A beautiful fractal tree built from the Pythagorean theorem. At each branch, two smaller squares sprout at an angle, forming a self-similar tree that grows exponentially with each level of recursion.
Each generation adds two squares whose sides satisfy a² + b² = c² (the Pythagorean theorem). The total area of all squares at any level equals the initial square — a visual proof!
Adjust branch angle, recursion depth and lean ratio. Toggle animation to watch the tree grow level by level.
The Pythagoras tree was first described by Albert Bosman in 1942. With symmetric 45° branching, at depth 10 there are 1,024 leaf squares — and they perfectly tile without overlap up to depth 7.