Re: random integer weirdness

*To*: mathgroup at smc.vnet.net*Subject*: [mg35793] Re: random integer weirdness*From*: "Christos Argyropoulos" <argchris at otenet.gr>*Date*: Wed, 31 Jul 2002 01:33:35 -0400 (EDT)*References*: <ai5tna$bqb$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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. >