Visual verification of pseudo-random number generators

We consider construction of uniformly distributed pseudo-random number sequences. To estimate the sequence randomness, simple visual criterion is implied. This test shows the most widespread generators based on the Mersenne twister, linear congruent sequence and some other principles do not provide satisfactory results. Therefore, construction of good generators is still an unsolved problem. Also, results of stochastic process calculations (e.g., molecular dynamics etc.) should be treated with caution.