Selection-rules for quasi-lattices

Theory of tiling in general and of quasiperiodic tiling in particular has been studied extensively since the discovery of quasicrystals. Several algorithms have been proposed to generate quasiperiodic tiling in two-dimensional plane as well as in three-dimensional space. A new algebraic approach to generate such tilings is developed and discussed. The four-integer representation of a two-dimensional quasiperiodic system is explored to arrive at the analytical conditions for generating quasiperiodic tiling.