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Fractal Curve 7

Fractal Curve 7
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2019-11-02 18:30
FunctionProbability & Statistics
This example demonstrates a complex fractal curve, illustrating self-similarity through iterative geometric constructions. Core math concepts include fractal geometry, probability & statistics, frequency distribution, polynomial functions, piecewise functions, and transformation theory. Construction highlights involve GeoGebra commands like PolyLine, Segment, and Rotate, utilizing multiple objects such as A, B, C, D, E, f, g, h, i, j, k, and their transformed versions. Suitable for high school and advanced learners exploring fractal patterns and mathematical applications.

GeoGebra Commands & Parameters

  1. PolyLine(A, B, C, D, E) → f
  2. Segment(A, B) → g
  3. Segment(B, C) → h
  4. Segment(C, D) → i
  5. Segment(D, E) → j
  6. Segment(A, E) → k
  7. Rotate(PolyLine[Dilate[A, g / k, A], Dilate[B, g / k, A], Dilate[C, g / k, A], Dilate[D, g / k, A], Dilate[E, g / k, A]], Angle[k, g], A) → A1
  8. Rotate(Translate[PolyLine[Dilate[A, h / k, A], Dilate[B, h / k, A], Dilate[C, h / k, A], Dilate[D, h / k, A], Dilate[E, h / k, A]], B - A], Angle[k, h], B) → B1
  9. Rotate(Translate[PolyLine[Dilate[A, i / k, A], Dilate[B, i / k, A], Dilate[C, i / k, A], Dilate[D, i / k, A], Dilate[E, i / k, A]], C - A], Angle[k, i], C) → C1
  10. Rotate(Translate[PolyLine[Dilate[A, j / k, A], Dilate[B, j / k, A], Dilate[C, j / k, A], Dilate[D, j / k, A], Dilate[E, j / k, A]], D - A], Angle[k, j], D) → D1
  11. Rotate(Dilate[{A1, B1, C1, D1}, g / k, A], Angle[k, g], A) → A2
  12. Rotate(Translate[Dilate[{A1, B1, C1, D1}, h / k, A], B - A], Angle[k, h], B) → B2
  13. Rotate(Translate[Dilate[{A1, B1, C1, D1}, i / k, A], C - A], Angle[k, i], C) → C2
  14. Rotate(Translate[Dilate[{A1, B1, C1, D1}, j / k, A], D - A], Angle[k, j], D) → D2
  15. Rotate(Dilate[{A2, B2, C2, D2}, g / k, A], Angle[k, g], A) → A3
  16. Rotate(Translate[Dilate[{A2, B2, C2, D2}, h / k, A], B - A], Angle[k, h], B) → B3
  17. Rotate(Translate[Dilate[{A2, B2, C2, D2}, i / k, A], C - A], Angle[k, i], C) → C3
  18. Rotate(Translate[Dilate[{A2, B2, C2, D2}, j / k, A], D - A], Angle[k, j], D) → D3
  19. Rotate(Dilate[{A3, B3, C3, D3}, g / k, A], Angle[k, g], A) → A4
  20. Rotate(Translate[Dilate[{A3, B3, C3, D3}, h / k, A], B - A], Angle[k, h], B) → B4
  21. Rotate(Translate[Dilate[{A3, B3, C3, D3}, i / k, A], C - A], Angle[k, i], C) → C4
  22. Rotate(Translate[Dilate[{A3, B3, C3, D3}, j / k, A], D - A], Angle[k, j], D) → D4
  23. Rotate(Dilate[{A4, B4, C4, D4}, g / k, A], Angle[k, g], A) → A5
  24. Rotate(Translate[Dilate[{A4, B4, C4, D4}, h / k, A], B - A], Angle[k, h], B) → B5
  25. Rotate(Translate[Dilate[{A4, B4, C4, D4}, i / k, A], C - A], Angle[k, i], C) → C5
  26. Rotate(Translate[Dilate[{A4, B4, C4, D4}, j / k, A], D - A], Angle[k, j], D) → D5
  27. Rotate(Dilate[{A5, B5, C5, D5}, g / k, A], Angle[k, g], A) → A6
  28. Rotate(Translate[Dilate[{A5, B5, C5, D5}, h / k, A], B - A], Angle[k, h], B) → B6
  29. Rotate(Translate[Dilate[{A5, B5, C5, D5}, i / k, A], C - A], Angle[k, i], C) → C6
  30. Rotate(Translate[Dilate[{A5, B5, C5, D5}, j / k, A], D - A], Angle[k, j], D) → D6