It is generally accepted by scholars that the ancient Romans and the Nabataeans were independently influenced by Alexandrian architectural style. Some of these similar influences can be observed in Roman wall paintings and Nabataean architecture. On the left is a Second Style painting from the Cubiculum M. of the Villa of Public Fannius Synistor, originally located in Boscoreale (near Pompeii) and on the right is an image of the facade of Al-Khazneh, a famous monument in Petra, Jordan. One of the Alexandrian influences on both examples is the broken pediment (architectural feature designed as an incomplete triangle).
Both of these examples also include a circular (tholos) structure. These circular structures were common in ancient architecture (as seen in Delphi, Greece), but the tholoi in Petra are unique: they are narrowly proportioned and decorated with Corinthian columns. The most distinct feature of these tholoi is a tent-like roof that is decorated with another Corinthian capital and an urn. The only other tholoi with this same combination of Nabataean features are found in Second Style Roman paintings from Pompeii. It appears that Alexandria is the architectural source for this type of tholos, particularly because both the Nabataeans and Romans employ other elements of Alexandrian architecture (such as the aforementioned broken pediment).1
It is unlikely that Petra and Pompeii had any direct contact or artistic influence on each other. Instead, both ancient societies were independently influenced by the Alexandrian style. Isn't that fascinating? Along these same lines, I recently found an interesting article that examines how Roman Third Style wall paintings include depictions of wind towers - triangular structures used on the roofs of Egyptian and Mesopotamian structures as a type of ventilation system.2 Neat-o.
1 For more information, see Judith McKenzie and Peter Roger Stuart Moorey, The Architecture of Alexandria and Egypt (New Haven, Connecticut: Yale University Press, 2007), 96-103.
2 Elfriede R. Knauer, "Wind Towers in Roman Wall Paintings?" Metropolitan Museum Journal 25 (1990): 5-20.
2 Elfriede R. Knauer, "Wind Towers in Roman Wall Paintings?" Metropolitan Museum Journal 25 (1990): 5-20.