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 ------------------------------------------------------------------------