Abstract
Non-periodic planar patterns generated by deterministic inflation rules are described. Several types of patterns with both unit and non-unit Pisot numbers as inflation factors are formed by triangular prototiles. When the inflation factor is the silver mean, the patterns can be obtained by superimposing two subpatterns and some of them can be converted into face-to-face patterns. The geometric constructions corresponding to 12-fold symmetry are also studied. The Fourier transform of point masses, placed in vertex positions of the transformed subpatterns, exhibit two-fold, four-fold and six-fold symmetries, although the peaks with highest intensities are situated in rings with apparent octagonal and dodecagonal symmetries.
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