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

Abstract

Hexagonal, octagonal and dodecagonal tilings of both simply and multiconnected flat spaces in two dimensions 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 δ-Scuti star V784 Cas. Observations of the V346 Ori light curve can be modelled with similar techniques.

Acknowledgements

The NASA ADS Abstract Service and the SIMBAD database at CDS-Strasbourg, France, were used to access data about V346 Ori (D.F.M. Folha) and for references. I thank the ICQ9 Committee – Ames Laboratory and Universidad Politécnica de Madrid for financial support.