Final answer:
Pergamum in Anatolia was a significant center for the mixing of Greek and Eastern cultures during the Hellenistic period, characterized by the establishment of Greek institutions and cultural blending encouraged by the policies of Hellenistic rulers.
Step-by-step explanation:
The mixing of Greek and Eastern cultures was quite prominent in Pergamum in Anatolia during the Hellenistic period. This period was marked by the establishment of new centers of Greek culture, such as in Pergamum, Antioch, and Alexandria. The blending of Greek and other cultures was a defining characteristic of this era, supported by the polices of Hellenistic rulers like Alexander the Great, who encouraged inter-marriage and took over the Persian system of governance to manage the diverse populations of his empire.
Despite being a minority, Greeks became a new elite class and established cities replete with Greek institutions like temples, theaters, agoras, and gymnasia. This facilitated an environment where Greek culture could flourish amongst the indigenous population. In cities like Pergamum, which were usually under the control of a Hellenistic kingdom, many Greeks turned from politics to personal pursuits and religious syncretism, further fostering cultural exchange and blending.