Re: bimodal ditribution form counting signs of Pi digits differences
- To: mathgroup at smc.vnet.net
- Subject: [mg51733] Re: bimodal ditribution form counting signs of Pi digits differences
- From: Roger Bagula <tftn at earthlink.net>
- Date: Sun, 31 Oct 2004 01:16:21 -0500 (EST)
- References: <clst68$3nf$1@smc.vnet.net>
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
Null hypothesis: the digits of Pi are random. To check make up a random set of base 10 digits using Mathematica using: Random[Integer,{0,9}] I picked a seed off the top of my head. The result is a revolting development. A trimodal distribution of noise pushed way positive. The Pi digits behave more like an "ideal" probablity than the Mathematica random! Anybody see what I did wrong? Dr. Bob you always have an opinion, ha, ha... (* random digit array base 10*) SeedRandom[123] a=Table[Random[Integer,{0,9}],{n,1,2000}]; b=Table[Sum[Sign[a[[m+1]]-a[[m]]],{m,1,n}],{n,1,Dimensions[a][[1]]-1}]; ListPlot[b,PlotJoined->True] (* distribution of the noise that results*) Max[b] Min[b] c=Table[Count[b,m],{m,Min[b]-1,Max[b]+1}] ListPlot[c,PlotJoined->True] Roger Bagula wrote: >This program is real slow on my machine. >Show a lean toward positive differences that is "slight" at 2000 digits. > >Digits=2000 >$MaxExtraPrecision = Digits >(* Sum of the sign of the differences between the first 2000 digits of Pi*) >f[m_]=Sum[Sign[Floor[Mod[10^(n+1)*Pi,10]]-Floor[Mod[10^n*Pi,10]]],{n,0,m}] >a=Table[{n,f[n]},{n,0,Digits-1}]; >ListPlot[a,PlotJoined->True] >b=Table[a[[n]][[2]],{n,1,Dimensions[a][[1]]}]; >(* distribution of the noise that results*) >c=Table[Count[b,m],{m,-12,12}] >ListPlot[c,PlotJoined->True] > >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 > > > -- 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