How did the art of the romans, Greeks, and Egyptians come to share certain characterstics?

The Greeks, the Romans, and the Egyptians were very nearby, and always at war with each other. However, this nearness would also cause people that are nearby to figure out a way to communicate. Eventually, they could learn from each other, and spread culture. For instance, Cleopatra actually had Greek roots, ruled over Egypt, and ended up falling in love with a Roman. When cultures mixed, so did art.