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Mandelbrot 画板

Mandelbrot 画板
几何画板及绘图内容加载中，请稍等……
2014-06-17 00:00
函数复数几何作图函数图像
①本范例通过拖动点'C'演示 Mandelbrot 集合的图像绘制过程；②涉及的核心数学概念包括复数、迭代、稳定性判断；③作图要点——使用了 GeoGebra 的 If 条件判断、Segment 线段绘制、Sum 求和命令，以及对象 c, A, a, A1 至 A28 等；④适合高中及以上数学学习者，用于理解复数迭代和分形几何。

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
  156. If(abs(A2) < 2, 1, 0) → C2
  157. If(abs(A3) < 2, 1, 0) → C3
  158. If(abs(A4) < 2, 1, 0) → C4
  159. If(abs(A5) < 2, 1, 0) → C5
  160. If(abs(A6) < 2, 1, 0) → C6
  161. If(abs(A7) < 2, 1, 0) → C7
  162. If(abs(A8) < 2, 1, 0) → C8
  163. If(abs(A9) < 2, 1, 0) → C9
  164. If(abs(A10) < 2, 1, 0) → C10
  165. If(abs(A11) < 2, 1, 0) → C11
  166. If(abs(A12) < 2, 1, 0) → C12
  167. If(abs(A13) < 2, 1, 0) → C13
  168. If(abs(A14) < 2, 1, 0) → C14
  169. If(abs(A15) < 2, 1, 0) → C15
  170. If(abs(A16) < 2, 1, 0) → C16
  171. If(abs(A17) < 2, 1, 0) → C17
  172. If(abs(A18) < 2, 1, 0) → C18
  173. If(abs(A19) < 2, 1, 0) → C19
  174. If(abs(A20) < 2, 1, 0) → C20
  175. If(abs(A21) < 2, 1, 0) → C21
  176. If(abs(A22) < 2, 1, 0) → C22
  177. If(abs(A23) < 2, 1, 0) → C23
  178. If(abs(A24) < 2, 1, 0) → C24
  179. If(abs(A25) < 2, 1, 0) → C25
  180. If(abs(A26) < 2, 1, 0) → C26
  181. If(abs(A27) < 2, 1, 0) → C27
  182. If(abs(A28) < 2, 1, 0) → C28
  183. If(abs(A29) < 2, 1, 0) → C29
  184. If(abs(A30) < 2, 1, 0) → C30
  185. If(abs(A31) < 2, 1, 0) → C31
  186. If(abs(A32) < 2, 1, 0) → C32
  187. If(abs(A33) < 2, 1, 0) → C33
  188. If(abs(A34) < 2, 1, 0) → C34
  189. If(abs(A35) < 2, 1, 0) → C35
  190. If(abs(A36) < 2, 1, 0) → C36
  191. If(abs(A37) < 2, 1, 0) → C37
  192. If(abs(A38) < 2, 1, 0) → C38
  193. If(abs(A39) < 2, 1, 0) → C39
  194. If(abs(A40) < 2, 1, 0) → C40
  195. If(abs(A41) < 2, 1, 0) → C41
  196. If(abs(A42) < 2, 1, 0) → C42
  197. If(abs(A43) < 2, 1, 0) → C43
  198. If(abs(A44) < 2, 1, 0) → C44
  199. If(abs(A45) < 2, 1, 0) → C45
  200. If(abs(A46) < 2, 1, 0) → C46
  201. If(abs(A47) < 2, 1, 0) → C47
  202. If(abs(A48) < 2, 1, 0) → C48
  203. If(abs(A49) < 2, 1, 0) → C49
  204. If(abs(A50) < 2, 1, 0) → C50
  205. If(abs(A51) < 2, 1, 0) → C51
  206. If(abs(A52) < 2, 1, 0) → C52
  207. If(abs(A53) < 2, 1, 0) → C53
  208. If(abs(A54) < 2, 1, 0) → C54
  209. If(abs(A55) < 2, 1, 0) → C55
  210. If(abs(A56) < 2, 1, 0) → C56
  211. If(abs(A57) < 2, 1, 0) → C57
  212. If(abs(A58) < 2, 1, 0) → C58
  213. If(abs(A59) < 2, 1, 0) → C59
  214. If(abs(A60) < 2, 1, 0) → C60
  215. If(abs(A61) < 2, 1, 0) → C61
  216. If(abs(A62) < 2, 1, 0) → C62
  217. If(abs(A63) < 2, 1, 0) → C63
  218. If(abs(A64) < 2, 1, 0) → C64
  219. If(abs(A65) < 2, 1, 0) → C65
  220. If(abs(A66) < 2, 1, 0) → C66
  221. If(abs(A67) < 2, 1, 0) → C67
  222. If(abs(A68) < 2, 1, 0) → C68
  223. If(abs(A69) < 2, 1, 0) → C69
  224. If(abs(A70) < 2, 1, 0) → C70
  225. If(abs(A71) < 2, 1, 0) → C71
  226. If(abs(A72) < 2, 1, 0) → C72
  227. If(abs(A73) < 2, 1, 0) → C73
  228. If(abs(A74) < 2, 1, 0) → C74
  229. If(abs(A75) < 2, 1, 0) → C75
  230. If(abs(A76) < 2, 1, 0) → C76
  231. If(abs(A77) < 2, 1, 0) → C77
  232. If(abs(A78) < 2, 1, 0) → C78
