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猫迷宫的副本

猫迷宫的副本
几何画板及绘图内容加载中，请稍等……
2018-01-07 19:42
函数三角函数数列概率统计几何作图
①这个范例演示了一个动态的猫迷宫路径生成过程；②涉及的核心数学概念包括逻辑、函数、内切圆、自然数、随机过程和线段；③作图要点提炼了GeoGebra命令中的Sequence（序列）、If（条件判断）、Conic（圆锥曲线）、Turtle（海龟绘图）、Point（点）、Segment（线段）、IndexOf（索引）、Shuffle（洗牌）、Random（随机）、Polygon（多边形）、Flatten（展平）、Min（最小值）；④适合高中及以上学生学习和探索随机过程与几何作图的结合应用。

GeoGebra 命令及参数

  1. Sequence(Segment[(-0.5 + i, -0.5), (-0.5 + i, 9.5)], i, 0, 10) → list1
  2. Sequence(Segment[(-0.5, -0.5 + i), (9.5, -0.5 + i)], i, 0, 10) → list2
  3. If(Mod[orient, 4] ≟ 0, "right", If[Mod[orient, 4] ≟ 1, "up", If[Mod[orient, 4] ≟ 2, "left", "down"]]) → facing
  4. Conic(A - (0.3, 0.3), A - (0.35, 0), A - (0.15, -0.2), A + (0.15, 0.25), A + (0.35, -0.25)) → c
  5. Turtle() → jack
  6. Point({x(jack) + (facing ≟ "right") - (facing ≟ "left"), y(jack) + (facing ≟ "up") - (facing ≟ "down")}) → laserpoint
  7. Segment((x(jack), y(jack)), laserpoint) → laserline
  8. Conic(A_1 - (0.3, 0.3), A_1 - (0.35, 0), A_1 - (0.15, -0.2), A_1 + (0.15, 0.25), A_1 + (0.35, -0.25)) → c_1
  9. Conic(A_2 - (0.3, 0.3), A_2 - (0.35, 0), A_2 - (0.15, -0.2), A_2 + (0.15, 0.25), A_2 + (0.35, -0.25)) → c_2
  10. Conic(A_3 - (0.3, 0.3), A_3 - (0.35, 0), A_3 - (0.15, -0.2), A_3 + (0.15, 0.25), A_3 + (0.35, -0.25)) → c_3
  11. Conic(A_4 - (0.3, 0.3), A_4 - (0.35, 0), A_4 - (0.15, -0.2), A_4 + (0.15, 0.25), A_4 + (0.35, -0.25)) → c_4
  12. Conic(A_5 - (0.3, 0.3), A_5 - (0.35, 0), A_5 - (0.15, -0.2), A_5 + (0.15, 0.25), A_5 + (0.35, -0.25)) → c_5
  13. Conic(A_6 - (0.3, 0.3), A_6 - (0.35, 0), A_6 - (0.15, -0.2), A_6 + (0.15, 0.25), A_6 + (0.35, -0.25)) → c_6
  14. Conic(A_7 - (0.3, 0.3), A_7 - (0.35, 0), A_7 - (0.15, -0.2), A_7 + (0.15, 0.25), A_7 + (0.35, -0.25)) → c_7
  15. Conic(A_8 - (0.3, 0.3), A_8 - (0.35, 0), A_8 - (0.15, -0.2), A_8 + (0.15, 0.25), A_8 + (0.35, -0.25)) → c_8
  16. Conic(A_9 - (0.3, 0.3), A_9 - (0.35, 0), A_9 - (0.15, -0.2), A_9 + (0.15, 0.25), A_9 + (0.35, -0.25)) → c_9
  17. Conic(A_{10} - (0.3, 0.3), A_{10} - (0.35, 0), A_{10} - (0.15, -0.2), A_{10} + (0.15, 0.25), A_{10} + (0.35, -0.25)) → c_{10}
  18. Conic(A_{11} - (0.3, 0.3), A_{11} - (0.35, 0), A_{11} - (0.15, -0.2), A_{11} + (0.15, 0.25), A_{11} + (0.35, -0.25)) → c_{11}
  19. Conic(A_{12} - (0.3, 0.3), A_{12} - (0.35, 0), A_{12} - (0.15, -0.2), A_{12} + (0.15, 0.25), A_{12} + (0.35, -0.25)) → c_{12}
  20. Conic(A_{13} - (0.3, 0.3), A_{13} - (0.35, 0), A_{13} - (0.15, -0.2), A_{13} + (0.15, 0.25), A_{13} + (0.35, -0.25)) → c_{13}
  21. Conic(A_{14} - (0.3, 0.3), A_{14} - (0.35, 0), A_{14} - (0.15, -0.2), A_{14} + (0.15, 0.25), A_{14} + (0.35, -0.25)) → c_{14}
  22. Conic(A_{15} - (0.3, 0.3), A_{15} - (0.35, 0), A_{15} - (0.15, -0.2), A_{15} + (0.15, 0.25), A_{15} + (0.35, -0.25)) → c_{15}
  23. IndexOf(laserpoint, icelist) → iceindex
  24. Shuffle(Remove[Flatten[Sequence[Sequence[(i, j), i, 0, 9], j, 0, 9]], {(0, 0)}]) → list5
  25. Random(1, 16) → icenumber
  26. Random(1, 16) → stonenumber
  27. Polygon((0.5, -0.5), (0.5, 0.5), (-0.5, 0.5), (-0.5, 9.5), (-0.5, 9.5), (9.5, 9.5), (9.5, -0.5)) → region, a, b, d, e, f, g, h
  28. Polygon((-0.5, -0.5), (-0.5, 9.5), (9.5, 9.5), (9.5, -0.5)) → background, i, j, k, l
  29. Flatten(Remove[Join[{{Sequence[Sequence[(i, j), i, -1, 10, 1], j, -1, 10, 11], Sequence[Sequence[(i, j), i, -1, 10, 11], j, 0, 9]}, icelist, stonelist}], meltedice]) → alltowers
  30. Min(RemoveUndefined[Sequence[If[Defined[IndexOf[jack + ((laserpoint - jack) * i), alltowers]], i], i, 1, 5]]) → blockage

AI 绘图提示语参考

画一个动态生成猫迷宫路径的图形，包含10x10的网格和随机路径。路径由多个线段组成，起点在左下角，终点在右上角。路径生成过程中涉及随机选择方向（上、下、左、右），并在网格中留下痕迹。路径的生成基于随机数和条件判断，最终形成一个迷宫状的路径。背景为白色，网格为黑色，路径为蓝色。
以上提示语为根据原始绘图命令整理而来，仅供参考。