Silverlight 画分形(Koch曲线)

Koch曲线是一类平面曲线：从一条线段中间三分之一的部分用等边三角形的两条边代替，形成的图形有四条边，五个节点。再依次组成边的每条线段做相同的处理。
迭代如图：


稍微变换一下，画成六边形的，凸起方向向两边，用随机颜色，画完后为雪花状。
程序代码：
private void LayoutRoot_Loaded(object sender, RoutedEventArgs ea)
{
    double sqrt3 = Math.Sqrt(3);

    Point a = new Point(50, (float)(100 + 50 * sqrt3));
    Point b = new Point(100, (float)(100 + 100 * sqrt3));
    Point c = new Point(200, (float)(100 + 100 * sqrt3));
    Point d = new Point(250, (float)(100 + 50 * sqrt3));
    Point e = new Point(200, 100);
    Point f = new Point(100, 100);

    line(a, b, 5);
    line(b, a, 5);

    line(b, c, 5);
    line(c, b, 5);

    line(c, d, 5);
    line(d, c, 5);

    line(d, e, 5);
    line(e, d, 5);

    line(e, f, 5);
    line(f, e, 5);

    line(f, a, 5);
    line(a, f, 5);
}

private void line(Point a, Point b, int n)
{
    if (n > 0)
    {
        double r = Math.Atan(Math.Abs(a.Y - b.Y) / Math.Abs(a.X - b.X)); //角度
        double v = 0;

        Point c = new Point(a.X + (b.X - a.X) / 3, a.Y + (b.Y - a.Y) / 3);
        Point d = new Point(a.X + 2 * (b.X - a.X) / 3, a.Y + 2 * (b.Y - a.Y) / 3);
        double l = Math.Sqrt((c.X - d.X) * (c.X - d.X) + (c.Y - d.Y) * (c.Y - d.Y));
        Point e;

        if (b.Y - a.Y >= 0 && b.X - a.X > 0)
        {
            v = r;
        }
        else if (b.Y - a.Y > 0 && b.X - a.X <= 0)
        {
            v = Math.PI - r;
        }
        else if (b.Y - a.Y <= 0 && b.X - a.X < 0)
        {
            v = Math.PI + r;
        }
        else if (b.Y - a.Y < 0 && b.X - a.X >= 0)
        {
            v = 2 * Math.PI - r;
        }


        e = new Point((float)(l * Math.Cos(v + Math.PI / 3) + c.X), (float)(c.Y + l * Math.Sin(v + Math.PI / 3)));


        line(a, c, n - 1);
        line(c, e, n - 1);
        line(e, d, n - 1);
        line(d, b, n - 1);
    }
    else
    {
        Line l = new Line();
        Random rnd = new Random();
        Color c = Color.FromArgb(255, (byte)rnd.Next(255), (byte)rnd.Next(255), (byte)rnd.Next());

        l.Stroke = new SolidColorBrush(c);
        l.X1 = a.X;
        l.Y1 = a.Y;
        l.X2 = b.X;
        l.Y2 = b.Y;

        LayoutRoot.Children.Add(l);
    }
}
运行结果如图： 

Koch曲线的每一部分都由4个跟它自身比例为1:3的形状相同的小曲线组成，那么它的豪斯多夫维数(分维数)为d=log(4)/log(3) =1.26185950714...