分形曲线4 by Steve Phelps

分形曲线4 by Steve Phelps
几何画板及绘图内容加载中,请稍等……
2019-10-28 07:24
该范例演示了分形曲线4的生成过程。涉及的核心数学概念包括分形几何和幂函数。通过使用PolyLine和Rotate命令,构造了一系列旋转的点,形成了复杂的分形图案。适合高中及以上学生学习分形几何和函数变换。

GeoGebra 命令及参数

  1. PolyLine(A, E, F, B) → f
  2. Rotate(A1, (4 * π / 3), B) → B1
  3. Rotate(Translate[A1, D - B], (2 * π / 3), D) → C1
  4. Rotate(Dilate[{A1, B1, C1}, 0.5], (-2 * π / 6)) → A2
  5. Rotate(A2, (4 * π / 3), B) → B2
  6. Rotate(Translate[A2, D - B], (2 * π / 3), D) → C2
  7. Rotate(Dilate[{A2, B2, C2}, 0.500000000000002], (-2 * π / 6)) → A3
  8. Rotate(A3, (4 * π / 3), B) → B3
  9. Rotate(Translate[A3, D - B], (2 * π / 3), D) → C3
  10. Rotate(Dilate[{A3, B3, C3}, 0.500000000000004], (-2 * π / 6)) → A4
  11. Rotate(A4, (4 * π / 3), B) → B4
  12. Rotate(Translate[A4, D - B], (2 * π / 3), D) → C4
  13. Rotate(Dilate[{A4, B4, C4}, 0.500000000000006], (-2 * π / 6)) → A5
  14. Rotate(A5, (4 * π / 3), B) → B5
  15. Rotate(Translate[A5, D - B], (2 * π / 3), D) → C5
  16. Rotate(Dilate[{A5, B5, C5}, 0.500000000000008], (-2 * π / 6)) → A6
  17. Rotate(A6, (4 * π / 3), B) → B6
  18. Rotate(Translate[A6, D - B], (2 * π / 3), D) → C6
  19. Rotate(Dilate[{A6, B6, C6}, 0.50000000000001], (-2 * π / 6)) → A7
  20. Rotate(A7, (4 * π / 3), B) → B7
  21. Rotate(Translate[A7, D - B], (2 * π / 3), D) → C7
  22. Rotate(Dilate[{A7, B7, C7}, 0.50000000000001], (-2 * π / 6)) → A8
  23. Rotate(A8, (4 * π / 3), B) → B8
  24. Rotate(Translate[A8, D - B], (2 * π / 3), D) → C8

AI 绘图提示语参考

绘制一个分形曲线,通过一系列旋转和缩放操作构建复杂图案。首先连接四个点形成初始多边形,然后依次对每个多边形进行旋转、平移和缩放,每次缩放后重复相同操作,形成递归分形结构,展示分形几何和幂函数的变换过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。