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Mandelbrot 迭代轨道

Mandelbrot 迭代轨道
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2013-08-16 01:30
三角函数数列复数几何作图函数图像
①本范例演示了复平面中点在 Mandelbrot 迭代下的轨道行为及其与著名 Mandelbrot 集合的对应关系；②涉及的核心数学概念包括复数运算、迭代序列、分形几何；③作图要点——从下方『构造摘要』提炼用到了 GeoGebra 命令/对象：If 条件判断、Segment 线段绘制；对象：c, A, a, A1, unitcirc, A2 至 A29, B2 至 B8；④适合的学段或用途——适合高中及以上数学学习者理解分形概念、复动力系统及算法可视化。

GeoGebra 命令及参数

  1. If(a ≟ 0, c, A1^(2) + c) → A2
  2. Segment(A1, A2) → B2
  3. Segment(A2, A3) → B3
  4. Segment(A3, A4) → B4
  5. Segment(A4, A5) → B5
  6. Segment(A5, A6) → B6
  7. Segment(A6, A7) → B7
  8. Segment(A7, A8) → B8
  9. Segment(A8, A9) → B9
  10. Segment(A9, A10) → B10
  11. Segment(A10, A11) → B11
  12. Segment(A11, A12) → B12
  13. Segment(A12, A13) → B13
  14. Segment(A13, A14) → B14
  15. Segment(A14, A15) → B15
  16. Segment(A15, A16) → B16
  17. Segment(A16, A17) → B17
  18. Segment(A17, A18) → B18
  19. Segment(A18, A19) → B19
  20. Segment(A19, A20) → B20
  21. Segment(A20, A21) → B21
  22. Segment(A21, A22) → B22
  23. Segment(A22, A23) → B23
  24. Segment(A23, A24) → B24
  25. Segment(A24, A25) → B25
  26. Segment(A25, A26) → B26
  27. Segment(A26, A27) → B27
  28. Segment(A27, A28) → B28
  29. Segment(A28, A29) → B29
  30. Segment(A29, A30) → B30
  31. Segment(A30, A31) → B31
  32. Segment(A31, A32) → B32
  33. Segment(A32, A33) → B33
  34. Segment(A33, A34) → B34
  35. Segment(A34, A35) → B35
  36. Segment(A35, A36) → B36
  37. Segment(A36, A37) → B37
  38. Segment(A37, A38) → B38
  39. Segment(A38, A39) → B39
  40. Segment(A39, A40) → B40
  41. Segment(A40, A41) → B41
  42. Segment(A41, A42) → B42
  43. Segment(A42, A43) → B43
  44. Segment(A43, A44) → B44
  45. Segment(A44, A45) → B45
  46. Segment(A45, A46) → B46
  47. Segment(A46, A47) → B47
  48. Segment(A47, A48) → B48
  49. Segment(A48, A49) → B49
  50. Segment(A49, A50) → B50
  51. Segment(A50, A51) → B51
  52. Segment(A51, A52) → B52
  53. Segment(A52, A53) → B53
  54. Segment(A53, A54) → B54
  55. Segment(A54, A55) → B55
  56. Segment(A55, A56) → B56
  57. Segment(A56, A57) → B57
  58. Segment(A57, A58) → B58
  59. Segment(A58, A59) → B59
  60. Segment(A59, A60) → B60
  61. Segment(A60, A61) → B61
  62. Segment(A61, A62) → B62
  63. Segment(A62, A63) → B63
  64. Segment(A63, A64) → B64
  65. Segment(A64, A65) → B65
  66. Segment(A65, A66) → B66
  67. Segment(A66, A67) → B67
  68. Segment(A67, A68) → B68
  69. Segment(A68, A69) → B69
  70. Segment(A69, A70) → B70
  71. Segment(A70, A71) → B71
  72. Segment(A71, A72) → B72
  73. Segment(A72, A73) → B73
  74. Segment(A73, A74) → B74
  75. Segment(A74, A75) → B75
  76. Segment(A75, A76) → B76
  77. Segment(A76, A77) → B77
  78. Segment(A77, A78) → B78
