Fractal Tree with Sliders: Iterative Branching via Geometric Transforms

This example demonstrates how to generate a fractal tree by controlling parameters with sliders and using recursive/iterative construction. By changing angle and scaling controls, learners can immediately see how the branching structure evolves. The key mathematical ideas include fractal geometry, iteration-based (recursive) generation, and geometric transformations—especially similarity scaling for branch length and direction—often parameterized with trigonometric (tangent-related) angle control. Construction-wise, the model uses GeoGebra commands Segment to create the initial and subsequent branches, Dilate to scale segments to reflect size reduction along the recursion, and IterationList to drive the iterative generation process from the initial segment. Slider-driven parameters (e.g., α, β, s1, s2) update objects such as A, B, C, D, the function f, and the displayed iteration outputs (ListOutPut / ListAll), enabling real-time exploration. Suitable for upper secondary to introductory college settings for teaching fractals, dynamic geometry, and algorithmic thinking.