Fractal Pythagoras Tree with Macros and Transformations

This GeoGebra example demonstrates how a Pythagoras tree fractal can be generated by repeatedly constructing right-triangle branches with consistent geometric relationships. It visualizes the self-similar growth produced by iterating a rule derived from the Pythagorean theorem. Key concepts include geometric interpretation of the Pythagorean relationship, triangle edge/angle dependencies, and parameter-controlled (and optionally stochastic-like) recursive construction that builds a fractal pattern. Construction relies on Polygon and Vertex/Point to define the initial triangle/polygon structure, Centroid to determine reference positioning, and Translate to move newly created components into place. Length and Angle are used to measure side sizes and compute the rotation angles for the left and right branches. Relevant construction parameters/controls include objects such as side, angL/angR, and sL/sR to govern branch geometry, while interactive controls (e.g., buttons and an iteration level n) drive the recursion depth and animation. Suitable for secondary mathematics enrichment and early university geometry/fractal visualization, especially for teaching how a theorem-based geometric rule yields an emergent fractal through iteration.