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Rotation Tessellation by adbarona

Rotation Tessellation by adbarona
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2013-07-20 13:46
TrigonometryTransformationGeometric Construction
In collections Rotations
This example demonstrates the creation of fractal patterns through rotation transformations. Core mathematical concepts include rotation, fractal geometry, and similarity transformations. Construction involves using GeoGebra commands like Segment, Line, and Rotate to manipulate points, segments, and shapes. Suitable for high school and above students exploring geometric transformations and fractal art.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, D) → c
  4. Segment(D, E) → d
  5. Segment(E, F) → e
  6. Segment(F, A) → f
  7. Line(F, D) → g
  8. Line(A, C) → h
  9. Line(B, E) → i
  10. Segment(C, G) → j
  11. Segment(G, H) → k
  12. Segment(H, I) → l
  13. Segment(I, J) → m
  14. Segment(J, K) → n
  15. Segment(K, L) → p
  16. Segment(L, M) → q
  17. Segment(M, D) → r
  18. Rotate(C, 240*°, C) → C'
  19. Rotate(D, 240*°, C) → D'
  20. Segment(C', D') → c'
  21. Rotate(C, 240*°, C) → C'_1
  22. Rotate(G, 240*°, C) → G'
  23. Segment(C'_1, G') → j'
  24. Rotate(G, 240*°, C) → G'_1
  25. Rotate(H, 240*°, C) → H'
  26. Segment(G'_1, H') → k'
  27. Rotate(H, 240*°, C) → H'_1
  28. Rotate(I, 240*°, C) → I'
  29. Segment(H'_1, I') → l'
  30. Rotate(I, 240*°, C) → I'_1
  31. Rotate(J, 240*°, C) → J'
  32. Segment(I'_1, J') → m'
  33. Rotate(J, 240*°, C) → J'_1
  34. Rotate(K, 240*°, C) → K'
  35. Segment(J'_1, K') → n'
  36. Rotate(K, 240*°, C) → K'_1
  37. Rotate(L, 240*°, C) → L'
  38. Segment(K'_1, L') → p'
  39. Rotate(L, 240*°, C) → L'_1
  40. Rotate(M, 240*°, C) → M'
  41. Segment(L'_1, M') → q'
  42. Rotate(M, 240*°, C) → M'_1
  43. Rotate(D, 240*°, C) → D'_1
  44. Segment(M'_1, D'_1) → r'

AI Drawing Prompt Reference

Draw a rotational fractal pattern formed by hexagons, start with a hexagon, then rotate adjacent sides outward by 240 degrees around one vertex, connecting the rotated endpoints to form nested hexagons repeatedly, demonstrating rotation, fractal geometry, and similarity transformations.
The prompt above was compiled from the original drawing commands and is for reference only.