积极 AI Logo 积极 AI

托马斯吸引子

托马斯吸引子
几何画板及绘图内容加载中，请稍等……
2017-08-30 18:37
函数参数方程
所属专题 UQ-Applied Mathematical Analysis
这个范例展示了托马斯吸引子的动态变化。托马斯吸引子是一种混沌吸引子，由参数方程定义。通过调整参数，可以观察到吸引子的形态变化。该范例使用了GeoGebra中的参数方程命令，适合高中数学教学和研究混沌理论。

GeoGebra 命令及参数

  1. Numeric strength(5)
  2. Numeric n(12)
  3. Numeric h(0.01)
  4. Numeric speed(1)
  5. Numeric t(4.41)
  6. Numeric b(0.208186)
  7. x(CornerThreeD[-1, 3])
  8. x(CornerThreeD[-1, 1])
  9. y(CornerThreeD[-1, 3])
  10. y(CornerThreeD[-1, 1])
  11. z(CornerThreeD[-1, 5])
  12. z(CornerThreeD[-1, 3])
  13. {(-3.088783806756721, 1.168136040091289, 2.4092146463877135), (-1.067266093085597, -4.526392273525671, -1.2647999308806441), (4.543682308993006, -0.8625165719344299, 3.758402273622612), (5.31874067749
  14. {4.035969339822303, 2.5640068684061235, -0.5488025204846856, 1.6973833705951398, -1.6089006075240053, 3.255710387114754, -1.2449332890219835, 0.44041183228428177, 1.6012293652475966, -1.90560109628771
  15. {2.733327134413032, -3.5747872338096442, 0.8433804981200355, 0.4696137096695083, -0.3634135696995436, -5.534989044346133, 1.1011617143616148, -2.2392210889929838, 0.7845254086839506, -0.45671631349686
  16. {2.8886657735972325, 1.4402279875984714, -1.3523016627727336, -0.37930893474328625, 0.25207991548283737, -2.745374055522856, -1.7256404176220146, 1.6141422251964177, -2.883298518282407, -0.30129472715
  17. {4.0188274657474246, 2.5974154682502486, -0.5634828276654941, 1.6832501793784087, -1.5960168705620137, 3.357840639225082, -1.2651891520660596, 0.48715650315538567, 1.5969562696763235, -1.8907077403827
  18. {2.75544405271308, -3.5907998692147105, 0.8705302878924062, 0.4752751566388502, -0.3669496704258893, -5.562715723832097, 1.1117752441773454, -2.2677237377267794, 0.8449377770925273, -0.447866117655487
  19. {2.9342290483083877, 1.429948070893332, -1.3379561392625487, -0.4149909263812776, 0.28584729899567424, -2.670452048143659, -1.7477251882917264, 1.6024807305199102, -2.908313334254466, -0.2615642672040
  20. {4.018944145262599, 2.597447943441865, -0.5639701335031142, 1.6832597064937516, -1.5960399724077812, 3.357900626825879, -1.2653412387215845, 0.487535439595482, 1.5972880854285365, -1.8908818901504358,
  21. {2.75589495234996, -3.5904696886653493, 0.870053976020716, 0.4760077145817293, -0.3676580062148446, -5.561035690594278, 1.1119269501779971, -2.2672851604418014, 0.8451808595859309, -0.4487660983664943
  22. {2.9337379831643204, 1.4299598809136986, -1.3378348979967352, -0.41449098804038825, 0.28539001606491615, -2.6689256977786524, -1.7481158058834454, 1.6021940059448658, -2.9080763482125427, -0.262070361
  23. {4.000970668974891, 2.6294993366879513, -0.5790601859665776, 1.669094113635437, -1.5831468273852227, 3.4580034165260995, -1.2857177025138662, 0.5343227749771753, 1.5932584430439134, -1.876118572243801
  24. {2.7775122031002066, -3.606085005399855, 0.8968066245626816, 0.48236157568022076, -0.3718702062845805, -5.586527643657149, 1.1223437798494862, -2.2953698777911393, 0.905344240154623, -0.44078037574610
  25. {2.977192464233033, 1.4188492949226017, -1.3233227695140966, -0.44984063058479073, 0.3188605759133678, -2.5915598602557766, -1.770606201293751, 1.590214769504517, -2.932865104308529, -0.22256788772390
  26. F(x, y, z) = (strength * (sin(y) - (b * x)))
  27. G(x, y, z) = (strength * (sin(z) - (b * y)))
  28. H(x, y, z) = (strength * (sin(x) - (b * z)))

AI 绘图提示语参考

绘制 Thomas' Attractor，这是一个由参数方程定义的混沌吸引子。首先设置参数 strength 为 5，n 为 12，h 为 0.01，speed 为 1，t 为 4.41，b 为 0.208186。然后根据这些参数，使用参数方程 F(x, y, z) = strength * (sin(y) - (b * x))，G(x, y, z) = strength * (sin(z) - (b * y)) 和 H(x, y, z) = strength * (sin(x) - (b * z)) 来绘制图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。