Let the user place Buttons in Java

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.

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());
    }
}