Two random walkers on a 2d plane

So I have this multithreadded program that generates 2 random walkers, each walker is a separate thread since I need them to move simultaneously. Each walker randomly moves in any of the 4 directions. The first problem is that i think stdDraw is not thread safe and therefore without having a lock around my entire function, it tends to draw random squares at random points for no reason and the whole thing become pretty glitchy. When i put a lock around my function then one thread becomes slower that the other since it sometimes has to wait for the lock. So the threas are not simultaneous anymore. Is there a solution to this? The other problem i have is I want it to break out of the loop when the two walkers intersect, but for some reason the two threads dont know about the position of the other. One thinks that the position of the other is always at (0,0). Thanks!

import java.awt.Color;
public class WalkerThread implements Runnable {

String name;
static Integer lock = new Integer(1000);
int num;
static int steps = 0, steps2 = 0;
static int x = 0, y = 0;
static int x2 = -1, y2 = -2;

public WalkerThread(String s, int n) {
    this.name = s;
    this.num = n;
}

@Override
public synchronized void run() {

    int N = 5;
    StdDraw.create(600, 600);
    StdDraw.setScale(-N, -N, +N, +N);
    StdDraw.clear(Color.gray);
    do {
        synchronized (lock) {

            if (num == 1) {
                StdDraw.go(x, y);
                StdDraw.setColor(Color.white);
                darker();
                StdDraw.spot(0.9, 0.9);

                double r = Math.random();
                if (r < 0.25)
                    x--;
                else if (r < 0.50)
                    x++;
                else if (r < 0.75)
                    y--;
                else if (r < 1.00)
                    y++;

                steps++;

                StdDraw.setColor(Color.blue);
                StdDraw.go(x, y);
                StdDraw.spot(0.9, 0.9);
                StdDraw.pause(400);

            }

            if (num == 2) {
                StdDraw.go(x2, y2);
                StdDraw.setColor(Color.yellow);
                StdDraw.spot(0.9, 0.9);
                double r2 = Math.random();
                if (r2 < 0.25)
                    x2--;
                else if (r2 < 0.50)
                    x2++;
                else if (r2 < 0.75)
                    y2--;
                else if (r2 < 1.00)
                    y2++;

                steps2++;
                StdDraw.setColor(Color.green);
                StdDraw.go(x2, y2);
                StdDraw.spot(0.9, 0.9);
                StdDraw.pause(400);

            }
        }// lock
        /*String pict = steps + ".png";
        StdDraw.save(pict);*/
            //if (posX == posX2 && posY == posY2) break;


    } while ((Math.abs(x) < N && Math.abs(y) < N) && (Math.abs(x2) < N && Math.abs(y2) < N));

    System.out.printf("Total steps of %s is %d and %d \n", name, steps, steps2);

}
}