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Optical Illusion Squares Generating a Fractal

Optical Illusion Squares Generating a Fractal
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2018-09-29 04:02
Polygon
This example demonstrates the geometric phenomenon of constructing a fractal using optical illusion squares. It involves core mathematical concepts like fractal geometry, parallelogram, arithmetic, binomial distribution, circumcircle, and bar chart. The construction utilizes GeoGebra commands/objects such as Circle, Point, Polygon, Rotate, Line, Mirror, and PointIn. It is suitable for high school and above students exploring geometric transformations and fractal generation processes.

GeoGebra Commands & Parameters

  1. Circle(F, 2) → c
  2. Point(c) → G
  3. Polygon(G, H, 4) → d, j, k, l, m, I, J
  4. Rotate(d, 45°, F) → d'
  5. Rotate(d', 45°, F) → d''
  6. Rotate(d'', 45°, F) → d'''
  7. Rotate(d''', 45°, F) → e
  8. Rotate(e, 45°, F) → e'
  9. Rotate(e', 45°, F) → e''
  10. Rotate(e'', 45°, F) → e'''
  11. Line(A, B) → f
  12. Mirror(J, f) → J'
  13. Mirror(I, f) → I'
  14. Mirror(d, f) → d'_1
  15. Mirror(d', f) → d''_1
  16. Mirror(d'', f) → d'''_1
  17. Mirror(d''', f) → a
  18. Mirror(e, f) → e'_1
  19. Mirror(e', f) → e''_1
  20. Mirror(e'', f) → e'''_1
  21. Mirror(e''', f) → b
  22. PointIn(d'_1) → C
  23. PointIn(b) → E
  24. PointIn(e'''_1) → L
  25. PointIn(e''_1) → N
  26. PointIn(e'_1) → P
  27. PointIn(a) → R
  28. PointIn(d'''_1) → T
  29. PointIn(d''_1) → W
  30. PointIn(b) → D
  31. PointIn(e'''_1) → K
  32. PointIn(e''_1) → M
  33. PointIn(e'_1) → O
  34. PointIn(a) → Q
  35. PointIn(d'''_1) → S
  36. PointIn(d''_1) → U
  37. PointIn(d'_1) → V