  233. If(abs(A79) < 2, 1, 0) → C79
  234. If(abs(A80) < 2, 1, 0) → C80
  235. If(abs(A81) < 2, 1, 0) → C81
  236. If(abs(A82) < 2, 1, 0) → C82
  237. If(abs(A83) < 2, 1, 0) → C83
  238. If(abs(A84) < 2, 1, 0) → C84
  239. If(abs(A85) < 2, 1, 0) → C85
  240. If(abs(A86) < 2, 1, 0) → C86
  241. If(abs(A87) < 2, 1, 0) → C87
  242. If(abs(A88) < 2, 1, 0) → C88
  243. If(abs(A89) < 2, 1, 0) → C89
  244. If(abs(A90) < 2, 1, 0) → C90
  245. If(abs(A91) < 2, 1, 0) → C91
  246. If(abs(A92) < 2, 1, 0) → C92
  247. If(abs(A93) < 2, 1, 0) → C93
  248. If(abs(A94) < 2, 1, 0) → C94
  249. If(abs(A95) < 2, 1, 0) → C95
  250. If(abs(A96) < 2, 1, 0) → C96
  251. If(abs(A97) < 2, 1, 0) → C97
  252. If(abs(A98) < 2, 1, 0) → C98
  253. If(abs(A99) < 2, 1, 0) → C99
  254. If(abs(A100) < 2, 1, 0) → C100
  255. If(abs(A101) < 2, 1, 0) → C101
  256. If(abs(A102) < 2, 1, 0) → C102
  257. If(abs(A103) < 2, 1, 0) → C103
  258. If(abs(A104) < 2, 1, 0) → C104
  259. If(abs(A105) < 2, 1, 0) → C105
  260. If(abs(A106) < 2, 1, 0) → C106
  261. If(abs(A107) < 2, 1, 0) → C107
  262. If(abs(A108) < 2, 1, 0) → C108
  263. If(abs(A109) < 2, 1, 0) → C109
  264. If(abs(A110) < 2, 1, 0) → C110
  265. If(abs(A111) < 2, 1, 0) → C111
  266. If(abs(A112) < 2, 1, 0) → C112
  267. If(abs(A113) < 2, 1, 0) → C113
  268. If(abs(A114) < 2, 1, 0) → C114
  269. If(abs(A115) < 2, 1, 0) → C115
  270. If(abs(A116) < 2, 1, 0) → C116
  271. If(abs(A117) < 2, 1, 0) → C117
  272. If(abs(A118) < 2, 1, 0) → C118
  273. If(abs(A119) < 2, 1, 0) → C119
  274. If(abs(A120) < 2, 1, 0) → C120
  275. If(abs(A121) < 2, 1, 0) → C121
  276. If(abs(A122) < 2, 1, 0) → C122
  277. If(abs(A123) < 2, 1, 0) → C123
  278. If(abs(A124) < 2, 1, 0) → C124
  279. If(abs(A125) < 2, 1, 0) → C125
  280. If(abs(A126) < 2, 1, 0) → C126
  281. If(abs(A127) < 2, 1, 0) → C127
  282. If(abs(A128) < 2, 1, 0) → C128
  283. If(abs(A129) < 2, 1, 0) → C129
  284. If(abs(A130) < 2, 1, 0) → C130
  285. If(abs(A131) < 2, 1, 0) → C131
  286. If(abs(A132) < 2, 1, 0) → C132
  287. If(abs(A133) < 2, 1, 0) → C133
  288. If(abs(A134) < 2, 1, 0) → C134
  289. If(abs(A135) < 2, 1, 0) → C135
  290. If(abs(A136) < 2, 1, 0) → C136
  291. If(abs(A137) < 2, 1, 0) → C137
  292. If(abs(A138) < 2, 1, 0) → C138
  293. If(abs(A139) < 2, 1, 0) → C139
  294. If(abs(A140) < 2, 1, 0) → C140
  295. If(abs(A141) < 2, 1, 0) → C141
  296. If(abs(A142) < 2, 1, 0) → C142
  297. If(abs(A143) < 2, 1, 0) → C143
  298. If(abs(A144) < 2, 1, 0) → C144
  299. If(abs(A145) < 2, 1, 0) → C145
  300. If(abs(A146) < 2, 1, 0) → C146
  301. If(abs(A147) < 2, 1, 0) → C147
  302. If(abs(A148) < 2, 1, 0) → C148
  303. If(abs(A149) < 2, 1, 0) → C149
  304. If(abs(A150) < 2, 1, 0) → C150
  305. If(abs(A151) < 2, 1, 0) → C151
  306. If(abs(A152) < 2, 1, 0) → C152
  307. If(abs(A153) < 2, 1, 0) → C153
  308. If(abs(A154) < 2, 1, 0) → C154
  309. If(abs(A155) < 2, 1, 0) → C155
  310. Sum(C150:C155) → D155
  311. Sum(C1:C155) → g

AI 绘图提示语参考

画一个展示 Mandelbrot 集合绘制过程的动态图，通过拖动点 C 来观察迭代过程。核心是展示复数迭代和稳定性判断，用线段依次连接迭代结果，从初始点开始，每一步的连接都基于前一步的输出，形成复杂的分形结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。