目录：

1.地毯理解及代码

2.三角形理解及代码

3.地毯+三角形+画图板表示

下图就是我在Java画图板上画出的一个谢尔宾斯地毯

1.地毯理解及代码

制作谢尔宾斯地毯我们需要用到——迭代

理解：

我们可以看出2图是由若干个1图这样的基本图形组成的

同样不管迭代多少次都是由基本图形组成

所以我们的任务就是画出1图这样的基本图形，剩下的就交给迭代去完成

算法

public void draw(Graphics g,int n,int x,int y,int width,int height) {

/**

*x:左上角x坐标，y:左上角y坐标

*width:宽，height：高

*n：迭代层次

*/

g.fillRect(x+width/3,y+height/3,width/3,height/3);

if(n==0)//递归结束条件

return;

n--;

//八个维度

draw(g,n,x, y, width/3, height/3); //1

draw(g,n,x+width/3, y, width/3, height/3);//2

draw(g,n,x+2*(width/3), y, width/3, height/3);//3

draw(g,n,x, y+height/3, width/3, height/3);//4

draw(g,n,x+2*(width/3), y+height/3, width/3, height/3);//5

draw(g,n,x, y+2*(height/3), width/3, height/3);//6

draw(g,n,x+width/3, y+2*(height/3), width/3, height/3);//7

draw(g,n,x+2*(width/3), y+2*(height/3), width/3, height/3);//8

}

2.三角形理解及代码

理解：

原理和地毯一样，都要用到迭代

这是最基础的谢尔宾斯三角形

最外面的大三角形的三个坐标是我们自己取的

我们只要知道六个顶点，画出六条直线，剩下的就可以交给递归了

假设最外层三角形的坐标分别为(x1,y1)(x2,y2)，(x3,y3)

那么三个中点的坐标就是

( (x1+x2)/2, (y1+y2)/2 )

( (x1+x3)/2, (y1+y3)/2 )

( (x3+x2)/2, (y3+y2)/2 )

public void drawtri(Graphics g,int n,int x1,int y1,int x2,int y2,int x3,int y3 ){

g.drawLine(x1,y1,x2,y2);

g.drawLine(x3,y3,x2,y2);

g.drawLine(x1,y1,x3,y3);

g.drawLine((x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);

g.drawLine((x1+x2)/2,(y1+y2)/2,(x2+x3)/2,(y2+y3)/2);

g.drawLine((x3+x2)/2,(y3+y2)/2,(x1+x3)/2,(y1+y3)/2);

if(n==0)

return;

n--;

drawtri(g,n,x1,y1,(x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);

drawtri(g,n,(x1+x2)/2,(y1+y2)/2,x2,y2,(x3+x2)/2,(y3+y2)/2);

drawtri(g,n,(x1+x3)/2,(y1+y3)/2,(x2+x3)/2,(y2+y3)/2,x3,y3);

}

3.地毯+三角形+画图板表示

我们在画图板上加上两个按钮，达到点击按钮

以鼠标点击与落下的线段作为地毯的对角线去绘制地毯

以我们在画图板上点击的三个点去绘制三角形

画图板类：

import javax.swing.JFrame; //窗体

import javax.swing.JButton; //按钮

import java.awt.FlowLayout; //流式布局器

import java.awt.Graphics; //画笔

public class DrawPad {

public static void main(String args[]){

DrawPad dp = new DrawPad();//创建画图板对象

dp.showUI();

}

public void showUI(){

JFrame jf = new JFrame();

DrawPadListener dl = new DrawPadListener();

String[] brnstrs = {"地毯","三角形"};

for (int i = 0; i < brnstrs.length; i++) {

JButton btn = new JButton(brnstrs[i]);

btn.setName(brnstrs[i]);

btn.addActionListener(dl);//按钮添加监听器

jf.add(btn);//将按钮添加到窗体上

}

FlowLayout fl = new FlowLayout();

