[Date Index]
[Thread Index]
[Author Index]
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**
| |