Mathematica 9 is now available
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

a terdragon like Rauzy Pisot tile IFS

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49711] a terdragon like Rauzy Pisot tile IFS
  • From: "Roger L. Bagula" <rlbtftn at netscape.net>
  • Date: Thu, 29 Jul 2004 07:43:30 -0400 (EDT)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

I did this after figuring out that the original Rauzy tile was like a 
fudge flake tile, so that an analog to the terdragon tile should exist.
It did.

(***********************************************************************

                     Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 3.0,
MathReader 3.0, or any compatible application. The data for the notebook
starts with the line of stars above.

To get the notebook into a Mathematica-compatible application, do one of
the following:

* Save the data starting with the line of stars above into a file
   with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
   clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the
word CacheID, otherwise Mathematica-compatible applications may try to
use invalid cache data.

For more information on notebooks and Mathematica-compatible
applications, contact Wolfram Research:
   web: http://www.wolfram.com
   email: info at wolfram.com
   phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from
Wolfram Research.
***********************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[      5259,        204]*)
(*NotebookOutlinePosition[      6343,        239]*)
(*  CellTagsIndexPosition[      6299,        235]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell["\<\
Solve[x^3-x^2-x-1==0,x]
\
\>", "Input",
   PageWidth->Infinity,
   InitializationCell->True,
   ShowSpecialCharacters->False,
   FormatType->InputForm],

Cell[BoxData[
     \({{x \[Rule]
           1\/3 + 1\/3\ \((19 - 3\ \@33)\)\^\(1/3\) +
             1\/3\ \((19 + 3\ \@33)\)\^\(1/3\)}, {
         x \[Rule]
           1\/3 - 1\/6\ \((1 + I\ \@3)\)\ \((19 - 3\ \@33)\)\^\(1/3\) -
             1\/6\ \((1 - I\ \@3)\)\ \((19 + 3\ \@33)\)\^\(1/3\)}, {
         x \[Rule]
           1\/3 - 1\/6\ \((1 - I\ \@3)\)\ \((19 - 3\ \@33)\)\^\(1/3\) -
             1\/6\ \((1 + I\ \@3)\)\ \((19 + 3\ \@33)\)\^\(1/3\)}}\)], 
"Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(NSolve[x^3 - x^2 - x - 1 == 0, x]\)], "Input"],

Cell[BoxData[
     \({{x \[Rule] \(-0.419643377607080569`\) - 0.606290729207199419`\ I}, {
         x \[Rule] \(-0.419643377607080569`\) + 0.606290729207199419`\ I}, {
         x \[Rule] 1.83928675521416113`}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(c = \(-0.419643377607080569\)\)], "Input"],

Cell[BoxData[
     \(\(-0.419643377607080569`17.9031\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(s = \(-0.606290729207199419\)\)], "Input"],

Cell[BoxData[
     \(\(-0.606290729207199419`17.9031\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(z = c + I*s\)], "Input"],

Cell[BoxData[
     \(\(-0.419643377607080569`17.9031\) - 0.606290729207199419`17.9031\ 
I\)],
   "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(z^2\)], "Input"],

Cell[BoxData[
     \(\(-0.19148788395311880508967465797`17.1489\) +
       0.50885177883273803553625813551`17.6021\ I\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(c1 = \(-0.19148788395311880508967465797\)\)], "Input"],

Cell[BoxData[
     \(\(-0.19148788395311880508967465797`28.301\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(s1 = 0.50885177883273803553625813551\)], "Input"],

Cell[BoxData[
     \(0.50885177883273803553625813551`28.9031\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(z^3\)], "Input"],

Cell[BoxData[
     \(0.38886873843980076415946686483`17.3279 -
       0.09743895037446135435716873396`16.7408\ I\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(c2 = 0.38886873843980076415946686483\)], "Input"],

Cell[BoxData[
     \(0.38886873843980076415946686483`28.6021\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
     \(\(\t\ts2 = \(-0.09743895037446135435716873396\)\)\)], "Input"],

Cell[BoxData[
     \(\(-0.09743895037446135435716873396`28.2041\)\)], "Output"]
}, Open  ]],

