* Warren D Smith <warren.wds@gmail.com> [Jun 25. 2015 13:41]:
Google found http://www.integers-ejcnt.org/a2nta2004/a2nta2004.pdf a large review paper by V.Berthe & A.Siegel 2005. Lots of my ideas were already known and already investigated way better.
[...]
Raw form of what I have collected (not: studied) containing "Rauzy". %\jjbibitem{}{Pierre Arnoux, Shunji Ito: %\jjbibtitle{Pisot Substitutions and Rauzy fractals}, %Bull. Belg. Math. Soc., vol.8, pp.181-207, \bdate{2001}. %URL: \url{http://homepage2.nifty.com/shunjiito/paper/ArnouxIto.pdf}.} %% shows the substitutions for the Rauzy fractal %\jjbibitem{}{Pierre Arnoux, Val\'{e}rie Berth\'{e}, Arnaud Hilion, Anne Siegel: %\jjbibtitle{Rauzy fractals for free group automorphisms}, %slides, \bdate{2006}. %URL: \url{http://www.lirmm.fr/~berthe/PDF/exposeABHS.pdf}.} % %% paper: "Fractal representation of the attractive lamination of an automorphism of the free group" %% http://junon.u-3mrs.fr/hilion/fichiers/fractal-ABHS.pdf %% very nice figures %\jjbibitem{}{Pierre Arnoux, Maki Furukado, Shunji Ito: %\jjbibtitle{Substitutions from Rauzy Induction on 4-interval exchange transformations and Quasi-periodic tilings}, %, \bdate{June-2010}. %URL: \url{http://www.math.kochi-u.ac.jp/komatsu/conf2010/RIMS_proceedings.html}.} %\jjbibitem{}{Pierre Arnoux: %\jjbibtitle{What Is\ldots a Rauzy Fractal?}, %Notices of the AMS, vol.61, no.5, \bdate{August-2014}. %URL: \url{http://www.ams.org/notices/201407/index.html}.} %\jjbibitem{}{Val\'{e}rie Berth\'{e}, Anne Siegel, J\"{o}rg Thuswaldner: %\jjbibtitle{Substitutions, Rauzy fractals, and tilings}, %In: {Berth\'{e}, Rigo, Combinatorics, automata, and number theory}, % Encyclopedia of Mathematics and its Applications 135. % Cambridge: Cambridge University Press. pp.248-323, \bdate{2010}. %URL: \url{http://www.liafa.jussieu.fr/~berthe/Articles/Chapter5.pdf}.} %\jjbibitem{}{Val\'{e}rie Berth\'{e}: %\jjbibtitle{Multidimensional Euclidean Algorithms, Numeration and Substitutions}, %INTEGERS: The Electronic Journal of Combinatorial Number Theory, vol.11B, \bdate{2011}. %URL: \url{http://www.integers-ejcnt.org/vol11b.html}.} %% The slides contain nice images (Rauzy fractal(s)): %\jjbibitem{}{Val\'{e}rie Berth\'{e}, Timo Jolivet, Anne Siegel: %\jjbibtitle{Connectedness of fractals associated with Arnoux-Rauzy substitutions}, % RAIRO-Theoretical Informatics and Applications, to appear. %, \bdate{2011}. %URL: \url{http://www.liafa.jussieu.fr/~berthe/publi.html}.} %\jjbibitem{}{Timo Jolivet: %\jjbibtitle{Rauzy fractals associated with cubic real number fields}, %, \bdate{2011}. %URL: \url{http://www.liafa.jussieu.fr/~jolivet/}.} %% very nice slides %\jjbibitem{}{Timo Jolivet, Beno{\^\i}t Loridant, Jun Luo: %\jjbibtitle{Rauzy fractals with countable fundamental group}, %arXiv:1312.7829 [math.DS], \bdate{}. %URL: \url{http://arxiv.org/abs/1312.7829}.} %\jjbibitem{}{Beno{\^\i}t Loridant: %\jjbibtitle{Topological properties of a class of cubic Rauzy fractals}, %arXiv:1411.7544 [math.DS], \bdate{27-November-2014}, %URL: \url{http://arxiv.org/abs/1411.7544}.} %% when certain substitutions correspond to a disk %\jjbibitem{appl-comb-words}{M.\ Lothaire: %\jjbibtitle{Applied Combinatorics on Words}, %Cambridge University Press, \bdate{2005}. %URL: \url{http://www-igm.univ-mlv.fr/~berstel/Lothaire/AppCWContents.html}.} %% chapter 1: algorithms on words, p.511: Rauzy fractal %\jjbibitem{}{Ali Messaoudi: %\jjbibtitle{Fronti\`{e}re du fractal de Rauzy et syst\`{e}me de num\'{e}ration complexe}, %Acta Arithmetica, \bdate{2000}. %URL: \url{http://matwbn.icm.edu.pl/ksiazki/aa/aa95/aa9531.pdf}.} %\jjbibitem{}{G\'{e}rard Rauzy: %\jjbibtitle{Nombres alg\'{e}briques et substitutions}, %Bulletin de la Soci\'{e}t\'{e} Math\'{e}matique de France, vol.110, pp.147-178, \bdate{1982}. %URL: \url{http://www.numdam.org/item?id=BSMF_1982__110__147_0}.} %\jjbibitem{}{Tarek Sellami, V\'{i}ctor F.\ Sirvent: %\jjbibtitle{Symmetric intersections of Rauzy fractals}, %arXiv:1410.6229 [math.DS], \bdate{23-October-2014}, %URL: \url{http://arxiv.org/abs/1410.6229}.} %\jjbibitem{}{Anne Siegel: %\jjbibtitle{Substitutions, Rauzy fractals and Tilings}, %slides, \bdate{2009}. %URL: \url{http://www.cant.ulg.ac.be/cant2009/}.} %\jjbibitem{}{Anne Siegel, J\"{o}rg M.\ Thuswaldner: %\jjbibtitle{Topological properties of Rauzy fractals}, %, \bdate{}. %URL: \url{http://www.dmg.tuwien.ac.at/nfn/Topological.pdf}.} %\jjbibitem{}{V\'{i}ctor F.\ Sirvent, Yang Wang: %\jjbibtitle{Self-affine tiling via substitution dynamical systems and Rauzy fractals}, %Pacific Journal of Mathematics, vol.206, no.2, \bdate{2002}. %URL: \url{http://pjm.math.berkeley.edu/pjm/2002/206-2/p11.xhtml}.} %%% domain (URL) in paper (http://www.pacjmath.org/) is dead %%% http://nyjm.albany.edu:8000/PacJ/p/2002/ %\jjbibitem{}{J\"{o}rg M.\ Thuswaldner: %\jjbibtitle{$S$-adic words, Rauzy fractals, and torus rotations}, %slides, \"{O}MG/DMV Congress, Innsbruck, \bdate{26-September-2013}. %URL: \url{}.} %%% per email from author Regards, jj