If one uses the output of a RNG to give position to plot a white pixel on the screen the screen should gradually and uniformly turn into white. If any patterns are visible the numbers are somehow not random.

Another way would be to fill the screen in an orderly manner (row at a time) with "randomly" selected colors. The result should be medium grey when looked at some distance. Again, if the result shows any scent then the numbers are propably not random.

Actually. True random numbers would give bright red screen (or any color of choise) if given enough tries. Same applies to the pattern test; truly random numbers would give picture of Eriks middle finger if one tries long enough.

With pseudo random figures there is the problem that those are so uniformly distributed. True randomness also includes patterns as part of the randomness - those patterns just appear randomly ;)