Moving balls in Tkinter Canvas

You should never put an infinite loop inside a GUI program — there’s already an infinite loop running. If you want your balls to move independently, simply take out the loop and have the move_ball method put a new call to itself on the event loop. With that, your balls will continue to move forever (which means you should put some sort of check in there to prevent that from happening)

I’ve modified your program slightly by removing the infinite loop, slowing down the animation a bit, and also using random values for the direction they move. All of that changes are inside the move_ball method.

from Tkinter import *
from random import randint

class Ball:
    def __init__(self, canvas, x1, y1, x2, y2):
        self.x1 = x1
        self.y1 = y1
        self.x2 = x2
        self.y2 = y2
        self.canvas = canvas
        self.ball = canvas.create_oval(self.x1, self.y1, self.x2, self.y2, fill="red")

    def move_ball(self):
        deltax = randint(0,5)
        deltay = randint(0,5)
        self.canvas.move(self.ball, deltax, deltay)
        self.canvas.after(50, self.move_ball)

# initialize root Window and canvas
root = Tk()
root.title("Balls")
root.resizable(False,False)
canvas = Canvas(root, width = 300, height = 300)
canvas.pack()

# create two ball objects and animate them
ball1 = Ball(canvas, 10, 10, 30, 30)
ball2 = Ball(canvas, 60, 60, 80, 80)

ball1.move_ball()
ball2.move_ball()

root.mainloop()