What blend of cultures is the Hellenistic culture?

A Greek overlay on a local culture - it arose from Alexander the Great's conquest of the Persian Empire, after which he tried to impose Greek culture and established Greek-style city-states as a civilising process. After his death, his generals split up his empire amongst them, and we call these new countries the Hellenistic Kingdoms (Egypt, Syria etc). The result was largely superficial and there was progressive reversion to the underlying cultures until the Muslim invasions swept much of it away.