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Fractal Spirograph by Juan Carlos Ponce Campuzano

Fractal Spirograph by Juan Carlos Ponce Campuzano
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2017-05-16 20:07
CircleTrigonometryParametric EquationGeometric ConstructionLocus
This example demonstrates the creation of a fractal spirograph by rotating and dilating circles, involving concepts like rotation, dilation, locus, and parametric equations. It uses commands such as Rotate, Circle, Dilate, Locus, and TableText in GeoGebra. Suitable for high school and above students to explore complex geometric properties.

GeoGebra Commands & Parameters

  1. Rotate((3, 0), a) → A_0
  2. Circle((0, 0), 3) → c_0
  3. Dilate(c_0, -1 / b, A_0) → c_1
  4. Rotate(A_0, (k * ((-a) + (3 * π / 2))), Center[c_1]) → A_1
  5. Dilate(c_1, -1 / b, A_1) → c_2
  6. Rotate(A_1, (k^(2) * (a + π / 2)), Center[c_2]) → A_2
  7. Dilate(c_2, -1 / b, A_2) → c_3
  8. Rotate(A_2, (k^(3) * (a + π / 2)), Center[c_3]) → A_3
  9. Dilate(c_3, -1 / b, A_3) → c_4
  10. Rotate(A_3, (k^(4) * (a + π / 2)), Center[c_4]) → A_4
  11. Dilate(c_4, -1 / b, A_4) → c_5
  12. Rotate(A_4, (k^(4) * (a + π / 2)), Center[c_5]) → A_5
  13. Dilate(c_5, -1 / b, A_5) → c_6
  14. Rotate(A_5, (k^(4) * (a + π / 2)), Center[c_6]) → A_6
  15. Dilate(c_6, -1 / b, A_6) → c_7
  16. Rotate(A_6, (k^(4) * (a + π / 2)), Center[c_7]) → A_7
  17. Locus(A_7, a) → loc1
  18. TableText({{LaTeX[xmax, true, true]}, {LaTeX[xmin, true, true]}, {LaTeX[ymax, true, true]}, {LaTeX[ymin, true, true]}}) → text1