A family of two-dimensional words with maximal pattern complexity $2k$

Maximal pattern complexity $p^*(k)$ is one of the counting functions over infinite words. In this paper we consider it over two-dimensional words. We construct an infinite family of two-dimensional words with the maximal pattern complexity $p^*(k)=2k$ for $k\in\mathbb N$. It is the minimum of maximal pattern complexity over two-dimensional and not two-periodic words. Bibliogr. 21.