Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: neat sums and pattered randomness

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52251] Re: neat sums and pattered randomness
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Wed, 17 Nov 2004 02:20:22 -0500 (EST)
  • References: <cnbn5l$9vq$1@smc.vnet.net>
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

Both pairs based on the projective line and ( Sqrt[n/(1+n)],Sqrt[1/(1+n])
have the property of giving space filling curves, but the
sorted iteration arrays are not very good  lines in several cases.
The Sqrt[] iteration broke my Mod[,1] output
 (I got numbers in (x,y) greater than one and diverging)
It appears the powers (2,1/2)  in the sum function
although increasing a kind of randomness,
do not make good b-normal candidate sums.
It isn't clear why the power functions cause this problem
or solution.

(* Pair Iteration   of projective line type *)
(* two sets of constants depend on if 1-n^2 or n^2-1 is used*)
(* no apparent pattern develops in the iteration: a space filling curve 
in 2d*)
x[n_]:=x[n]=Mod[x[n-1]*2+If[Mod[n,2]==1,2*n/(n^2+1),(1-n^2)/(n^2+1)],1]
y[n_]:=y[n]=Mod[y[n-1]*2+If[Mod[n,2]==1,(1-n^2)/(n^2+1),2*n/(n^2+1)],1]
x[0]=0;y[0]=0;
a0=Table[{x[n],y[n]},{n,0, 200}];
ListPlot[a0,PlotJoined->True, PlotRange->All]
(* positive version*)
Clear[x,y,a,b,s,g,a0]
x[n_]:=x[n]=Mod[x[n-1]*2+If[Mod[n,2]==1,2*n/(n^2+1),(-1+n^2)/(n^2+1)],1]
y[n_]:=y[n]=Mod[y[n-1]*2+If[Mod[n,2]==1,(-1+n^2)/(n^2+1),2*n/(n^2+1)],1]
x[0]=0;y[0]=0;
a0=Table[{x[n],y[n]},{n,0, 200}];
ListPlot[a0,PlotJoined->True, PlotRange->All]

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



  • Prev by Date: Re: 64 bit cpu and Mathematica on windows.
  • Next by Date: Re: Help in solving PDF equations
  • Previous by thread: neat sums and pattered randomness
  • Next by thread: Re: neat sums and pattered randomness