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A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs. First, we construct an infinite family of n× n 2D strings with Ω(n^3) distinct tandems. Second, we construct an infinite family of n× n 2D strings with Ω(n^2log n) distinct quartics. Third, we construct an infinite family of n× n 2D strings with Ω(n^2log n)arXiv:2105.14903v1 fatcat:5e2bbap4lvedvgtvgibcdeb5e4