Cantor三分集

原文http://blog.csdn.net/fyzhao/archive/2007/01/18/1486592.aspx
     Cantor三分集的构造如下图所示，一条线段ab被均分为三段，保留其两边的两段，中间一段去掉，然后把得到的每一段再继续进行划分，如此反复。
    

      Cantor 三分集的绘制十分简单，是一种最简单的分形实例，它的算法如下：

cx = ax + ( bx – ax ) / 3

cy = ay + h

dx = bx – ( bx – ax ) / 3

dy = by + h

ay = ay – h

by = by – h

其中 h 为两层之间的距离。

        Cantor 三分集的 python 程序实现及其运行结果如下：

from Tkinter import *

class Cantor(Frame):
    
    limit = 1

    def __init__(self, master=None):
        Frame.__init__(self, master)
        self.grid()
        self.createWidgets()

    def createWidgets(self):
        self.draw = Canvas(self, width=800, height=500)
        self.draw.pack(side=LEFT)
        self.drawCanvas(100,100,700,100)

    def drawCanvas(self,ax,ay,bx,by):
        self.draw.create_line(ax,ay,bx,by)
        if ((bx-ax)>self.limit):
            cx = ax + (bx - ax) / 3;
            cy = ay + 50;
            dx = bx - (bx - ax) / 3;
            dy = by + 50;
            ay = ay + 50;
            by = by + 50;
            self.drawCanvas(ax,ay,cx,cy)
            self.drawCanvas(dx,dy,bx,by)
            



app = Cantor()
app.master.title("Cantor (recursive)")
app.mainloop()