If they were rich enough, Greeks living in the 4th century would decorate their floors with mosaics. These would take the form of everything from detailed geometric patterns to scenes of animals, people and gods. Roman mosaics commonly used Greek key patterns as borders. One example is the "guilloche" -- used to give the impression of an inter-twined rope border.
Following the collapse of the Roman Empire, a different form of mosaic began to emerge concurrent with the rise of the Byzantine Empire. Starting from around the 5th century, the Byzantium mosaics used a special type of glass and were mounted on walls or ceilings. The patterns were heavily influenced by Eastern tastes and often featured simplistic depictions of animals or religious figures. These patterns were non-symmetrical; more closely resembling paintings.
By contrast, the Moors created mosaics using patterns that were heavily based on mathematics and geometry. One Arabic style, known as "zillij," uses ceramic shapes that are individually designed so that they can tessellate, or fit togehter.