Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation
Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation
Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the ``ordered'' and ``chaotic'' distribution of such pairs by solving the eigenvalue problem for two-dimensional modular transformations over integers. We conjecture that the optimal uniformity for pair distribution is obtained when …