Iris

Grid 8×8 Symmetry
Palette

About this lab

Roman mosaics (opus tessellatum) were assembled from small stone or glass cubes called tesserae, typically 1–2 cm across. Floor mosaics in villas, baths, and public buildings featured geometric borders and pictorial scenes. The finest work, opus vermiculatum, used tiny tesserae (under 4mm) to achieve almost painterly detail — the Alexander Mosaic from Pompeii contains roughly 1.5 million pieces.

The geometric vocabulary of Roman mosaics draws on repeating motifs: the meander (Greek key) symbolizes infinity and the eternal flow of life; the guilloche is a braided band pattern found from Mesopotamia through Rome; wave patterns (often called “running dog”) border larger compositions. These patterns all exploit translational and rotational symmetry — the same mathematical groups that govern crystallography and Islamic geometric art.

The mathematics of tiling connects Roman mosaics to deep results in geometry. The 17 wallpaper groups classify all possible periodic symmetries of a plane pattern, and Roman artisans intuitively employed many of them. Islamic artists later pushed these ideas further, achieving all 17 groups in the Alhambra. The rosette patterns in this lab use rotational symmetry groups (cyclic and dihedral), while the meander patterns use frieze groups — the seven symmetry types of a strip pattern.