import java.awt.Dimension;
import java.awt.Frame;
import java.awt.Point;
 
import javax.swing.JFrame;
 
 
public class MainQuu extends Frame{
 
	static Point a;
	static Point b;
	static Point c;
	static TriangleQuu tryAngle;
	static JFrame frame;
 
 
	private static final long serialVersionUID = 1L;
 
	//frame setup taken from:
	//http://java.sun.com/docs/books/tutorial/uiswing/examples/components/FrameDemoProject/src/components/FrameDemo.java
    private static void createAndShowGUI() {
    	//Create and set up the window.
        frame = new JFrame("Fractal: Sierpinski's Triangle");
    	a = new Point(0, 443);
    	b = new Point(512, 443);
    	c = new Point(256, 0);
    	tryAngle = new TriangleQuu(a, b, c);
 
        tryAngle.setPreferredSize(new Dimension(514, 446));
        //frame.add(tryAngle);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
 
        frame.getContentPane().add(tryAngle);
 
        //Display the window.
        frame.pack();
        frame.setVisible(true);
    }
 
    public static void main(String[] args) {
           //Schedule a job for the event-dispatching thread:
        //creating and showing this application's GUI.
        javax.swing.SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                createAndShowGUI();
            }
        });
    }
}

import java.awt.Component;
import java.awt.Graphics;
import java.awt.Point;
 
class TriangleQuu extends Component{
 
	private static final long serialVersionUID = 1L;
 
	//A, B, C initial triangle-points, assigned in the constructor
	private Point A, B, C;
 
	public TriangleQuu(Point a, Point b, Point c){
		this.A = a; 
		this.B = b; 
		this.C = c;
		}
 
 
	public void drawFractal(int level, Graphics g, Point a, Point b, Point c){
		if (level == 1) {
			/**
			 * draw inner reversed triangle
			 **/
			//AB
			g.drawLine(a.x, a.y, b.x, b.y);
			//AC
			g.drawLine(a.x, a.y, c.x, c.y);
			//BC
			g.drawLine(b.x, b.y, c.x, c.y);
		} else {
 
			//lower left triangle coordinates
			Point A1 = new Point(a.x, a.y);
			Point B1 = new Point(c.x, b.y);
			Point C1 = new Point((a.x+c.x)/2, (c.y+a.y)/2);
 
			//lower right triangle coordinates
			Point A2 = new Point(c.x, b.y);
			Point B2 = new Point(b.x, b.y);
			Point C2 = new Point((c.x+b.x)/2, (c.y+a.y)/2);
 
			//upper triangle coordinates
			Point A3 =  new Point((a.x+c.x)/2, (c.y+a.y)/2);
			Point B3 = new Point((c.x+b.x)/2, (c.y+a.y)/2);
			Point C3 = new Point(c.x, c.y);
 
 
			drawFractal(level-1,g, A1, B1, C1);
			drawFractal(level-1,g, A2, B2, C2);
			drawFractal(level-1,g, A3, B3, C3);
		}
	}
 
 
	public void paint(Graphics g){
		drawFractal(8, g, A, B, C);
	}
}

You can offer to user to enter this. And then pass it as a parameter into method.

if ((level == 1) ||(minLineLength < 12))

if ((level == 1) ||(minLineLength < 12))
{
//here
}

//you call your method with 8 length
drawFractal(8,g, A, B, C);
....
//if we reach the condition (because our screen resolution doesn't allow us to draw more triangles - as you specify) for example level=2
if ((level == 1) ||(minLineLength < 12))
{
//here we set the value, that will remember the leves remained to do
}

level	if (level == 1)
1	1
2	4
3	13
4	40
5	121
6	364
7	1093
8	3280
9	9841
10	29524
11	88573
12	265720
13	797161
14	2391484
15	7174453
16	21523360
17	64570081