Cell["\<\
(* Wellin IFS program type*)
(* Rauzy tile of 2nd Kind*)
f1[{x_,y_}] = {-(x*c-s*y), -(s*x+c*y)};
f3[{x_,y_}] = {(x*c1-s1*y)+c1, (s1*x+c1*y)+s1};
f2[{x_,y_}] = {(x*c2-s2*y)+c2, (s2*x+c2*y)+s2};
\
\>", "Input",
   InitializationCell->True,
   AspectRatioFixed->True],

Cell["\<\
f[x_] := Which[(r=Random[]) <= 96/176, f1[x],
\tr <=124/176, f2[x],r <= 1.00, f3[x]]\t\
\>", "Input",
   InitializationCell->True,
   AspectRatioFixed->True],

Cell["\<\
ifs[n_] := Show[Graphics[{PointSize[.001],
\tMap[Point, NestList[f, {0,0}, n]]}],
\t\tPlotRange->All,AspectRatio->Automatic]\
\>", "Input",
   InitializationCell->True,
   AspectRatioFixed->True],

Cell[CellGroupData[{

Cell["ifs[20000]", "Input",
   AspectRatioFixed->True],

Cell[BoxData[
     TagBox[\(\[SkeletonIndicator]  Graphics  \[SkeletonIndicator]\),
       False,
       Editable->False]], "Output"]
}, Open  ]]
},
FrontEndVersion->"Macintosh 3.0",
ScreenRectangle->{{0, 1920}, {0, 1060}},
AutoGeneratedPackage->None,
WindowToolbars->{},
CellGrouping->Manual,
WindowSize->{774, 859},
WindowMargins->{{208, Automatic}, {Automatic, 63}},
PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}},
ShowCellLabel->True,
ShowCellTags->False,
RenderingOptions->{"ObjectDithering"->True,
"RasterDithering"->False},
MacintoshSystemPageSetup->"\<\
00/0001804P000000_@2@?olonh35@9B7`<5:@?l0040004/0B`000003509H04/
02d5X5k/02H20@4101P00BL?00400@0000000000000000010000000000000000
0000000000000002000000@210D00000\>"
]


(***********************************************************************
Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of
the file.  The cache data will then be recreated when you save this file
from within Mathematica.
***********************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{

Cell[CellGroupData[{
Cell[1731, 51, 157, 7, 42, "Input",
   InitializationCell->True],
Cell[1891, 60, 466, 9, 104, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[2394, 74, 66, 1, 27, "Input"],
Cell[2463, 77, 220, 3, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[2720, 85, 62, 1, 27, "Input"],
Cell[2785, 88, 67, 1, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[2889, 94, 62, 1, 27, "Input"],
Cell[2954, 97, 67, 1, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3058, 103, 44, 1, 27, "Input"],
Cell[3105, 106, 104, 2, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3246, 113, 36, 1, 27, "Input"],
Cell[3285, 116, 130, 2, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3452, 123, 74, 1, 27, "Input"],
Cell[3529, 126, 77, 1, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3643, 132, 69, 1, 27, "Input"],
Cell[3715, 135, 73, 1, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3825, 141, 36, 1, 27, "Input"],
Cell[3864, 144, 125, 2, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[4026, 151, 69, 1, 27, "Input"],
Cell[4098, 154, 73, 1, 26, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[4208, 160, 82, 1, 27, "Input"],
Cell[4293, 163, 78, 1, 26, "Output"]
}, Open  ]],
Cell[4386, 167, 272, 9, 102, "Input",
   InitializationCell->True],
Cell[4661, 178, 165, 5, 42, "Input",
   InitializationCell->True],
Cell[4829, 185, 203, 6, 57, "Input",
   InitializationCell->True],

Cell[CellGroupData[{
Cell[5057, 195, 53, 1, 27, "Input"],
Cell[5113, 198, 130, 3, 26, "Output"]
}, Open  ]]
}
]
*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)


Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 
619-5610814 :
URL :  http://home.earthlink.net/~tftn
URL :  http://victorian.fortunecity.com/carmelita/435/


  • Prev by Date: Re: Q: extract all k-tuple from a list of n elements
  • Next by Date: Re: how to effectively define a subsection function
  • Previous by thread: Follow up: Help wanted ... bounding function is pierced for n even > 10^7.
  • Next by thread: Question about composing a complex function.