A Random Question

[Paul Dale]

(06-10-2017 02:28 PM)lrdheat Wrote:  Back in they day with my hp-67 (wish I still had it), I made a primitive random number generator simply by using the 10th through 12th digits of sin (X) where X was in radians, and X incremented up by 1 for each new random number generation.

Taking the middle order digits of \( x_n = frac\left(e^{2 x_{n-1} + 1}\right) \) starting with \( x_0 = frac\left(\pi\right) \) produces a fairly well distributed random number, at least in binary. This passes the dieharder tests and only fails a couple of the TestU01 suite. It is a good example of a simple function that appears to produce random output, yet is completely and obviously deterministic. It is also straightforward to show that rounding is not coming into play.


Pauli