I have written some code to place dots all around the screen randomly; however, it does not cover the entire screen:
import turtle
import random
t = turtle.Turtle()
color = ["red", "green", "blue", "pink", "yellow", "purple"]
t.speed(-1)
for i in range(0, 500):
print(turtle.Screen().screensize())
z = turtle.Screen().screensize()
x = z[0]
y = z[1]
t.color(color[random.randint(0,5)])
t.dot(4)
t.setposition(random.randint(-x,x), random.randint(-y,y))
turtle.done()