Let the user place Buttons in Java

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I want to code a little tool that simulates a deterministic, finite automaton (like JFLAP) for myself.

My JFrame is just blank. How can I let the user place buttons on left click? And how do I assign the right values to that button (like which function to call when pressed).

I know I can place a button with

JButton button = new JButton("Press me");
frame.add(button);

But I don't know how I could dynamically code that.

Any help is welcome. Also if you think it's stupid to solve my problem with buttons, I'd like to hear suggestions for improvement.

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The following code will add a JButton to a "blank" JFrame every time the mouse is clicked inside the JFrame. The JButton will be placed where the mouse click occurred. The JButton text will be a number. Each JButton will display a different number.

import java.awt.Dimension;
import java.awt.EventQueue;

import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.util.ArrayList;
import java.util.List;

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.WindowConstants;

public class AdButton extends MouseAdapter implements Runnable {
    private int  counter;
    private JFrame  frame;
    private JPanel  contentPane;

    public void mouseClicked(MouseEvent event) {
        int x = event.getX();
        int y = event.getY();
        JButton button = new JButton(String.valueOf(++counter));
        Dimension dim = button.getPreferredSize();
        button.setBounds(x, y, dim.width, dim.height);
        contentPane.add(button);
        contentPane.revalidate();
        contentPane.repaint();
    }

    @Override
    public void run() {
        showGui();
    }

    private void showGui() {
        frame = new JFrame();
        frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
        contentPane = (JPanel) frame.getContentPane();
        contentPane.setLayout(null);
        contentPane.addMouseListener(this);
        frame.setSize(400, 450);
        frame.setLocationByPlatform(true);
        frame.setVisible(true);
    }

    public static void main(String[] args) {
        EventQueue.invokeLater(new AdButton());
    }
}