Can Sierpinski triangle be created recursively using Java?

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Yes, the Sierpinski triangle can be created recursively using Java. Here is an example code:

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

public class SierpinskiTriangle extends JFrame {
    private int order = 0;  // Initial order of Sierpinski triangle

    public SierpinskiTriangle() {
        setLayout(new BorderLayout());
        add(new TrianglePanel(order));  // Add TrianglePanel to JFrame
    }

    // Define TrianglePanel
    static class TrianglePanel extends JPanel {
        private int order;  // Order of current Sierpinski triangle

        public TrianglePanel(int order) {
            this.order = order;
        }

        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);

            // Define triangle vertices
            int x1 = getWidth() / 2;
            int y1 = 10;
            int x2 = 10;
            int y2 = getHeight() - 10;
            int x3 = getWidth() - 10;
            int y3 = getHeight() - 10;

            // Draw Sierpinski triangle recursively
            displayTriangles(g, order, x1, y1, x2, y2, x3, y3);
        }

        // Draw Sierpinski triangle recursively
        private void displayTriangles(Graphics g, int order, 
                                      int x1, int y1, int x2, int y2, int x3, int y3) {
            if (order == 0) {
                // Base case: draw triangle
                g.drawLine(x1, y1, x2, y2);
                g.drawLine(x1, y1, x3, y3);
                g.drawLine(x2, y2, x3, y3);
            } else {
                // Recursive case: draw smaller triangles
                int x12 = (x1 + x2) / 2;
                int y12 = (y1 + y2) / 2;
                int x23 = (x2 + x3) / 2;
                int y23 = (y2 + y3) / 2;
                int x31 = (x3 + x1) / 2;
                int y31 = (y3 + y1) / 2;

                displayTriangles(g, order - 1, x1, y1, x12, y12, x31, y31);
                displayTriangles(g, order - 1, x12, y12, x2, y2, x23, y23);
                displayTriangles(g, order - 1, x31, y31, x23, y23, x3, y3);
            }
        }
    }

    public static void main(String[] args) {
        JFrame frame = new SierpinskiTriangle();
        frame.setTitle("Sierpinski Triangle");
        frame.setSize(400, 400);
        frame.setLocationRelativeTo(null);  // Center frame
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setVisible(true);
    }
}

This code defines a TrianglePanel class that extends JPanel and draws a Sierpinski triangle recursively using the displayTriangles method. The SierpinskiTriangle class is a JFrame that contains a TrianglePanel and sets the initial order of the Sierpinski triangle to 0. The main method creates an instance of SierpinskiTriangle, sets the title, size, and location of the JFrame, and makes it visible.