Chaos-to-order (cont'd)

• To: mathgroup at smc.vnet.net
• Subject: [mg27367] Chaos-to-order (cont'd)
• From: Roberto Brambilla <rlbrambilla at cesi.it>
• Date: Thu, 22 Feb 2001 02:25:11 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
refeerring to my previous e-mail [mg27308]
and taking into account suggestions of some of
you, I have the points orbit in te unit square

T[t_]:={{2 Cos[t],Cos[t]-Sin[t]},{Cos[t]+Sin[t],Cos[t]}};
(*0<=t<=pi/2*)
Orbit[t_,p_,n_Integer] := With[{tau = T[t]},
NestList[Mod[tau.#, 1] &, p, n]
]

es. two orbits generate by two different initial points:

t0=Pi/3.;
l1=Orbit[t0,{.4,.7},1000];
ListPlot[l1,Frame->True,Axes->False,AspectRatio->1,
PlotStyle->Hue[.9]]

l2=Orbit[t0,{.5,.2},1000];
ListPlot[l1,Frame->True,Axes->False,AspectRatio->1,
PlotStyle->Hue[.7]]

The two figures looks very different.
Both lists contain 1001 points, but the first suggests that there are
returning points, i.e a finite sequence, or closed orbit.
In a more coarse precision the first list would have repeated points.
I think that a quick way to detect closed orbits
(or quasi closed orbits) may be counting colored pixels
in the unit square and counting the background white pixels.
Any idea?
Many thanks, Roberto
Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.2.2125.5875
fax +39.2.2125.610
rlbrambilla at cesi.it

```

• Prev by Date: The usage of emmathfnt on Mac
• Next by Date: Re: SetDelayed problems with matrix operation
• Previous by thread: The usage of emmathfnt on Mac
• Next by thread: Re: A bug of Integrate[] in Mathematica 4.1 (and 4.0)