Substitutional structures in simply and multiconnected flat spaces, with astrophysical applications

Abstract\n Hexagonal, octagonal and dodecagonal tilings of both simply and multiconnected flat spaces in 2D are considered. The tessellations of the euclidean plane have in common arrowed prototiles, which are used for the construction of fundamental polygons for the flat torus and the Klein bottle. Non deterministic derivations in formal grammars, producing non periodic ordered structures, have been introduced recently also for the analysis of variable stars with multiple periods, like the semiregular star UW Her and the Delta-Scuti star V784 Cas. Observations of the V346 Ori light curve can be modelled with similar techniques.