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Escher Bird Pattern

Escher Bird Pattern
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2013-02-26 03:07
PolygonTransformationGeometric Construction
This example demonstrates the creation of Escher-like patterns based on the principle of symmetry, where shapes removed from one edge are added to another, allowing seamless fitting. Key mathematical concepts include symmetry, polygon construction, rotation transformations, and vector operations. The construction utilizes GeoGebra commands such as Polygon, Rotate, Point, CircumcircleArc, and Segment. It is suitable for high school and above students studying geometric transformations, spatial reasoning, and the intersection of art and mathematics.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → veelhoek1, a, b, c, d
  2. Polygon(A, E, F, B) → veelhoek2, a_1, e, f, b_1
  3. Rotate(A, 90*°, B) → A'
  4. Rotate(E, 90*°, B) → E'
  5. Rotate(F, 90*°, B) → F'
  6. Rotate(B, 90*°, B) → B'
  7. Polygon(A', E', F', B') → veelhoek2', a', e', f', b'
  8. Point(c) → H
  9. CircumcircleArc(C, G, H) → g
  10. CircumcircleArc(H, I, D) → h
  11. Rotate(H, 90*°, D) → H'
  12. Rotate(I, 90*°, D) → I'
  13. Rotate(D, 90*°, D) → D'
  14. CircumcircleArc(H', I', D') → h'
  15. Rotate(C, 90*°, D) → C'
  16. Rotate(G, 90*°, D) → G'
  17. Rotate(H, 90*°, D) → H'_1
  18. CircumcircleArc(C', G', H'_1) → g'
  19. Rotate(A, 90*°, D) → A'_1
  20. Rotate(B, 90*°, D) → B'_1
  21. Rotate(C, 90*°, D) → C'_1
  22. Rotate(D, 90*°, D) → D'_1
  23. Polygon(A'_1, B'_1, C'_1, D'_1) → veelhoek1', a'_1, b'_1, c'_1, d'_1
  24. Rotate(A, 90*°, D) → A'_2
  25. Rotate(E, 90*°, D) → E'_1
  26. Rotate(F, 90*°, D) → F'_1
  27. Rotate(B, 90*°, D) → B'_2
  28. Polygon(A'_2, E'_1, F'_1, B'_2) → veelhoek2'_1, a'_2, e'_1, f'_1, b'_2
  29. Rotate(A', 90*°, D) → A''
  30. Rotate(E', 90*°, D) → E''
  31. Rotate(F', 90*°, D) → F''
  32. Rotate(B', 90*°, D) → B''
  33. Polygon(A'', E'', F'', B'') → veelhoek2'', a'', e'', f'', b''
  34. Rotate(H, 90*°, D) → H'_2
  35. Rotate(I, 90*°, D) → I'_1
  36. Rotate(D, 90*°, D) → D'_2
  37. CircumcircleArc(H'_2, I'_1, D'_2) → h'_1
  38. Rotate(H', 90*°, D) → H''
  39. Rotate(I', 90*°, D) → I''
  40. Rotate(D', 90*°, D) → D''
  41. CircumcircleArc(H'', I'', D'') → h''
  42. Rotate(C', 90*°, D) → C''
  43. Rotate(G', 90*°, D) → G''
  44. Rotate(H'_1, 90*°, D) → J
  45. CircumcircleArc(C'', G'', J) → g''
  46. Rotate(A, 180*°, D'_1) → A'_3
  47. Rotate(B, 180*°, D'_1) → B'_3
  48. Rotate(C, 180*°, D'_1) → C'_2
  49. Rotate(D, 180*°, D'_1) → D'_3
  50. Polygon(A'_3, B'_3, C'_2, D'_3) → veelhoek1'_1, a'_3, b'_3, c'_2, d'_3
  51. Rotate(A, 180*°, D'_1) → A'_4
  52. Rotate(E, 180*°, D'_1) → E'_2
  53. Rotate(F, 180*°, D'_1) → F'_2
  54. Rotate(B, 180*°, D'_1) → B'_4
  55. Polygon(A'_4, E'_2, F'_2, B'_4) → veelhoek2'_2, a'_4, e'_2, f'_2, b'_4
  56. Rotate(A', 180*°, D'_1) → A''_1
  57. Rotate(E', 180*°, D'_1) → E''_1
  58. Rotate(F', 180*°, D'_1) → F''_1
  59. Rotate(B', 180*°, D'_1) → B''_1
  60. Polygon(A''_1, E''_1, F''_1, B''_1) → veelhoek2''_1, a''_1, e''_1, f''_1, b''_1
  61. Rotate(H, 180*°, D'_1) → H'_3
  62. Rotate(I, 180*°, D'_1) → I'_2
  63. Rotate(D, 180*°, D'_1) → D'_4
  64. CircumcircleArc(H'_3, I'_2, D'_4) → h'_2
  65. Rotate(H', 180*°, D'_1) → H''_1
  66. Rotate(I', 180*°, D'_1) → I''_1
  67. Rotate(D', 180*°, D'_1) → D''_1
  68. CircumcircleArc(H''_1, I''_1, D''_1) → h''_1
  69. Rotate(C', 180*°, D'_1) → C''_1
  70. Rotate(G', 180*°, D'_1) → G''_1
  71. Rotate(H'_1, 180*°, D'_1) → K
  72. CircumcircleArc(C''_1, G''_1, K) → g''_1
  73. Rotate(H'_2, 180*°, D'_1) → L
  74. Rotate(I'_1, 180*°, D'_1) → M
  75. Rotate(D'_2, 180*°, D'_1) → N
  76. CircumcircleArc(L, M, N) → k
  77. Rotate(C'_1, 180*°, D'_1) → O
  78. Rotate(D'_1, 180*°, D'_1) → P
  79. Segment(O, P) → i
  80. Rotate(D'', 180*°, D'_1) → D'''
  81. Rotate(A, 270*°, D'_2) → A'_5
  82. Rotate(B, 270*°, D'_2) → B'_5
  83. Rotate(C, 270*°, D'_2) → C'_3
  84. Rotate(D, 270*°, D'_2) → D'_5
  85. Polygon(A'_5, B'_5, C'_3, D'_5) → veelhoek1'_2, a'_5, b'_5, c'_3, d'_5
  86. Rotate(A, 270*°, D'_2) → A'_6
  87. Rotate(E, 270*°, D'_2) → E'_3
  88. Rotate(F, 270*°, D'_2) → F'_3
  89. Rotate(B, 270*°, D'_2) → B'_6
  90. Polygon(A'_6, E'_3, F'_3, B'_6) → veelhoek2'_3, a'_6, e'_3, f'_3, b'_6
  91. Rotate(A', 270*°, D'_2) → A''_2
  92. Rotate(E', 270*°, D'_2) → E''_2
  93. Rotate(F', 270*°, D'_2) → F''_2
  94. Rotate(B', 270*°, D'_2) → B''_2
  95. Polygon(A''_2, E''_2, F''_2, B''_2) → veelhoek2''_2, a''_2, e''_2, f''_2, b''_2

AI Drawing Prompt Reference

Create an Escher-like bird pattern using symmetry, rotating and reflecting a quadrilateral and its adjacent parts by 90 degrees repeatedly to form a seamless loop. The design consists of multiple quadrilaterals and circular arcs connected through rotations and circumcircle arcs, showcasing symmetry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.