Explore the fascinating world of mathematical fractals with our interactive Pythagoras Tree generator. Customize every aspect of your fractal tree and watch as beautiful patterns emerge from simple mathematical rules.
The Pythagoras Tree is a plane fractal constructed from squares. It's named after the ancient Greek mathematician Pythagoras because each triple of touching squares includes a right triangle that relates to his famous theorem.
The construction begins with a square. Upon this square are constructed two squares, each scaled down by a factor of √2/2, which form a right triangle with the original square. This process is then repeated recursively for each of the new squares.
The Pythagoras Tree beautifully demonstrates self-similarity, a key property of fractals. Despite its simple construction rules, it can produce incredibly complex and beautiful patterns. The fractal dimension of the Pythagoras Tree varies depending on the angle used in its construction.
Our generator allows you to adjust several parameters: