattern produced is the rhombitrihexagonal tiling, an array of hexagons bordered by the constructing squares.