A walk through Pyrgi, an island town with a population around 1,000, is a colorful tour of geometric designs and motifs. As one of the “mastic villages” that once made the picturesque Greek island of Chios renowned and rich—the sap obtained exclusively from its mastic trees to make medicines, foods, liqueurs, and natural chewing gum was a highly valued product from the time of the ancient Greeks through the Ottoman era—it is little changed since medieval times. Mastic production remains a proud tradition and critical for the local economy, but…