Building a Fractal Tree with Scaling and Segments (GeoGebra Step 1)

This example demonstrates how to create a fractal tree in GeoGebra by repeatedly branching from a main trunk segment, generating smaller sub-branches at endpoints to form a self-similar tree structure. The key mathematical ideas include geometric similarity expressed via ratios, the self-similarity principle behind fractals, and constructing new branch geometry from existing points/segments. In the construction, Segment is used to create the trunk and branch line segments, Point defines the critical endpoints and control locations, and Dilate applies a scaling (dilation) transformation about a center to place the new branches at the correct size. The listed objects such as Setup and points A–E serve as control geometry, while f and ListOutPut help store and output the generated collections of segments, matching a step-by-step (recursive) branching workflow. Suitable for secondary geometry/transformations lessons and introductory exploration of fractals and recursive construction.