Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation

Details Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation

1998-08-07

arxiv.org/abs/chao-dyn/9808008v1

Nonlinear Sciences

Chaotic Dynamics

13 pages, Revtex - 7 Figs - Int. J. Mod. Phys. C, in press

Scientific paper

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 the slope of linear modular eigenspaces takes the value $n_{opt} = maxint(p /\sqrt{p-1})$, where $p$ is a prime number. We then propose a new generator of pairs of independent pseudo-random numbers, which realizes an optimal uniform distribution (in the ``statistical'' sense) of points on the unit square $(0,1] \times (0,1]$. The method can be easily generalized to the generation of $k$-tuples of random numbers (with $k>2$)

Affiliated with

Also associated with

No associations

Rating

Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616817