A Drawing Method for Banna'i Patterns and Ma'qeli Scripts: Symmetry-Based Pixel Coding (Examples from Samarkand, Bukhara and the Topkapı Scroll)

Preprint, not peer reviewed. Submitted to Symmetry: Culture and Science, October 2026. Banna'i (hazarbaf) patterns, built from glazed and unglazed bricks, are usually documented with photographs and drawings, which makes it hard for different people to reapply a pattern with the same dimensions and cell layout. This study proposes Symmetry-Based Pixel Coding (SBPC), a method developed by the author in four steps: (1) finding the smallest translating unit (the motif grid); (2) testing horizontal and vertical reflection to find the code grid; (3) expressing the grid numerically with colour classes, code lengths and weights; and (4) deriving the full pattern from the code and comparing it with the source. The method is limited to translation and reflection symmetry. Patterns fall into four types: horizontal reflection only (Type I), vertical only (Type II), both axes (Type III) and none (Type IV). SBPC is applied to four real patterns from the Tilya-Kori and Sher-Dor Madrasas in Samarkand and the Ulugh Beg Madrasa in Bukhara. The Ma'qeli (square Kufic) script in the Sher-Dor Type IV pattern matches a square-grid drawing in the Topkapı Scroll (TSMK H.1956), and a second scroll panel is also coded. Weight totals give production data such as area, units per colour and number of translations. Two multiple-choice questions illustrate use in teaching.