Complex Systems

Hexagonal Lattice Systems Based on Rotationally Invariant
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Leah A. Chrestien

St. Stephen's College
University Enclave, North Campus
Delhi 110007, India

Abstract

In this paper, periodic and aperiodic patterns on hexagonal lattices are developed and studied using a given set of constraints. On exhaustively enumerating all possible two-color patterns for up to a combination of four constraints, 106 distinct periodic tilings are obtained. Only one set of four constraints out of a total of 24157 possible sets generated a pattern that is aperiodic in nature.