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Chaos Game by Steve Phelps

Chaos Game by Steve Phelps
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2019-11-09 23:28
This example demonstrates the chaos game, a method for generating fractal geometric patterns. Key mathematical concepts include geometric transformations and stochastic processes. Using GeoGebra commands such as Polygon, PointIn, and Dilate, a series of points are generated, ultimately forming a fractal pattern. Suitable for high school students or math enthusiasts to learn about fractal geometry and stochastic processes.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. PointIn(poly1) → D
  3. Dilate(A1, 1 / 2, RandomElement[{A, B, C}]) → A2
  4. Dilate(A2, 1 / 2, RandomElement[{A, B, C}]) → A3
  5. Dilate(A3, 1 / 2, RandomElement[{A, B, C}]) → A4
  6. Dilate(A4, 1 / 2, RandomElement[{A, B, C}]) → A5
  7. Dilate(A5, 1 / 2, RandomElement[{A, B, C}]) → A6
  8. Dilate(A6, 1 / 2, RandomElement[{A, B, C}]) → A7
  9. Dilate(A7, 1 / 2, RandomElement[{A, B, C}]) → A8
  10. Dilate(A8, 1 / 2, RandomElement[{A, B, C}]) → A9
  11. Dilate(A9, 1 / 2, RandomElement[{A, B, C}]) → A10
  12. Dilate(A10, 1 / 2, RandomElement[{A, B, C}]) → A11
  13. Dilate(A11, 1 / 2, RandomElement[{A, B, C}]) → A12
  14. Dilate(A12, 1 / 2, RandomElement[{A, B, C}]) → A13
  15. Dilate(A13, 1 / 2, RandomElement[{A, B, C}]) → A14
  16. Dilate(A14, 1 / 2, RandomElement[{A, B, C}]) → A15
  17. Dilate(A15, 1 / 2, RandomElement[{A, B, C}]) → A16
  18. Dilate(A16, 1 / 2, RandomElement[{A, B, C}]) → A17
  19. Dilate(A17, 1 / 2, RandomElement[{A, B, C}]) → A18
  20. Dilate(A18, 1 / 2, RandomElement[{A, B, C}]) → A19
  21. Dilate(A19, 1 / 2, RandomElement[{A, B, C}]) → A20
  22. Dilate(A20, 1 / 2, RandomElement[{A, B, C}]) → A21
  23. Dilate(A21, 1 / 2, RandomElement[{A, B, C}]) → A22
  24. Dilate(A22, 1 / 2, RandomElement[{A, B, C}]) → A23
  25. Dilate(A23, 1 / 2, RandomElement[{A, B, C}]) → A24
  26. Dilate(A24, 1 / 2, RandomElement[{A, B, C}]) → A25
  27. Dilate(A25, 1 / 2, RandomElement[{A, B, C}]) → A26
  28. Dilate(A26, 1 / 2, RandomElement[{A, B, C}]) → A27
  29. Dilate(A27, 1 / 2, RandomElement[{A, B, C}]) → A28
  30. Dilate(A28, 1 / 2, RandomElement[{A, B, C}]) → A29
  31. Dilate(A29, 1 / 2, RandomElement[{A, B, C}]) → A30
  32. Dilate(A30, 1 / 2, RandomElement[{A, B, C}]) → A31
  33. Dilate(A31, 1 / 2, RandomElement[{A, B, C}]) → A32
  34. Dilate(A32, 1 / 2, RandomElement[{A, B, C}]) → A33
  35. Dilate(A33, 1 / 2, RandomElement[{A, B, C}]) → A34
  36. Dilate(A34, 1 / 2, RandomElement[{A, B, C}]) → A35
  37. Dilate(A35, 1 / 2, RandomElement[{A, B, C}]) → A36
  38. Dilate(A36, 1 / 2, RandomElement[{A, B, C}]) → A37
  39. Dilate(A37, 1 / 2, RandomElement[{A, B, C}]) → A38
  40. Dilate(A38, 1 / 2, RandomElement[{A, B, C}]) → A39
  41. Dilate(A39, 1 / 2, RandomElement[{A, B, C}]) → A40
  42. Dilate(A40, 1 / 2, RandomElement[{A, B, C}]) → A41
  43. Dilate(A41, 1 / 2, RandomElement[{A, B, C}]) → A42
  44. Dilate(A42, 1 / 2, RandomElement[{A, B, C}]) → A43
  45. Dilate(A43, 1 / 2, RandomElement[{A, B, C}]) → A44
  46. Dilate(A44, 1 / 2, RandomElement[{A, B, C}]) → A45
