Yemeni Squares

Having noted the simple but elegant design of a tiling pattern in a Yemeni mosque based on the division of a square into 10 × 10 small squares or cells, the authors have created Yemeni squares by generalizing the design to a square consisting of 2n × 2n cells. They prove an algebraic property of such squares and enumerate by computer all such squares up to n = 6. The original Yemeni square spells out the name Ali in square Kufic script; the reader may be able to find other examples of words in the figures provided in the article.