分形之——递归

学习了递归之后，可以实现很多有规律并且漂亮的图形，如：科赫曲线，漂亮的雪花，谢尔宾斯基三角形，毕哥拉斯树等等
[img]http://dl2.iteye.com/upload/attachment/0086/2524/5cd6e8d4-b0a8-3251-ba88-43691153f658.png" alt="[/img]

[img]http://dl2.iteye.com/upload/attachment/0086/2526/88529b66-6d97-303a-86d3-27447ecd5530.png" alt="[/img]

[img]http://dl2.iteye.com/upload/attachment/0086/2528/9c57617c-289b-3664-ac7b-1d092196ebf6.png" alt="[/img]

[img]http://dl2.iteye.com/upload/attachment/0086/2530/e602ac67-b1be-3ae8-a649-8918dca1f8e8.png" alt="[/img]

[img]http://dl2.iteye.com/upload/attachment/0086/2533/9f2dd30f-5509-3e6f-b068-cba768b117ee.png" alt="[/img]

各个图形相应代码如下：

package digui; 
import java.awt.Dimension; 
import java.awt.FlowLayout; 
import java.awt.event.ActionListener; 

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

public class Arts extends JFrame{ 
public static void main(String[] args) { 
Arts sf = new Arts(); 
sf.InitUI(); 
} 

private void InitUI() { 
this.setSize(new Dimension(700, 700)); 
this.setTitle("picture"); 
this.setDefaultCloseOperation(3); 
this.setLayout(new FlowLayout()); 
this.setLocationRelativeTo(null); 
       String S[]={"Kehe","Line","square","xtriangle"}; 
       For(int i=0;i 



[code="java"]package Kehe; 

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

import javax.swing.JFrame; 

public class SListener implements ActionListener { 

private JFrame jf; 
int count; 
int PI; 

public SListener(JFrame jf) { 
this.jf = jf; 
} 

public void actionPerformed(ActionEvent e) { 
String v = e.getActionCommand(); 
Graphics g = jf.getGraphics(); 
Color c = new Color(230, 20, 230); 
g.setColor(c); 
if (v.equals("Kehe")) { 
Draw(8, 150, 500, 550, 500, g); 
} 

public void Draw(int count, double x1, double y1, double x2, double y2, 
Graphics g) { 

if (count == 0) { 
System.out.println("" + x1 + y1 + "" + x2 + "" + y2 + ""); 
g.drawLine((int) x1, (int) y1, (int) x2, (int) y2); 
} else { 
// 取最接近的数 
double x3 = Math.round(x1 + (x2 - x1) / 3.0); 
double y3 = Math.round(y1 + (y2 - y1) / 3.0); 
double x4 = Math.round(2 * (x2 - x1) / 3 + x1); 
double y4 = Math.round(y1 - 2 * (y1 - y2) / 3); 
double l = Math.sqrt((x4 - x3) * (x4 - x3) + (y4 - y3) * (y4 - y3)); 
double angle = getAngle(x1, y1, x2, y2); 
double x5 = Math.round(x3 + l * Math.cos(angle)); 
double y5 = Math.round(y3 - l * Math.sin(angle)); 
Draw(count - 1, x1, y1, x3, y3, g); 
Draw(count - 1, x3, y3, x5, y5, g); 
Draw(count - 1, x5, y5, x4, y4, g); 
Draw(count - 1, x4, y4, x2, y2, g); 

} 
} 

 
谢尔宾斯基三角形代码如下：

package Kehe; 

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

import javax.swing.JFrame; 

public class SListener implements ActionListener { 

private JFrame jf; 
int count; 
int PI; 

public SListener(JFrame jf) { 
this.jf = jf; 
} 

public void actionPerformed(ActionEvent e) { 
String v = e.getActionCommand(); 
Graphics g = jf.getGraphics(); 
Color c = new Color(230, 20, 230); 
g.setColor(c); 
if (v.equals(""xtriangle"")) { 
                xtriangle(g,100,400,400,4);} 
public void xtriangle(Graphics g, int x1, int x2, int y1, int count) { 
g.setColor(Color.blue); 
if (count == 0) 
return; 
/**  
     * 定义绘制谢尔宾斯基三角形的方法  
     * @param x1 三角形左下角横坐标  
     * @param x2 三角形右下角横坐标  
     * @param y1 三角形左下角纵坐标  
     * @param count 递归过程中的计数器  
     */  

