There is no single "Mediterranean look." The Mediterranean basin spans three continents (Europe, Africa, Asia) and over 20 countries with millennia of migration, trade, and conquest.
Physical appearance reflects complex genetic histories: Neolithic farmers, Bronze Age migrants, Phoenicians, Greeks, Romans, Arabs, Berbers, Turks, Slavs, Sub-Saharan Africans, and more. The Mediterranean is a genetic crossroads, not a monolith.