Generating pseudo-random numbers by shuffling a Fibonacci sequence

Abstract:

M. D. MacLaren and G. Marsaglia [2] have proposed to mix two pseudo-random number generators in the following way: The first generator is used at the beginning to fill an array with pseudo-random numbers; whenever a random number is needed, the second generator determines which element of the array is to be used and replaced by a new number from the first generator. In this study, only one generator is utilized for both purposes; moreover, the generator chosen (a Fibonacci sequence) is by itself a rather poor one. Nevertheless, the final sequence of pseudo-random numbers passed all statistical tests applied to it, including ${\chi ^2} -$ tests of the maximum and minimum of two to ten succeeding numbers and tests applied to sequences immediately following a small number or two almost equal ones.