数学的艺术——迭代函数下的图案（Java绘图）

Posted 2020-12-20 hou-cg-blog

　　迭代，其实就是一个重复反馈的过程，利用旧值推新值，即：x_n+1=f(x_n)。

　　当我们要在一个平面上绘图的时候就需要一个坐标(x,y),我们只要把每一个迭代后的(x_n+1,y_n+1)绘制出来就好了。

　　下面给出了几个比较简单有趣的迭代函数（来源：http://paulbourke.net/fractals/ifs/）：

　　Maple Leaf:　　x_n+1 = a x_n + b y_n + e

　　　　　　　　　 y_n+1 = c x_n + d y_n + f

　　　　　参数：    

                    set 1     set 2     set 3     set 4
             a     0.1400    0.4300    0.4500    0.4900
             b     0.0100    0.5200   -0.4900    0.0000
             c     0.0000   -0.4500    0.4700    0.0000
             d     0.5100    0.5000    0.4700    0.5100
             e    -0.0800    1.4900   -1.6200    0.0200
             f    -1.3100   -0.7500   -0.7400    1.6200



   TREE:     xn+1 = axn + byn + e

　　　　　　　　　 y_n+1 = cx_n + dy_n + f

　　　　　参数：

       　　　　　　　　set 1     set 2     set 3     set 4
             a     0.0100   -0.0100    0.4200    0.4200
             b     0.0000    0.0000   -0.4200    0.4200
             c     0.0000    0.0000    0.4200   -0.4200
             d     0.4500   -0.4500    0.4200    0.4200
             e     0.0000    0.0000    0.0000    0.0000
             f     0.0000    0.4000    0.4000    0.4000

　TREE的代码（在MouseListener中实现）

 1 import java.awt.Color;
 2 import java.awt.Graphics;
 3 import java.awt.event.MouseEvent;
 4 import java.awt.event.MouseListener;
 5 import java.util.Random;
 6 
 7 public class Listener implements MouseListener {
 8     Graphics g;
 9     double[] a = {0.0100,-0.0100,0.4200,0.4200};
10     double[] b = {0.0000,0.0000,-0.4200,0.4200};
11     double[] c = {0.0000,0.0000,0.4200,-0.4200};
12     double[] d = {0.4500,-0.4500,0.4200,0.4200};
13     double[] e1 = {0.0000,0.0000,0.0000,0.0000};
14     double[] f = {0.0000,0.4000,0.4000,0.4000};
15     
16     @Override
17     public void mouseClicked(MouseEvent e) {
18         // TODO Auto-generated method stub
19         double x = 0 , y = 0;
20         Random t = new Random();
21         Color cl = new Color(200,70,43);
22         g.setColor(cl);
23         for (int i = 0 ; i < 1500000 ; i++)
24         {
25             int n = t.nextInt(499)%4;
26             double tempx = a[n]*x+b[n]*y+e1[n];
27             double tempy = c[n]*x+d[n]*y+f[n];
28             x = tempx;
29             y = tempy;
30             int px = (int)(tempx*500)+e.getX();
31             int py = -((int)(tempy*500)+e.getY())+3*e.getX();
32             g.drawLine(px, py, px, py);
33             
34         }
35     }
36 
37     @Override
38     public void mousePressed(MouseEvent e) {
39         // TODO Auto-generated method stub
40         
41     }
42 
43     @Override
44     public void mouseReleased(MouseEvent e) {
45         // TODO Auto-generated method stub
46         
47     }
48 
49     @Override
50     public void mouseEntered(MouseEvent e) {
51         // TODO Auto-generated method stub
52         g.setColor(Color.white);
53         g.fillRect(0, 0, 800, 800);
54     }
55 
56     @Override
57     public void mouseExited(MouseEvent e) {
58         // TODO Auto-generated method stub
59         
60     }
61 }

　　效果：