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MathGroup Archive 2004

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minimal Pisot tile {2,3] type definition in Mathematic

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52123] minimal Pisot tile {2,3] type definition in Mathematic
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Thu, 11 Nov 2004 04:52:46 -0500 (EST)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com


There is an IFS rotation procedure used with twin dragon tile to make
Heighway dragon tile called a Riddle rotation.
I found this tile using that type of experiment on my IFS.
Hinsley has the same tile as well.
The [1,5] and [2,3] are the powers of the base
Minimal Pisot complex number polynomial solution.
(* minimal Pisot tile {2,3] type definition in Mathematica*)
c=0.868837
a=220.328
r0=c
w0=Pi*a/180
x0=r0*Cos[w0]
y0=r0*Sin[w0]
x5=r03*Cos[3*w0]
y5=r03*Sin[3*w0]
x3=r02*Cos[2*w0]
y3=r02*Sin[2*w0]
t=1
aa=(x*x5-y*y5)
bb=(x*y5+y*x5)
cc=Cos[t*Pi]
ss=Sin[t*Pi]
x1=aa*cc-bb*ss+x5+(x5)*t
y1=aa*ss+bb*cc+y5-(x5)*t
(* Wellin IFS program type*)
(* Akiyama_23: curley tile*)
f1[{x_,y_}] = {x*x3-y*y3+x3, x3*y+y3*x+y3};
f2[{x_,y_}] = {x1, y1};
f[x_] := Which[(r=Random[]) <= 1/2, f1[x],
   r <= 1.00, f2[x]]   ifs[n_] := Show[Graphics[{PointSize[.001],
   Map[Point, NestList[f, {0,0}, n]]}],
       PlotRange->All,AspectRatio->Automatic]
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


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