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Mandelbrot Painter

Mandelbrot Painter
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2014-06-17 00:00
FunctionComplex NumberGeometric ConstructionGraphing
This example demonstrates the drawing process of the Mandelbrot set by dragging point 'C'. It involves core math concepts like complex numbers, iteration, and stability determination. Constructed using GeoGebra's If, Segment, Sum commands and objects like c, A, a, A1-A28. Suitable for high school and above learners to understand complex iteration and fractal geometry.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a dynamic illustration showing the Mandelbrot set drawing process by dragging point C. Focus on complex number iteration and stability determination, visually connecting each iteration step with line segments, starting from an initial point and sequentially linking outputs to form a complex fractal structure.
The prompt above was compiled from the original drawing commands and is for reference only.