Sierpinski Triangle A sierpinski is composed of an infinite number of sub-triang

Question

Sierpinski Triangle A sierpinski is composed of an infinite number of sub-triangles, so it is almost impossible to draw. However, we can produce an algorithm that can produce various levels that approximate the actual fractal. A sierpinski triangle is created as follows: 1. Draw an equilateral triangle. This is considered to be a Sierpinski fractal of level 1, as seen in fig.01. This initial triangle has three points (p1, p2, p3) set in proportions to the frame size. Fig.01: Sierpinski triangle level: 1 2. At level 2, draw three smaller triangles that are contained within the original triangle. Fig.02: Sierpinski triangle level: 2 3. Apply this process in a recursive manner. Just as we replaced the original triangle with three inner triangles, we replace each of the three triangles in level 2 with three inner triangles to

Explanation / Answer

here is your program : ------------->>>>>>>>>

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

public class Sierpinski extends JFrame implements ActionListener{
private Point p1;
private Point p2;
private Point p3;
private JPanel pan1;
private int level;
private JTextField lab;
private SierpinskiPanel pan;
private JButton bplus,bminus;

public Sierpinski(){
  super("Sierpinski");
  setSize(600,600);
  setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
  setLayout(new BorderLayout());
  pan = new SierpinskiPanel();
  add(pan,BorderLayout.CENTER);
  bplus = new JButton(" + ");
  bplus.addActionListener(this);
  bminus = new JButton(" - ");
  bminus.addActionListener(this);
  pan1 = new JPanel();
  lab = new JTextField(" n = "+level);
  lab.setEditable(false);
  pan1.setLayout(new FlowLayout());
  pan1.add(bplus);
  pan1.add(bminus);
  pan1.add(lab);
  add(pan1,BorderLayout.SOUTH);
  level = 3;
  p1 = new Point();
  p2 = new Point();
  p3 = new Point();
  p1.setLocation(100,490);
  p2.setLocation(300,90);
  p3.setLocation(500,490);
  setVisible(true);
}

public void actionPerformed(ActionEvent e){
  if(e.getSource() == bplus){
   level++;
   if(level > 1){
    bminus.setEnabled(true);
   }
   lab.setText(" n = "+level);
   repaint();
  }else if(e.getSource() == bminus && level != 1){
   level--;
   lab.setText(" n = "+level);
   if(level == 1){
    bminus.setEnabled(false);
   }
   repaint();
  }
}

public void paint(Graphics g){
  int[] x = new int[3];
  int[] y = new int[3];
  

  x[0] = (int)(Math.abs(p1.getX()));
  x[1] = (int)(Math.abs(p2.getX()));
  x[2] = (int)(Math.abs(p3.getX()));
  y[0] = (int)(Math.abs(p1.getY()));
  y[1] = (int)(Math.abs(p2.getY()));
  y[2] = (int)(Math.abs(p3.getY()));

  Polygon pp = new Polygon(x,y,3);
  g.setColor(Color.BLACK);
  g.fillPolygon(pp);
  pan.drawTriangle(g,level-1,p1,p2,p3);
}

public static void main(String[] args) {
  Sierpinski s = new Sierpinski();
  s.repaint();
}

}

class SierpinskiPanel extends JPanel{
public SierpinskiPanel(){
  setSize(500,500);
  setVisible(true);
}

public void drawTriangle(Graphics pen,int l,Point p1,Point p2,Point p3){
  if(l == 0){
   return;
  }
  int[] x = new int[3];
  int[] y = new int[3];

  x[0] = (int)(Math.abs(p1.getX() + p2.getX())/2);
  x[1] = (int)(Math.abs(p1.getX() + p3.getX())/2);
  x[2] = (int)(Math.abs(p2.getX() + p3.getX())/2);
  y[0] = (int)(Math.abs(p1.getY() + p2.getY())/2);
  y[1] = (int)(Math.abs(p1.getY() + p3.getY())/2);
  y[2] = (int)(Math.abs(p2.getY() + p3.getY())/2);

  Polygon p = new Polygon(x,y,3);

  pen.setColor(Color.WHITE);
  pen.fillPolygon(p);
  Point temp1 = new Point();
  Point temp2 = new Point();
  temp1.setLocation(x[1],y[1]);
  temp2.setLocation(x[0],y[0]);
  drawTriangle(pen,l-1,p1,temp1,temp2);
  temp1.setLocation(x[2],y[2]);
  drawTriangle(pen,l-1,temp2,p2,temp1);
  temp2.setLocation(x[1],y[1]);
  drawTriangle(pen,l-1,temp2,temp1,p3);

}
}

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