       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