  47. Dilate(A45, 1 / 2, RandomElement[{A, B, C}]) → A46
  48. Dilate(A46, 1 / 2, RandomElement[{A, B, C}]) → A47
  49. Dilate(A47, 1 / 2, RandomElement[{A, B, C}]) → A48
  50. Dilate(A48, 1 / 2, RandomElement[{A, B, C}]) → A49
  51. Dilate(A49, 1 / 2, RandomElement[{A, B, C}]) → A50
  52. Dilate(A50, 1 / 2, RandomElement[{A, B, C}]) → A51
  53. Dilate(A51, 1 / 2, RandomElement[{A, B, C}]) → A52
  54. Dilate(A52, 1 / 2, RandomElement[{A, B, C}]) → A53
  55. Dilate(A53, 1 / 2, RandomElement[{A, B, C}]) → A54
  56. Dilate(A54, 1 / 2, RandomElement[{A, B, C}]) → A55
  57. Dilate(A55, 1 / 2, RandomElement[{A, B, C}]) → A56
  58. Dilate(A56, 1 / 2, RandomElement[{A, B, C}]) → A57
  59. Dilate(A57, 1 / 2, RandomElement[{A, B, C}]) → A58
  60. Dilate(A58, 1 / 2, RandomElement[{A, B, C}]) → A59
  61. Dilate(A59, 1 / 2, RandomElement[{A, B, C}]) → A60
  62. Dilate(A60, 1 / 2, RandomElement[{A, B, C}]) → A61
  63. Dilate(A61, 1 / 2, RandomElement[{A, B, C}]) → A62
  64. Dilate(A62, 1 / 2, RandomElement[{A, B, C}]) → A63
  65. Dilate(A63, 1 / 2, RandomElement[{A, B, C}]) → A64
  66. Dilate(A64, 1 / 2, RandomElement[{A, B, C}]) → A65
  67. Dilate(A65, 1 / 2, RandomElement[{A, B, C}]) → A66
  68. Dilate(A66, 1 / 2, RandomElement[{A, B, C}]) → A67
  69. Dilate(A67, 1 / 2, RandomElement[{A, B, C}]) → A68
  70. Dilate(A68, 1 / 2, RandomElement[{A, B, C}]) → A69
  71. Dilate(A69, 1 / 2, RandomElement[{A, B, C}]) → A70
  72. Dilate(A70, 1 / 2, RandomElement[{A, B, C}]) → A71
  73. Dilate(A71, 1 / 2, RandomElement[{A, B, C}]) → A72
  74. Dilate(A72, 1 / 2, RandomElement[{A, B, C}]) → A73
  75. Dilate(A73, 1 / 2, RandomElement[{A, B, C}]) → A74
  76. Dilate(A74, 1 / 2, RandomElement[{A, B, C}]) → A75
  77. Dilate(A75, 1 / 2, RandomElement[{A, B, C}]) → A76
  78. Dilate(A76, 1 / 2, RandomElement[{A, B, C}]) → A77
  79. Dilate(A77, 1 / 2, RandomElement[{A, B, C}]) → A78
  80. Dilate(A78, 1 / 2, RandomElement[{A, B, C}]) → A79
  81. Dilate(A79, 1 / 2, RandomElement[{A, B, C}]) → A80
  82. Dilate(A80, 1 / 2, RandomElement[{A, B, C}]) → A81
  83. Dilate(A81, 1 / 2, RandomElement[{A, B, C}]) → A82
  84. Dilate(A82, 1 / 2, RandomElement[{A, B, C}]) → A83
  85. Dilate(A83, 1 / 2, RandomElement[{A, B, C}]) → A84
  86. Dilate(A84, 1 / 2, RandomElement[{A, B, C}]) → A85
  87. Dilate(A85, 1 / 2, RandomElement[{A, B, C}]) → A86
  88. Dilate(A86, 1 / 2, RandomElement[{A, B, C}]) → A87
  89. Dilate(A87, 1 / 2, RandomElement[{A, B, C}]) → A88
  90. Dilate(A88, 1 / 2, RandomElement[{A, B, C}]) → A89
  91. Dilate(A89, 1 / 2, RandomElement[{A, B, C}]) → A90
  92. Dilate(A90, 1 / 2, RandomElement[{A, B, C}]) → A91
  93. Dilate(A91, 1 / 2, RandomElement[{A, B, C}]) → A92
  94. Dilate(A92, 1 / 2, RandomElement[{A, B, C}]) → A93
  95. Dilate(A93, 1 / 2, RandomElement[{A, B, C}]) → A94
  96. Dilate(A94, 1 / 2, RandomElement[{A, B, C}]) → A95
  97. Dilate(A95, 1 / 2, RandomElement[{A, B, C}]) → A96
  98. Dilate(A96, 1 / 2, RandomElement[{A, B, C}]) → A97
  99. Dilate(A97, 1 / 2, RandomElement[{A, B, C}]) → A98
  100. Dilate(A98, 1 / 2, RandomElement[{A, B, C}]) → A99
  101. Dilate(A99, 1 / 2, RandomElement[{A, B, C}]) → A100