Mathematical Determination of the Cultural Interaction between Medieval Groups

Abstract

A mathematical classification of two-dimensional ornaments into 17 plane symmetry groups is presented, which were created by five medieval cultural groups of Middle East. The data are considered representative for the cultural groups. By applying a correlation algorithm on the individual use of symmetry classes by each cultural group, the strength of the interaction between the pairs of groups are quantitatively determined. The analysis shows that the strongest similarity in the creation of periodic ornaments is between Rum Seljuks and Arab Muslims. It is also found that the Rum Seljuks, followed by Armenians, are the most interactive cultures. This report is the first attempt to quantify cultural communication by mathematical means.