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Spline Fractal Curve

Spline Fractal Curve
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2019-10-31 17:41
FunctionGeometric Construction
This example demonstrates the construction of a fractal curve using spline interpolation. It involves core mathematical concepts such as fractal geometry, spline functions, and geometric transformations. Key GeoGebra commands and objects used include Intersect, Spline, Rotate, and PolyLine, along with points A, B, C, D, E, and parameters n, f. It is suitable for high school and above students to explore the generation process of fractal curves and the application of spline functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Spline({A, D, E, B}, 3) → A1
  3. Rotate(A1, ((-π)) / 2, B) → B1
  4. Rotate(Dilate[{A1, B1}, 1 / sqrt(2), A], ((-π)) / 4, A) → A2
  5. Rotate(A2, ((-π)) / 2, B) → B2
  6. Rotate(Dilate[{A2, B2}, 1 / sqrt(2), A], ((-π)) / 4, A) → A3
  7. Rotate(A3, ((-π)) / 2, B) → B3
  8. Rotate(Dilate[{A3, B3}, 1 / sqrt(2), A], ((-π)) / 4, A) → A4
  9. Rotate(A4, ((-π)) / 2, B) → B4
  10. PolyLine(A, B, C) → f