Re: A problem in Pi digits as Lattice space filling

*To*: mathgroup at smc.vnet.net*Subject*: [mg93900] Re: A problem in Pi digits as Lattice space filling*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Fri, 28 Nov 2008 05:07:15 -0500 (EST)*References*: <ggj7co$j2i$1@smc.vnet.net> <200811261222.HAA22459@smc.vnet.net> <gglss8$8fg$1@smc.vnet.net>

DrMajorBob wrote: >>first some picky things. The digits in Pi are not normal, but uniformly >>distributed >> >> > >I doubt that (uniformity) is actually known. Is it? > >Bobby > > > > Dr. Bob, I remembered I had this and searched it up: ( it is a combination of Dr. Frame's driven IFS and Dr. Lictenbau's color IFS programs that I did for driven experiments) (*rule driven array based on the BBP Pi digits modulo 4array*) dlst = Table[1 + Floor[Mod[(4/(8*n + 1) - 2/(8*n + 4) - 1/(8*n + 5) - 1/(8* n + 6))*16^n, 4]], {n, 50000}]; Length[dlst] f[j_, {x_, y_}] := 0.5*{x, y} + 0.5*Reverse[IntegerDigits[j - 1, 2, 2]] pt = {0.5, 0.5}; cr[n_] = If[n - 1 == 0, RGBColor[0, 0, 1], If[n - 2 == 0, RGBColor[0, 1, 0], If[n - 3 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]]; ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]}, {j, Length[dlst]}]; Null Show[Graphics[Join[{PointSize[.001]}, ptlst]], AspectRatio -> Automatic, PlotRange -> All] The first array takes forever on my machine... the rest is fast. I don't see any pattern like a actual driven array gives you: it appears to rival pseudorandom numbers in output at 50000 digits. You can try it at higher output. Happy Thanksgiving! Respectfully, Roger L. Bagula 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :http://www.geocities.com/rlbagulatftn/Index.html alternative email: rlbagula at sbcglobal.net

**References**:**Re: A problem in Pi digits as Lattice space filling***From:*dh <dh@metrohm.com>