Examples of three so-called linear congruential random number generators. In each case they start with the number 1, then successively multiply by the specified multiplier, keeping only the rightmost 31 digits in the base 2 representation of the number obtained at each step. A version of the case with multiplier 3 was already shown on page 120. Multiplier 65539 was used as the random number generator on many computer systems, starting with mainframes in the 1960s. The last two pictures in each row above give the distribution of points whose coordinates in two and three dimensions are obtained by taking successive numbers from the linear congruential generator. If the output from the generator was perfectly random, then in each case these points would be uniformly distributed. But as the pictures demonstrate, stripes are visible in either two or three dimensions, or both.
Showing Web View For Page 320 | Show full page with images