Pythagoras Tree
"The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle." - Read more
This fractal´s number of branches increases exponentially with the amount of iterations. The exact number of squares you can see here is \(\sum^n_{k=0}2^k\).
Besides changing the angle for this fractal, you can also switch to 'random angle' mode, which randomly assigns an individual angle to every square. Press key 'R' to switch modes.