Mirror Curves

Slavik Jablan
Bridges: Mathematical Connections in Art, Music, and Science (2001)
Pages 233–246


Mirror curves are present in ethnical art, as Tamil threshold designs or Tchokwe sand drawings. Historically, they are to be found in the art of most peoples surrounding the Mediterranean, the Black and Caspian Seas, in the art of Egyptians, Greeks, Romans, Byzantines, Moors, Persians, Turks, Arabs, Syrians, Hebrews and African tribes. Highlights are Celtic interlacing knotworks, Islamic layered patterns and Moorish floor and wall decorations. In this paper mirror curves are considered from the point of view of geometry, tiling theory, graph theory and knot theory. After the enumeration of mirror curves in a rectangular square grid, and a discussion of mirror curves in polyominoes and uniform tessellations, the construction of mirror curves is generalized to any surface.