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朱利亚集边界演示

朱利亚集边界演示
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2016-04-25 22:07
函数复数几何作图函数图像
①本范例演示了复平面中朱利亚集的边界稳定性区域，通过移动C点观察迭代公式z->z^2+C的稳定性变化；②涉及核心数学概念包括复数运算、迭代函数、分形几何；③构造要点使用了GeoGebra命令对象A, A1, C, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38进行图形绘制与动态演示；④适合高中及以上数学学习者、复分析初学者或对分形艺术感兴趣者使用。

GeoGebra 命令及参数

  1. Point A(0.6020044513897775, 1.9253924034948553)
  2. A
  3. Point C(0.0, 0.0)
  4. (((Random[0, 1] * 2) - 1) * sqrt(A1 - C))
  5. (((Random[0, 1] * 2) - 1) * sqrt(A2 - C))
  6. (((Random[0, 1] * 2) - 1) * sqrt(A3 - C))
  7. (((Random[0, 1] * 2) - 1) * sqrt(A4 - C))
  8. (((Random[0, 1] * 2) - 1) * sqrt(A5 - C))
  9. (((Random[0, 1] * 2) - 1) * sqrt(A6 - C))
  10. (((Random[0, 1] * 2) - 1) * sqrt(A7 - C))
  11. (((Random[0, 1] * 2) - 1) * sqrt(A8 - C))
  12. (((Random[0, 1] * 2) - 1) * sqrt(A9 - C))
  13. (((Random[0, 1] * 2) - 1) * sqrt(A10 - C))
  14. (((Random[0, 1] * 2) - 1) * sqrt(A11 - C))
  15. (((Random[0, 1] * 2) - 1) * sqrt(A12 - C))
  16. (((Random[0, 1] * 2) - 1) * sqrt(A13 - C))
  17. (((Random[0, 1] * 2) - 1) * sqrt(A14 - C))
  18. (((Random[0, 1] * 2) - 1) * sqrt(A15 - C))
  19. (((Random[0, 1] * 2) - 1) * sqrt(A16 - C))
  20. (((Random[0, 1] * 2) - 1) * sqrt(A17 - C))
  21. (((Random[0, 1] * 2) - 1) * sqrt(A18 - C))
  22. (((Random[0, 1] * 2) - 1) * sqrt(A19 - C))
  23. (((Random[0, 1] * 2) - 1) * sqrt(A20 - C))
  24. (((Random[0, 1] * 2) - 1) * sqrt(A21 - C))
  25. (((Random[0, 1] * 2) - 1) * sqrt(A22 - C))
  26. (((Random[0, 1] * 2) - 1) * sqrt(A23 - C))
  27. (((Random[0, 1] * 2) - 1) * sqrt(A24 - C))
  28. (((Random[0, 1] * 2) - 1) * sqrt(A25 - C))
  29. (((Random[0, 1] * 2) - 1) * sqrt(A26 - C))
  30. (((Random[0, 1] * 2) - 1) * sqrt(A27 - C))
  31. (((Random[0, 1] * 2) - 1) * sqrt(A28 - C))
  32. (((Random[0, 1] * 2) - 1) * sqrt(A29 - C))
  33. (((Random[0, 1] * 2) - 1) * sqrt(A30 - C))
  34. (((Random[0, 1] * 2) - 1) * sqrt(A31 - C))
  35. (((Random[0, 1] * 2) - 1) * sqrt(A32 - C))
  36. (((Random[0, 1] * 2) - 1) * sqrt(A33 - C))
  37. (((Random[0, 1] * 2) - 1) * sqrt(A34 - C))
  38. (((Random[0, 1] * 2) - 1) * sqrt(A35 - C))
  39. (((Random[0, 1] * 2) - 1) * sqrt(A36 - C))
  40. (((Random[0, 1] * 2) - 1) * sqrt(A37 - C))
  41. (((Random[0, 1] * 2) - 1) * sqrt(A38 - C))
  42. (((Random[0, 1] * 2) - 1) * sqrt(A39 - C))
  43. (((Random[0, 1] * 2) - 1) * sqrt(A40 - C))
  44. (((Random[0, 1] * 2) - 1) * sqrt(A41 - C))
  45. (((Random[0, 1] * 2) - 1) * sqrt(A42 - C))
  46. (((Random[0, 1] * 2) - 1) * sqrt(A43 - C))
  47. (((Random[0, 1] * 2) - 1) * sqrt(A44 - C))
  48. (((Random[0, 1] * 2) - 1) * sqrt(A45 - C))
  49. (((Random[0, 1] * 2) - 1) * sqrt(A46 - C))
  50. (((Random[0, 1] * 2) - 1) * sqrt(A47 - C))
  51. (((Random[0, 1] * 2) - 1) * sqrt(A48 - C))
  52. (((Random[0, 1] * 2) - 1) * sqrt(A49 - C))
  53. (((Random[0, 1] * 2) - 1) * sqrt(A50 - C))
  54. (((Random[0, 1] * 2) - 1) * sqrt(A51 - C))
  55. (((Random[0, 1] * 2) - 1) * sqrt(A52 - C))
  56. (((Random[0, 1] * 2) - 1) * sqrt(A53 - C))
  57. (((Random[0, 1] * 2) - 1) * sqrt(A54 - C))
  58. (((Random[0, 1] * 2) - 1) * sqrt(A55 - C))
  59. (((Random[0, 1] * 2) - 1) * sqrt(A56 - C))
  60. (((Random[0, 1] * 2) - 1) * sqrt(A57 - C))

AI 绘图提示语参考

绘制一个复平面的 Julia 集边界，以点A(0.602, 1.925)为中心，点C为原点。通过迭代公式z -> z^2 + C，观察点A及其周围点的动态变化，展示 Julia 集的边界结构。随机生成多个点A1到A38，每个点通过公式 (((Random[0, 1] * 2) - 1) * sqrt(Ai - C)) 与点C相关联，形成 Julia 集的动态可视化。
以上提示语为根据原始绘图命令整理而来，仅供参考。