Dynamic Pythagorean Tree

CindyJS geometry fractals recursion

The Pythagorean tree is a fractal constructed from squares. Starting with a square, two smaller squares are attached to one side such that they form a right triangle with the original square’s edge as hypotenuse.

The construction uses the Pythagorean theorem: if the original square has side length $c$, and the two new squares have side lengths $a$ and $b$, then:

\[a^2 + b^2 = c^2\]

This process is repeated recursively. In this interactive version, you can drag the point on the semicircle to change the angle of the triangle, affecting the ratio between $a$ and $b$.

Use the slider to control the recursion depth.