Fractal Tree via Iteration: Change Color and Thickness in GeoGebra

This example demonstrates how to construct a fractal tree using iterative geometry and how to emphasize its branching depth by changing color and line thickness across iterations. The key mathematical ideas include fractal geometry, iterative (recursive) construction, self-similarity, and geometric transformation—especially scaling (dilation). Construction in GeoGebra uses Segment to build the initial trunk, Point to define key endpoints, Dilate to create scaled child branches, and Iteration to repeatedly apply the transformation layer by layer to generate the fractal structure. The workflow is organized with objects such as Setup, a control button (button1), list outputs (ListOutPut), per-step/level references (L1–L9), and parameters like n and Ln that drive both the geometry generation and the visual styling. Suitable for upper secondary students through introductory university coursework, particularly for math visualization, modeling, and geometry construction lessons.