Hilbert Curve: Fractal Construction of a Space-Filling Curve

① This example demonstrates the Hilbert curve, a well-known space-filling curve that recursively subdivides the plane to eventually pass through every point. ② Core mathematical concepts include fractal geometry, recursion, limits, space-filling curves, and the property of being continuous but nowhere differentiable. ③ Construction highlights: using GeoGebra commands Join and Translate, along with multiple point objects (LP0 to LP6) and segment objects (PL1 to PL6), controlled by checkboxes (ChkPL1 to ChkPL6) to display different iteration levels, enabling step-by-step generation of the curve. ④ Suitable for high school to university students to explore fractal geometry, recursive algorithms, and dynamic geometry software, and can serve as a teaching or demonstration resource.