Chaos game-混沌游戏

      In mathematics, the term chaos game, as coined by Michael Barnsley,originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating a sequence of points, starting with the initial random point, in which each point in the sequence is a given fraction of the distance between the previous point and one of the vertices of the polygon; the vertex is chosen at random in each iteration. Repeating this iterative process a large number of times, selecting the vertex at random on each iteration, and throwing out the first few points in the sequence, will often (but not always) produce a fractal shape. Using a regular triangle and the factor 1/2 will result in the Sierpinski triangle, while creating the proper arrangement with four points and a factor 1/2 will create a display of a "Sierpinski Tetrahedron", the three-dimensional analogue of the Sierpinski triangle. As the number of points is increased to a number N, the arrangement forms a corresponding (N-1)-dimensional Sierpinski Simplex.

Sierpinski triangle的原理图：

我的计算机图形学基础教程中绘制的Sierpinski triangle效果图：

Chaos game之Sierpinski triangle代码（孔令德编写）：

void CTestView::ChaosGame(int n)

{

     CClientDC dc(this);

     double x=100,y=100;

     double x1,y1;

     double xa=MaxX/2,ya=MaxY/2-300;//三角形顶点A的坐标

     double xb=MaxX/2-300,yb=MaxY/2+300;//三角形顶点B的坐标

     double xc=MaxX/2+300,yc=MaxY/2+300;//三角形顶点C的坐标

    for(int k=n;k>0;k--)

    {

          double r=double(rand())/RAND_MAX;

          if(r<=0.3)//计算随机产生的三角形顶点A和上一点连线的中点坐标

         {

                x1=(x+xa)/2;y1=(y+ya)/2;

         }

        else if(r<=0.6)//计算随机产生的三角形顶点B和上一点连线的中点坐标

         {

              x1=(x+xb)/2;y1=(y+yb)/2;

         }

         else//计算随机产生的三角形顶点C和上一点连线的中点坐标

        {

              x1=(x+xc)/2;y1=(y+yc)/2;

        }

         x=x1;y=y1;

         dc.SetPixelV((ROUND(x)),ROUND((y)),RGB(x*r,r*200,y*r*1000));      

      }
}  

我绘制的Sierpinski Tetrahedron效果图：