A family of non-periodic tilings of the plane by right golden triangles (Q2671174)

The author in this paper deals with right ``golden'' triangles and planar tilings with such \textit{proto-tiles}. The author studies a family of substitution tilings with similar right triangles of two sizes which is obtained using the substitution rule introduced by \textit{L. Danzer} and \textit{G. van Ophuysen} [``A species of planar triangular tilings with inflation factor \(\sqrt{-\tau }\)'', Res. Bull. Panjab Univ. Sci. 50, No. 1--4, 137--175 (2000)]. These authors proved that this family of tilings can be obtained from a local rule using decorated tiles. Based on the work of Danzer and van Ophuysen, the author develops new ideas and presents a more intuitive and simple demonstration of these facts.