公式和递归实现的初步分形【2-递归篇】

陌陌天使

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基础知识总结

上一篇介绍了一些有数学公式实现分型的例子，下面将介绍一些由递归实现的分形。

由递归实现分形是应该注意：1.一定要用一个标志来结束循环，不然会系统会抛出堆溢出错误

2.尽量把思路理清，把代码简化

谢宾斯基三角形

升级版谢宾斯基三角形，有3D效果

谢宾斯基地毯

科赫曲线

科赫雪花

package cn.kml.递归20130706;

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;

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

public class Triangle extends JFrame{
	
	//窗体可见后，获取窗体上的画布对象
	private Graphics g;
	
	//程序的入口主函数
	public static void main(String[] args) {
		
		
		Triangle tr = new Triangle();
		tr.unitUI();
	}   
		public void unitUI(){
			this.setTitle("Recursion");
			this.setSize(900,700);
			//在窗体上实例化一个面板对象
			JPanel jp = new JPanel();
			//设置面板的大小
			jp.setPreferredSize(new Dimension(150,0));
			//在面板上加一个按钮对象
			JButton bu = new JButton("Sierpinske");
			JButton bu1 = new JButton("Rectangle");
			JButton bu3 = new JButton("Koch-Snow");
			JButton bu2 = new JButton("Koch Curve");
			JButton bu4 = new JButton("Tree");
			jp.add(bu);
			jp.add(bu1);
			jp.add(bu2);
			jp.add(bu3);
			jp.add(bu4);
			bu.setForeground(Color.BLUE);
			bu1.setForeground(Color.BLUE);
			bu2.setForeground(Color.BLUE);
			bu3.setForeground(Color.BLUE);
			bu4.setForeground(Color.BLUE);
			bu.setBackground(Color.LIGHT_GRAY);
			bu1.setBackground(Color.LIGHT_GRAY);
			bu2.setBackground(Color.LIGHT_GRAY);
			bu3.setBackground(Color.LIGHT_GRAY);
			bu4.setBackground(Color.LIGHT_GRAY);
			//把面板加到窗体上
			this.add(jp,BorderLayout.EAST);
			this.setLocationRelativeTo(null);
			this.setDefaultCloseOperation(3);
			this.getContentPane().setBackground(Color.BLACK);//设置背景颜色
			this.setVisible(true);
			//窗体可见后，获取画布对象
			g= this.getGraphics();
			RecuesionListener rl = new RecuesionListener(g);
			bu.addActionListener(rl);
			bu1.addActionListener(rl);
			bu2.addActionListener(rl);
			bu3.addActionListener(rl);
			bu4.addActionListener(rl);
		}
		
		
}

package cn.kml.递归20130706;

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

public class RecuesionListener implements ActionListener{
	private Graphics g;
	static int state=10;
	static int state1=6;
	static int state2=2;
	static int state3=7;
	static int state4=7;
	static int state5=10;
	
	public RecuesionListener(Graphics g){
		this.g=g;
	}
	public void actionPerformed(ActionEvent e) {
//		g.clearRect(0, 0, 750, 690);
		if(e.getActionCommand().equals("Sierpinske")){
			g.setColor(Color.WHITE);
			draw(350, 60, 50, (int)(50+300*Math.sqrt(3))+10, 650, (int)(50+300*Math.sqrt(3))+10, state);
//			g.setColor(new Color(210,210,200));
//			draw(340, 65, 40, (int)(50+300*Math.sqrt(3))+15, 640, (int)(50+300*Math.sqrt(3))+15, state);
//			g.setColor(new Color(180,180,170));
//			draw(330, 70, 30, (int)(50+300*Math.sqrt(3))+20, 630, (int)(50+300*Math.sqrt(3))+20, state);
			
