C++ 生成洛伦兹的蝴蝶

这里使用 C++ 计算轨迹，生成 Python 文件，使用 matplotlib 绘图。

 // simulator.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
 //

 #include "pch.h" //预编译头，自行添加相关头文件

 struct vec
 {
     double x;
     double y;
     double z;
 };

 vec operator*(vec v, double n)
 {
     return { v.x * n , v.y * n , v.z * n};
 }

 vec operator+(vec &x, vec &y)
 {
     return {x.x + y.x, x.y + y.y, x.z + y.z};
 }

 //参数
 double a = ;
 double b = ;
 double c = ;

 vec velocity(vec &pos)
 {
     vec velocity;
     velocity.x = a * (pos.y - pos.x);
     velocity.y = pos.x * (b - pos.z) - pos.y;
     velocity.z = pos.x * pos.y - c * pos.z;

     return velocity;
 }

 //时间微元
 double dt = 0.001;

 int main()
 {
     std::vector<vec> state;

 　　 //初始条件
     vec init_state = { 5.0, 5.0 , 5.0};

     vec p = init_state;

     int ii = ;
     for (int i = ; i < ii; ++i)
     {
         vec v = velocity(p);
         vec dp = v * dt;
         p = p + dp;
         state.push_back(p);
         printf("\r[%2.1lf%%|%5d] p -> (%lf,%lf,%lf)", (double)i / ii * , i, p.x, p.y, p.z);
     }

     printf("\n\nsaving...");

     //输出python文件

     std::ostringstream ox;
     std::ostringstream oy;
     std::ostringstream oz;

     ox << "[";
     oy << "[";
     oz << "[";

     for (size_t i = ; i < state.size(); ++i)
     {
         ox << state[i].x;
         oy << state[i].y;
         oz << state[i].z;

         ox << ",";
         oy << ",";
         oz << ",";

         if ((i + ) %  == )
         {
             ox << std::endl;
             oy << std::endl;
             oz << std::endl;
         }
     }

     ox << "]";
     oy << "]";
     oz << "]";

     std::ofstream f;
     f.open("output.py");

     f << "import numpy as np" << std::endl;
     f << "import matplotlib.pyplot as plt" << std::endl;
     f << "from mpl_toolkits.mplot3d import Axes3D" << std::endl;

     f << "x = " << ox.str();
     f << std::endl;
     f << "y = " << oy.str();
     f << std::endl;
     f << "z = " << oz.str();
     f << std::endl;

     f << "X = np.array(x)" << std::endl;
     f << "Y = np.array(y)" << std::endl;
     f << "Z = np.array(z)" << std::endl;

     f << std::endl;

     // f << "" << std::endl;
     f << "fig = plt.figure()" << std::endl;
     f << "ax = Axes3D(fig)" << std::endl;
     f << "ax.plot(X, Y, Z)" << std::endl;
     f << "plt.show()" << std::endl;
     f << "" << std::endl;

     f.close();
 }

然后会输出 output.py

依赖的包有：numpy, matplotlib

然后直接执行 >python output.py即可

结果：