Spiky Feathers: Iterated Parametric Fractal Curves

This example demonstrates how a “spiky feathers” pattern emerges on the plane by iterating and sampling a parametric curve, producing a fractal-like texture from discrete points. Key concepts include parametric curves, logic-based conditional generation, fractal geometry via iterative structure, dilation (scale transformation), and the role of scatter plots and arithmetic mean in aggregating/controlling the pattern. The construction uses GeoGebra commands and objects reflected in the construct summary: CurveCartesian to create the Cartesian parametric curve; Sequence to drive iteration; power together with functions f1, f2, f, and g to define the functional forms (e.g., power-law behavior); max to limit iteration; b, move, l1, l2, pointsToSkip to control point sampling/stepping and which points to render; and ShowPoints, ShowSegments, and ShowCurve to display the evolving curve and its spike-like segments. Export_1, Export_2, and text1 support exporting and labeling the result. Designed for students and educators exploring function graphs, sequences, and iterative fractal construction through dynamic geometry visualization.