Pythagoras Tree Generator

The Pythagoras tree is a fractal constructed from squares, named after the Pythagorean theorem which it visually demonstrates at every branching point. It was first created by the Dutch mathematics teacher Albert E. Bosman in 1942.

• Construction: Start with a square (the trunk). On its top edge, construct a right triangle. Then attach smaller squares to the two non-hypotenuse sides and repeat.
• Pythagorean theorem: At each branch, the area of the parent square equals the sum of the areas of the two child squares (a² + b² = c²).
• Symmetry: When the branch angle is 45°, the tree is perfectly symmetric. Other angles produce asymmetric, leaning trees.
• Binary tree connection: The structure mirrors a binary tree in computer science, with each square branching into exactly two children.
• Bounding area: The total area of the tree is bounded and converges, even though the number of squares grows exponentially.