Drawing graphics to separate JPanels

I have a program that extends JFrame and that is what my paint method is drawing on. I am trying to have a JFrame with multiple JPanels within that JFrame, which is not a problem, but how could I have separate paint methods for separate JPanels within one class?

import java.awt.*;
import java.awt.image.BufferedImage;
import javax.swing.*;
import java.awt.event.*;
 
public class Mandelbrot extends JFrame implements ActionListener {
 
	private JPanel ctrlPanel;
	private JPanel imgPanel;
    private final int numIter = 1000;
    private final double zoom = 150;
    private BufferedImage I;
    private double zx, zy, cx, cy, temp;
    private int xMove, yMove = 0;
 
    public Mandelbrot() {
        super("Mandelbrot Set");
        setBounds(100, 100, 800, 600);
        setResizable(false);
        setDefaultCloseOperation(EXIT_ON_CLOSE);
        plotPoints();
        
        Container contentPane = getContentPane();
        
        
        ctrlPanel = new JPanel();
        ctrlPanel.setBounds(600,0,200,600);
        
        imgPanel = new JPanel();
        imgPanel.setBounds(0,0,600,600);
        imgPanel.repaint();
        
        contentPane.add(ctrlPanel);
        contentPane.add(imgPanel);
    }
 
    public void plotPoints(){
    	I = new BufferedImage(getWidth(), getHeight(), BufferedImage.TYPE_INT_RGB);
        for (int y = 0; y < getHeight(); y++) {
            for (int x = 0; x < getWidth(); x++) {
                zx = zy = 0;
                cx = (x - 400 +xMove) / zoom;
                cy = (y - 300 +yMove) / zoom;
                int iter = numIter;
                while (zx * zx + zy * zy < 4 && iter > 0) {
                    temp = zx * zx - zy * zy + cx;
                    zy = 2 * zx * zy + cy;
                    zx = temp;
                    iter--;
                }
                I.setRGB(x, y, iter | (iter << 20));
            }
        }
    }
    
    public void actionPerformed(ActionEvent ae){
    	String event = ae.getActionCommand();
    	
    	
    }
    
    
    @Override
    public void paint(Graphics g) {
    	
        g.drawImage(I, 0, 0, this);
    }
 
    public static void main(String[] args) {
        new Mandelbrot().setVisible(true);
    }
}

as you can see, I have 2 JPanels. In one of them I'd like to place my graphics (imgPanel), and in the other I would like to have other swing objects. Is it possible to allocate a specific JPanel for graphics?

Much thanks!