non-Markov base ten random number generator based on Pi

*To*: mathgroup at smc.vnet.net*Subject*: [mg52020] non-Markov base ten random number generator based on Pi*From*: Roger Bagula <tftn at earthlink.net>*Date*: Sun, 7 Nov 2004 01:03:55 -0500 (EST)*Reply-to*: tftn at earthlink.net*Sender*: owner-wri-mathgroup at wolfram.com

This result is an experimental random number generator. It uses the PSLQ Bailey Pi digits rational polynomial to generate digits in the 0 to 9 range using a process that loses information , but generally behaves like the Pi digits. It is not Markov, in that there is no previous behavior involved in calculating the next random number. (* Bailey formula with digit drop base 80*) (* base 10 random number generator that isn't Markov *) (* use integer seed as the number of digits in to start calculation*) (* other PSLQ functions of transcendental numbers could be used to do this same kind of random number*) f[n_]=Floor[Mod[80^n*(4/(8*n+1)-2/(8*n+4)-1/(8*n+5)-1/(8*n+6))/16^n,10]] Digits=4000;rdpi=Table[f[n],{n,0,Digits}]; c1=Drop[FoldList[Plus,0,Sign[Drop[rdpi,1]-Drop[rdpi,-1]]],1]; ListPlot[c1,PlotJoined->True]; (* Rowe Count*) d1=Flatten@{0,Length/@Split[Sort@c1], 0} Dimensions[d1][[1]] ListPlot[d1,PlotJoined->True]; a=Table[f[n],{n,0,200}] {3,0,1,2,7,5,0,7,7,7,4,9,2,0,3,9,9,8,2,0,5,6,3,0,9,3,6,6,4,8,7,2,3,8,4,3,2,1, 1,2,4,7,5,8,5,0,8,4,3,2,6,6,7,4,6,9,6,5,9,5,4,1,8,9,7,2,8,5,4,3,0,3,3,0,5,7, 6,2,0,1,4,0,1,6,9,7,2,0,4,0,1,8,1,8,8,2,9,3,1,4,4,3,0,1,3,4,0,5,8,8,9,6,8,3, 5,1,5,5,4,5,1,4,6,5,7,1,9,8,8,2,3,1,6,0,8,7,1,6,7,6,2,5,3,5,7,7,7,2,7,6,1,4, 7,4,9,3,4,8,3,5,5,5,9,3,0,8,4,8,5,8,4,0,9,8,3,8,2,6,7,0,5,8,9,3,7,8,4,2,9,0, 1,2,6,1,2,9,1,7,0,7,6} Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn at netscape.net URL : http://home.earthlink.net/~tftn