//流式布局器，使得添加到窗体上的组件从上到下，从左到右排列

//JFrame默认是

jf.setTitle("可视化"); //名称

jf.setSize(800,600); //尺寸

jf.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); //关闭进程

jf.setLayout(fl); //设置流式布局

jf.setResizable(false); //不可以改变窗体大小

jf.setLocationRelativeTo(null);//居中显示

jf.addMouseListener(dl);

jf.setVisible(true); //设置窗体可视

Graphics g = jf.getGraphics(); //取画笔

dl.g = g;

}

}

监听器类：

package 分形;

import java.awt.Color; //颜色

import java.awt.Graphics; //画笔

import java.awt.event.ActionEvent;

import java.awt.event.ActionListener;//动作监听器

import java.awt.event.MouseEvent;

import java.awt.event.MouseListener; //鼠标监听器

import java.util.Random;

public class DrawPadListener implements MouseListener, ActionListener{

String btnstr;

Graphics g;

int x1,x2,y1,y2,x3,y3,x4,y4,x5,y5;

int count = 0;

int n = 1;

Random r = new Random();

public void actionPerformed(ActionEvent e){

btnstr = e.getActionCommand();

System.out.println("actionPerformed方法被调用，btnstr为："+btnstr);

}

public void mouseClicked(MouseEvent e){

System.out.println("点击");

}

public void mousePressed(MouseEvent e){

System.out.println("按下");

x1=e.getX();

y1=e.getY();

double a,b,c,d;

if(btnstr.equals("三角形")){

if(count == 0){

x3 = e.getX();

y3 = e.getY();

count++;

}else if(count==1){

x4 = e.getX();

y4 = e.getY();

count++;

}else if(count==2){

x5 = e.getX();

y5 = e.getY();

drawtri(g,n,x3,y3,x4,y4,x5,y5);

count = 0;

}

}

}

public void mouseReleased(MouseEvent e){

System.out.println("释放");

x2=e.getX();

y2=e.getY();//释放点的坐标

if(btnstr.equals("地毯"))

drawcpt(g,n,x1,y1,x2-x1,y2-y1);

}

public void mouseEntered(MouseEvent e){

System.out.println("进入");

}

public void mouseExited(MouseEvent e){

System.out.println("退出");

}

//谢尔宾斯地毯

public void drawcpt(Graphics g,int n,int x,int y,int width,int height) {

g.fillRect(x+width/3,y+height/3,width/3,height/3);

if(n==0)//递归结束条件

return;

n--;

drawcpt(g,n,x, y, width/3, height/3);

drawcpt(g,n,x+width/3, y, width/3, height/3);

drawcpt(g,n,x+2*(width/3), y, width/3, height/3);

drawcpt(g,n,x, y+height/3, width/3, height/3);

drawcpt(g,n,x+2*(width/3), y+height/3, width/3, height/3);

drawcpt(g,n,x, y+2*(height/3), width/3, height/3);

drawcpt(g,n,x+width/3, y+2*(height/3), width/3, height/3);

drawcpt(g,n,x+2*(width/3), y+2*(height/3), width/3, height/3);

}

//谢尔宾斯三角形

public void drawtri(Graphics g,int n,int x1,int y1,int x2,int y2,int x3,int y3 ){

g.drawLine(x1,y1,x2,y2);

g.drawLine(x3,y3,x2,y2);

g.drawLine(x1,y1,x3,y3);

g.drawLine((x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);

g.drawLine((x1+x2)/2,(y1+y2)/2,(x2+x3)/2,(y2+y3)/2);

g.drawLine((x3+x2)/2,(y3+y2)/2,(x1+x3)/2,(y1+y3)/2);

if(n==0)

return;

n--;

drawtri(g,n,x1,y1,(x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);

drawtri(g,n,(x1+x2)/2,(y1+y2)/2,x2,y2,(x3+x2)/2,(y3+y2)/2);

drawtri(g,n,(x1+x3)/2,(y1+y3)/2,(x2+x3)/2,(y2+y3)/2,x3,y3);

}

}