Point processes for decagonal quasiperiodic tilings

A general construction principle of inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of an expansion and a division of the tiles, where the expanded tiles can be divided arbitrarily as far as the set of prototiles is maintained. A certain kind of point decoration processes turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quarternary and the other ternary. Properties of the ternary tilings with rhombic, pentagonal, and hexagonal prototiles are investigated in detail.