// 画最大的三角形,x1,x2,y1,y2,z1,z2分别表示最大的三角形的三个顶点坐标 
int y2 = x2; 
g.drawLine(x1, x2, y1, y2); 
int z2 = (int) (x2 - Math.sqrt(3) * Math.abs(y1 - x1) / 2); 
int z1 = (int) (x1 / 2 + y1 / 2); 
g.drawLine(z1, z2, x1, x2); 
g.drawLine(z1, z2, y1, y2); 
// a1,a2,b1,b2,c1,c2分别表示内部第一个三角形的三个顶点 
int a1 = x1 / 2 + z1 / 2; 
int a2 = x2 / 2 + z2 / 2; 
int b1 = z1 / 2 + y1 / 2; 
int b2 = z2 / 2 + y2 / 2; 
int c1 = x1 / 2 + y1 / 2; 
int c2 = x2; 

// 内部第一个三角形 
g.drawLine(a1, a2, b1, b2); 
g.drawLine(a1, a2, c1, c2); 
g.drawLine(b1, b2, c1, c2); 

// 用m1,m2,m3,m4表示新增上边的小三角形的底边 
// 用n1,n2,n3,n4表示新增左边的小三角形的底边 
// 用p1,p2,p3,p4表示新增右边的小三角形的底边 
int m1 = a1; 
int m2 = a2; 
int m3 = b1; 
int n1 = x1; 
int n2 = x2; 
int n3 = z1; 
int p1 = c1; 
int p2 = c2; 
int p3 = y1; 

xtriangle(g, m1, m2, m3, count - 1); 
xtriangle(g, n1, n2, n3, count - 1); 
xtriangle(g, p1, p2, p3, count - 1); 

} 
} 

 
雪花的代码如下：

package digui; 
/** 
* 雪花 
*/ 

import java.awt.event.MouseListener; 
import java.awt.Color; 
import java.awt.Graphics; 
import java.awt.event.MouseEvent; 

public class IceListener implements MouseListener { 
Graphics g; 
int depth = 10; 

public IceListener(Graphics g) { 
this.g = g; 
} 

public void mouseClicked(MouseEvent e) { 
digui1(100, 200, 600, 200, this.depth); 
digui2(100, 200, 350, 633, this.depth); 
digui3(600, 200, 350, 633, this.depth); 
} 

public void mouseEntered(MouseEvent arg0) { 

} 

public void mouseExited(MouseEvent arg0) { 

} 

public void mousePressed(MouseEvent arg0) { 

} 

public void mouseReleased(MouseEvent arg0) { 

} 

// 第一个递归函数 
public void digui1(double x1, double y1, double x2, double y2, int depth) { 
g.setColor(Color.blue); 
if (depth  0) { 
x5 = x2; 
y5 = y3; 
} 
} 
digui1(x1, y1, x3, y3, depth - 1); 
digui1(x3, y3, x5, y5, depth - 1); 
digui1(x5, y5, x4, y4, depth - 1); 
digui1(x4, y4, x2, y2, depth - 1); 
} 
} 

// 第二个递归函数 
public void digui2(double x1, double y1, double x2, double y2, int depth) { 
g.setColor(Color.red); 
if (depth  0) { 
x5 = x1; 
y5 = y4; 
} 
} 
digui2(x1, y1, x3, y3, depth - 1); 
digui2(x3, y3, x5, y5, depth - 1); 
digui2(x5, y5, x4, y4, depth - 1); 
digui2(x4, y4, x2, y2, depth - 1); 
} 
} 

public void digui3(double x1, double y1, double x2, double y2, int depth) { 
g.setColor(Color.yellow); 
if (depth  0) { 
x5 = x2; 
y5 = y3; 
} 
} 
digui3(x1, y1, x3, y3, depth - 1); 
digui3(x3, y3, x5, y5, depth - 1); 
digui3(x5, y5, x4, y4, depth - 1); 
digui3(x4, y4, x2, y2, depth - 1); 
} 
} 

 
等分线的代码：

public void Draw1(Graphics g, int x1, int y1, int x2, int y2, int count) { 
if (count == 0) 
return; 
g.drawLine(x1, y1, x2, y2); 
// 递归定义变量时要为局部变量 
int x3, y3, x4, y4, x5, y5, x6, y6; 
int gap = 50; 
x3 = x1 + gap; 
y3 = y1; 
x4 = gap + x2; 
y4 = (y2 - y1) / 3 + y1; 
x5 = x1 + gap; 
y5 = y2 - 1 * (y2 - y1) / 3; 
x6 = x2 + gap; 
y6 = y2; 
g.drawLine(x3, y3, x4, y4); 
g.drawLine(x5, y5, x6, y6); 
// 调用自身方法 
Draw1(g, x3, y3, x4, y4, count - 1); 
Draw1(g, x5, y5, x6, y6, count - 1); 

}