Comparing Rule 30 Pseudorandoms to a Uniform Distribution

The Demonstration "Using Rule 30 to Generate Pseudorandom Real Numbers" demonstrates an algorithm that uses the rule 30 cellular automaton to generate numbers that can be regarded as nearly random selections from the unit interval. This Demonstration compares the distribution of the numbers generated by that algorithm for a range of initial seeds with a uniform distribution over the unit interval.

The blue histogram displays the distribution of the pseudorandom numbers generated using rule 30 with the number of initial seeds selected. The area of each blue rectangle is the fraction of rule 30-generated pseudorandoms that fall in the interval that forms its base. The thick red line is the height the rectangles would be if these numbers were distributed in a perfectly uniform way among the intervals over which the rectangles sit.

The closeness of the blue area to the rectangle under the red line illustrates that rule 30-generated pseudorandom numbers in the unit interval are fairly uniform over that interval, that is, as likely to come from one section of it as any other of equal size. This uniformity makes rule 30 a good engine for generating pseudorandom numbers.