  79. Segment(A78, A79) → B79
  80. Segment(A79, A80) → B80
  81. Segment(A80, A81) → B81
  82. Segment(A81, A82) → B82
  83. Segment(A82, A83) → B83
  84. Segment(A83, A84) → B84
  85. Segment(A84, A85) → B85
  86. Segment(A85, A86) → B86
  87. Segment(A86, A87) → B87
  88. Segment(A87, A88) → B88
  89. Segment(A88, A89) → B89
  90. Segment(A89, A90) → B90
  91. Segment(A90, A91) → B91
  92. Segment(A91, A92) → B92
  93. Segment(A92, A93) → B93
  94. Segment(A93, A94) → B94
  95. Segment(A94, A95) → B95
  96. Segment(A95, A96) → B96
  97. Segment(A96, A97) → B97
  98. Segment(A97, A98) → B98
  99. Segment(A98, A99) → B99
  100. Segment(A99, A100) → B100
  101. Segment(A100, A101) → B101
  102. Segment(A101, A102) → B102
  103. Segment(A102, A103) → B103
  104. Segment(A103, A104) → B104
  105. Segment(A104, A105) → B105
  106. Segment(A105, A106) → B106
  107. Segment(A106, A107) → B107
  108. Segment(A107, A108) → B108
  109. Segment(A108, A109) → B109
  110. Segment(A109, A110) → B110
  111. Segment(A110, A111) → B111
  112. Segment(A111, A112) → B112
  113. Segment(A112, A113) → B113
  114. Segment(A113, A114) → B114
  115. Segment(A114, A115) → B115
  116. Segment(A115, A116) → B116
  117. Segment(A116, A117) → B117
  118. Segment(A117, A118) → B118
  119. Segment(A118, A119) → B119
  120. Segment(A119, A120) → B120
  121. Segment(A120, A121) → B121
  122. Segment(A121, A122) → B122
  123. Segment(A122, A123) → B123
  124. Segment(A123, A124) → B124
  125. Segment(A124, A125) → B125
  126. Segment(A125, A126) → B126
  127. Segment(A126, A127) → B127
  128. Segment(A127, A128) → B128
  129. Segment(A128, A129) → B129
  130. Segment(A129, A130) → B130
  131. Segment(A130, A131) → B131
  132. Segment(A131, A132) → B132
  133. Segment(A132, A133) → B133
  134. Segment(A133, A134) → B134
  135. Segment(A134, A135) → B135
  136. Segment(A135, A136) → B136
  137. Segment(A136, A137) → B137
  138. Segment(A137, A138) → B138
  139. Segment(A138, A139) → B139
  140. Segment(A139, A140) → B140
  141. Segment(A140, A141) → B141
  142. Segment(A141, A142) → B142
  143. Segment(A142, A143) → B143
  144. Segment(A143, A144) → B144
  145. Segment(A144, A145) → B145
  146. Segment(A145, A146) → B146
  147. Segment(A146, A147) → B147
  148. Segment(A147, A148) → B148
  149. Segment(A148, A149) → B149
  150. Segment(A149, A150) → B150
  151. Segment(A150, A151) → B151
  152. Segment(A151, A152) → B152
  153. Segment(A152, A153) → B153
  154. Segment(A153, A154) → B154
  155. Segment(A154, A155) → B155

AI 绘图提示语参考

在复平面上绘制点在Mandelbrot迭代下的轨道，展示其如何转化为著名的Mandelbrot集合。从初始点开始，根据迭代规则生成一系列点，并用线段依次连接这些点，形成动态的轨迹。整个过程需体现复数运算、迭代序列和分形几何的核心概念，通过分段连接可视化迭代过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。