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ATC蛛网图示例

ATC蛛网图示例
几何画板及绘图内容加载中，请稍等……
2017-07-08 05:15
函数
所属专题 ATC Cobwebs and Linear Difference Equations
该示例演示了ATC蛛网图，这是一种用于分析非线性映射稳定性的图形方法。核心数学概念包括函数、迭代和收敛性。通过使用GeoGebra命令如Point、Segment等，可以动态展示映射的迭代过程。适合高中数学教学和研究。

GeoGebra 命令及参数

  1. Point(yAxis) → B
  2. Point(xAxis) → A
  3. Segment(A, (x(A), f(x(A)))) → c
  4. Segment((A1, A2), (A2, A2)) → B1
  5. Segment((A2, A2), (A2, A3)) → C1
  6. Segment((A2, A3), (A3, A3)) → B2
  7. Segment((A3, A3), (A3, A4)) → C2
  8. Segment((A3, A4), (A4, A4)) → B3
  9. Segment((A4, A4), (A4, A5)) → C3
  10. Segment((A4, A5), (A5, A5)) → B4
  11. Segment((A5, A5), (A5, A6)) → C4
  12. Segment((A5, A6), (A6, A6)) → B5
  13. Segment((A6, A6), (A6, A7)) → C5
  14. Segment((A6, A7), (A7, A7)) → B6
  15. Segment((A7, A7), (A7, A8)) → C6
  16. Segment((A7, A8), (A8, A8)) → B7
  17. Segment((A8, A8), (A8, A9)) → C7
  18. Segment((A8, A9), (A9, A9)) → B8
  19. Segment((A9, A9), (A9, A10)) → C8
  20. Segment((A9, A10), (A10, A10)) → B9
  21. Segment((A10, A10), (A10, A11)) → C9
  22. Segment((A10, A11), (A11, A11)) → B10
  23. Segment((A11, A11), (A11, A12)) → C10
  24. Segment((A11, A12), (A12, A12)) → B11
  25. Segment((A12, A12), (A12, A13)) → C11
  26. Segment((A12, A13), (A13, A13)) → B12
  27. Segment((A13, A13), (A13, A14)) → C12
  28. Segment((A13, A14), (A14, A14)) → B13
  29. Segment((A14, A14), (A14, A15)) → C13
  30. Segment((A14, A15), (A15, A15)) → B14
  31. Segment((A15, A15), (A15, A16)) → C14
  32. Segment((A15, A16), (A16, A16)) → B15
  33. Segment((A16, A16), (A16, A17)) → C15
  34. Segment((A16, A17), (A17, A17)) → B16
  35. Segment((A17, A17), (A17, A18)) → C16
  36. Segment((A17, A18), (A18, A18)) → B17
  37. Segment((A18, A18), (A18, A19)) → C17
  38. Segment((A18, A19), (A19, A19)) → B18
  39. Segment((A19, A19), (A19, A20)) → C18
  40. Segment((A19, A20), (A20, A20)) → B19
  41. Segment((A20, A20), (A20, A21)) → C19
  42. Segment((A20, A21), (A21, A21)) → B20
  43. Segment((A21, A21), (A21, A22)) → C20
  44. Segment((A21, A22), (A22, A22)) → B21
  45. Segment((A22, A22), (A22, A23)) → C21
  46. Segment((A22, A23), (A23, A23)) → B22
  47. Segment((A23, A23), (A23, A24)) → C22
  48. Segment((A23, A24), (A24, A24)) → B23
  49. Segment((A24, A24), (A24, A25)) → C23
  50. Segment((A24, A25), (A25, A25)) → B24
  51. Segment((A25, A25), (A25, A26)) → C24
  52. Segment((A25, A26), (A26, A26)) → B25
  53. Segment((A26, A26), (A26, A27)) → C25
  54. Segment((A26, A27), (A27, A27)) → B26
  55. Segment((A27, A27), (A27, A28)) → C26
  56. Segment((A27, A28), (A28, A28)) → B27
  57. Segment((A28, A28), (A28, A29)) → C27
  58. Segment((A28, A29), (A29, A29)) → B28
  59. Segment((A29, A29), (A29, A30)) → C28
  60. Segment((A29, A30), (A30, A30)) → B29
  61. Segment((A30, A30), (A30, A31)) → C29
  62. Segment((A30, A31), (A31, A31)) → B30
  63. Segment((A31, A31), (A31, A32)) → C30
  64. Segment((A31, A32), (A32, A32)) → B31
  65. Segment((A32, A32), (A32, A33)) → C31
  66. Segment((A32, A33), (A33, A33)) → B32
  67. Segment((A33, A33), (A33, A34)) → C32
  68. Segment((A33, A34), (A34, A34)) → B33
  69. Segment((A34, A34), (A34, A35)) → C33
  70. Segment((A34, A35), (A35, A35)) → B34
  71. Segment((A35, A35), (A35, A36)) → C34
  72. Segment((A35, A36), (A36, A36)) → B35
  73. Segment((A36, A36), (A36, A37)) → C35
  74. Segment((A36, A37), (A37, A37)) → B36
  75. Segment((A37, A37), (A37, A38)) → C36
  76. Segment((A37, A38), (A38, A38)) → B37
  77. Segment((A38, A38), (A38, A39)) → C37
  78. Segment((A38, A39), (A39, A39)) → B38
  79. Segment((A39, A39), (A39, A40)) → C38

AI 绘图提示语参考

在坐标平面上绘制一个蛛网图，用于展示非线性映射的迭代过程。首先在坐标轴上选取两个初始点，一个位于纵轴，一个位于横轴。从横轴上的点出发，作一条垂直线段连接到函数曲线上的对应点，然后从该点作水平线段连接到直线y=x上的点，如此反复交替，形成一系列阶梯状的折线。这些折线逐步逼近函数曲线与对角线的交点，直观呈现迭代收敛的趋势。图形包含函数曲线、对角线、坐标轴以及多组垂直和水平线段，整体呈现清晰的蛛网结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。