		}
		
		if(e.getActionCommand().equals("Rectangle")){
			drawRec(50,50,650,state1);
		}
		if(e.getActionCommand().equals("Koch Curve")){
			drawKoch(50,600,700,600,state3);
		}
		if(e.getActionCommand().equals("Koch-Snow")){
			drawSnow(700,550,400,(int)(550-Math.sqrt(3)*300),100,550,state4);
		}
		if(e.getActionCommand().equals("Tree")){
			drawTree1(300,600,100,5,1);
		}
	}
	public void draw(int x1,int y1,int x2,int y2,int x3,int y3,int state){
		state--;
		if(state>0){
		//画出最外面的三角形
			g.drawLine(x1, y1, x2, y2);
			g.drawLine(x1, y1, x3, y3);
			g.drawLine(x2, y2, x3, y3);
			//算出任意两点的中点坐标
				int x12=(int)((x1+x2)/2);
				int y12=(int)((y1+y2)/2);
				int x23=(int)((x2+x3)/2);    
				int y23=(int)((y2+y3)/2);
				int x13=(int)((x1+x3)/2);
				int y13=(int)((y1+y3)/2);
				g.drawLine(x12, y12, x13, y13);
				g.drawLine(x12, y12, x23, y23);
				g.drawLine(x13, y13, x23, y23);
	
	//递归调用
	draw(x1,y1,x12,y12,x13,y13,state);
	draw(x12,y12,x2,y2,x23,y23,state);
	draw(x13,y13,x23,y23,x3,y3,state);
	}else{
		return;
	}
	}
	
	public void drawRec(int x1,int y1,int x2,int state1){
		state1--;
		//先画出最外围的正方形
		g.drawLine(50,50,650,50);
		g.drawLine(50,50,50,650);
		g.drawLine(650,50,650,650);
		g.drawLine(50,650,650,650);
		//循环化出里面的正方形
		if(state1>0){
			int x11=(int)((x2-x1)/3+x1);
			int x22=(int)(2*(x2-x1)/3+x1);
			int y11=(int)((x2-x1)/3+y1);
			int y22=(int)(2*(x2-x1)/3+y1);
			g.fillRect(x11, y11, x22-x11,x22-x11);
		//递归调用函数
			drawRec(x1,y1,x11,state1);
			drawRec(x22,y1,x2,state1);
			drawRec(x1,y22,x11,state1);
			drawRec(x22,y22,x2,state1);
			drawRec(x11,y1,x22,state1);
			drawRec(x22,y11,x2,state1);
			drawRec(x11,y22,x22,state1);
			drawRec(x1,y11,x11,state1);
		}else{
			return;
		}
	}
	
	public void drawKoch(int x1,int y1,int x2,int y2,int state3){
		int x3 = (2*x1+x2)/3;
		int x4 = (x1+2*x2)/3;
		int y3 = (2*y1+y2)/3;
		int y4 = (y1+2*y2)/3;
		int x5=0,y5=0;
		g.setColor(Color.BLUE);
		if(y1 == y2){
			x5 = (x3+x4)/2;
			y5 = (int)(y1-Math.sqrt(3)*(x4-x3)/2);
		}else if(y1>y2){
			if(x1<x2){
				x5 = x1;
				y5 = y4;
			}else if(x1>x2){
				x5 = x2;
				y5 = y3;
			}
			}else if(y1<y2){
				if(x1>x2){
					x5 = x1;
					y5 = y4;
				}else if(x1<x2){
					x5 = x2;
					y5 = y3;
				}
			}
		if(state3==1){
			g.drawLine(x1, y1, x2, y2);
			}
		if(state3<=0){
			return;
		}
		drawKoch(x1,y1,x3,y3,state3-1);
		drawKoch(x3,y3,x5,y5,state3-1);
		drawKoch(x5,y5,x4,y4,state3-1);
		drawKoch(x4,y4,x2,y2,state3-1);
		}
	public void drawSnow(int x1,int y1,int x2,int y2,int x3,int y3,int state4){
		g.setColor(Color.BLUE);
		if(state4>0){
		drawKoch(x2,y2,x1,y1,state4-1);
		drawKoch(x3,y3,x2,y2,state4-1);
		drawKoch(x1,y1,x3,y3,state4-1);
		}else{
			return;
		}
		
	
	}

	}