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Re: random integer weirdness


I tried to evaluate the expression with j ranging from 0 to 20000 step of 1.
Something obviously periodic seems to be going on (just plot the sim data).
Since running this program takes for ever, I have prepared and (can email to
anyone interested) a flat text file with the output of Mark's program (the
"sim" data for j ranging from 0 to 20000 in steps of 1).
It is my understanding that the period of the rule 30-cellular automata RNG
(if any) used by MATHEMATICA has not been extensively studied. Could we use
the data geenrated to do so ?

Christos Argyropoulos


"Mark Fisher" <mark at markfisher.net> wrote in message
news:ai5tna$bqb$1 at smc.vnet.net...
> There is some real weirdness with Random[Integer, j] for some large
> values of j but not others (for both 4.1 and 4.2 versions).
>
> <<Statistics`
> n = 1000;
> sim = Table[{j, (2/2^j) * Mean[Table[Random[Integer, 2^j], {n}]]},
>       {j, 45, 65, 1/8}];
> ListPlot[sim];
>
> All the points should be near one if the random number generator were
> working properly. What gives? Is this just a (very stark) symptom of
> what Daniel Lichtblau mentioned in his May 2000 post?
>
> >> The other failure only is apparent in very large big
> >> integers, and I do not know exactly how to categorize it.
>
> I just find this very troubling.
>
> --Mark.
>




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