Greeks would wear "Petasos", which we know as hats. They appeared around 1200 BC and were made to protect the greeks from weather. Just like in the photo, the "Petasos" would have chin straps so when they were not being used the hat would still ahng down the greeks back.
One of the most influential 19th century books on architectural patterns is The Grammar of Ornament, by Owen Jones, published in England in 1853. It fanned interest in decorative schemes for molding, tile, and wallpaper from a wide variety of sources. The page above describes Greek motives from friezes and pottery.