c# 实现雪花分形的示例

public partial class Form1 : Form
 {
  public Form1()
  {
   InitializeComponent();
  }

  private void Form1_Paint(object sender, PaintEventArgs e)
  {
   DrawKochSnow(e.Graphics);
  }

  private void ZheXian(Point p1, Point p2, Graphics g) // 4条基本线段组成的折线
  {
   Point p3 = new Point(p1.X + (p2.X - p1.X) / 3, p1.Y + (p2.Y - p1.Y) / 3); // 三等分点坐标
   Point p4 = new Point(p1.X + (p2.X - p1.X) * 2 / 3, p1.Y + (p2.Y - p1.Y) * 2 / 3); // 三等分点坐标
   Point p4XD3 = new Point(p4.X - p3.X, p4.Y - p3.Y); // p4相对于p3点的坐标
   //int x = (int)(p4XD3.X * Math.Cos(Math.PI / 3) - p4XD3.Y * Math.Sin(Math.PI / 3));
   //int y = (int)(p4XD3.X * Math.Sin(Math.PI / 3) + p4XD3.Y * Math.Cos(Math.PI / 3));
   // 注意计算机的屏幕垂直坐标和数学上相反，所以数学上逆时针旋转在计算机上相当于顺时针旋转
   int x = (int)Math.Round(p4XD3.X * Math.Cos(Math.PI / 3) + p4XD3.Y * Math.Sin(Math.PI / 3));
   int y = (int)Math.Round(p4XD3.Y * Math.Cos(Math.PI / 3) - p4XD3.X * Math.Sin(Math.PI / 3));
   Point p5XD3 = new Point(x, y); // 凸起点p5相对于p3点的坐标
   Point p5 = new Point(p3.X + x, p3.Y + y); // p5相对于原点的坐标
   Pen pen = new Pen(Brushes.Black, 1);
   double length = Math.Sqrt(Math.Pow(p2.X - p1.X, 2) + Math.Pow(p2.Y - p1.Y, 2)) / 3;
   //Console.WriteLine(length);
   if (length > 20) // 通过最终线段长度可以控制迭代
   {
    ZheXian(p1, p3, g);
    ZheXian(p3, p5, g);
    ZheXian(p5, p4, g);
    ZheXian(p4, p2, g);
   }
   else
   {
    g.DrawLine(pen, p1, p3);
    g.DrawLine(pen, p3, p5);
    g.DrawLine(pen, p5, p4);
    g.DrawLine(pen, p4, p2);
   }
  }

  private void DrawKochSnow(Graphics g) // 科赫雪花(瑞典人科赫于1904年提出了著名的“雪花”曲线)
  {
   int length = 480;
   Point origin = new Point(this.ClientSize.Width / 2, this.ClientSize.Height / 2);
   g.FillEllipse(Brushes.Blue, new RectangleF(origin, new Size(10, 10)));
   // 计算三角形的顶点让其中心和窗体的中心重合
   Point A = new Point(origin.X - length / 2, (int)(origin.Y + length / (2 * Math.Sqrt(3))));
   Point B = new Point(origin.X, (int)(origin.Y - length / Math.Sqrt(3)));
   Point C = new Point(origin.X + length / 2, (int)(origin.Y + length / (2 * Math.Sqrt(3))));
   ZheXian(A, B, g);
   ZheXian(B, C, g);
   ZheXian(C, A, g);
  }
 }