遞迴分形樹 --》 此做法相當於二叉樹先序遍歷  --  先畫出此樹幹，再遞迴畫出兩個枝幹。

畫枝幹時需要求出兩個枝幹的終點，需要運用一個幾何的方法--- 
通過 repaint 呼叫paintComponent 來補充樹幹--
atan2 和 atan 的 區別  --  atan（x/y）時，y = 0 就會出錯，我開始的程式碼在n=10左右時就出錯了，看了老師的程式碼然後改為了atan2就可以了。

程式執行如圖所示：

程式碼：

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class Recursive extends JFrame{
	private Tree t = new Tree();
	private JButton jb = new JButton("Increase");
	public Recursive(){
		this.add(t);
		JPanel panel = new JPanel();
		panel.add(jb);
		this.add(panel,BorderLayout.SOUTH);
		jb.addActionListener(new ActionListener() {
			@Override
			public void actionPerformed(ActionEvent e) {
				t.run();
			}
		});
	}
	public static void main(String[] args) {
		Recursive f = new Recursive();
		f.setTitle("遞迴分形樹");
		f.setSize(600,600);
		f.setLocationRelativeTo(null);
		f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
		f.setVisible(true);
	}
}

class Tree extends JPanel{
	private int n = 0;
	private double A,B,C;
	private double PI = Math.acos(-1.0);
	protected void paintComponent(Graphics g){
		super.paintComponent(g);
		g.setColor(Color.red);
		Point p1 = new Point(this.getWidth()/2,this.getHeight()-10);
		Point p2 = new Point(this.getWidth()/2,this.getHeight()/2);
		display(g,n,p1,p2);
	}
	public void run(){
		n++;
		repaint();
	}
	private void display(Graphics g,int n,Point p1,Point p2){
		if (n>=0){
			g.drawLine(p1.x, p1.y, p2.x, p2.y);
			Point p3 = mid1(p1,p2);
			Point p4 = mid2(p1,p2);
			//System.out.println(p1.x+" "+p1.y+" "+p2.x+" "+p2.y);
			display(g, n-1, p2, p3);
			display(g, n-1, p2, p4);
		}
	}
	private Point mid1(Point p1,Point p2){
		Point p = new Point();
		A = Math.atan2(p2.x-p1.x,p1.y-p2.y);
		//A = Math.atan((double)(p2.x-p1.x)/(p1.y-p2.y));
		B = A - PI/6;
		C = Math.sqrt((p2.x-p1.x)*(p2.x-p1.x)+(p2.y-p1.y)*(p2.y-p1.y))/2;
		p.x= (int)(p2.x + C*Math.sin(B));
		p.y= (int)(p2.y - C*Math.cos(B));
		return p;
	}
	private Point mid2(Point p1,Point p2){
		Point p = new Point();
		A = Math.atan2(p2.x-p1.x,p1.y-p2.y);
		B = A + PI/6;
		C = Math.sqrt((p2.x-p1.x)*(p2.x-p1.x)+(p2.y-p1.y)*(p2.y-p1.y))/2;
		p.x= (int)(p2.x + C*Math.sin(B));
		p.y= (int)(p2.y - C*Math.cos(B));
		if (p.x==0){
			System.out.println(p1.x+" "+p1.y+" "+p2.x+" "+p2.y+" "+A);
		}
		return p;
	}
}