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Steve's Fives Fractal

Steve's Fives Fractal
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2019-11-03 22:53
CalculusGeometric Construction
This example demonstrates a fractal pattern created by Maestro Steve Phelps, showcasing complex geometric constructions through iterative processes. Key math concepts include Fractal Geometry, Percentages, Upper and Lower Sum or Riemann Sum, Terms, Conic Sections, and Combinatorics. The construction utilizes GeoGebra commands like PolyLine, Segment, Rotate, and Polygon, involving objects A, B, C, D, E, and various others. Suitable for high school and above, it illustrates principles of fractal construction and geometric transformations.

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
  31. Polygon(F, G, 5) → poly1, l, m, p, q, r, H, I, J