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MathGroup Archive 2004

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Akiyama-Thurston [1,5] minimal Pisot tile

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52122] Akiyama-Thurston [1,5] minimal Pisot tile
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Thu, 11 Nov 2004 04:52:43 -0500 (EST)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

This tile was proposed by Dr. Thurston in one of his lectures,
but only actually found by Dr. Akiyama.
The IFS form was found by S. R. Hinsley.
(*Akiyama-Thurston [1,5] minimal Pisot tile*)
NSolve[x3-x-1==0,x]
c=-0.662358978622373051
s=-0.562279512062301289
c1=0.460202188254280750782172413
s1=0.1825822545574430797121307804
(* Wellin IFS program type*)
(* Akiyama_Hinsley*)
f1[{x_,y_}] = {x*c-s*y+c, s*x+c*y+s};
f2[{x_,y_}] = {x*c1-s1*y+c1, s1*x+c1*y+s1};
f[x_] := Which[(r=Random[]) <= 3/4, f1[x],
   r <= 1.00, f2[x]]
a=NestList[f, {0,0}, 10000];
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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