The meaning of a castle
From Ian Mortimer’s fine biography of Edward III:
[He] was leading the royal family in a recreation of a semi-legendary realm. His purpose was a demonstration of absolute royalty. It was the biggest pro-royal propaganda statement since his grandfather Edward I had constructed a whole series of castles in the newly conquered north of Wales, including one (Carnarvon) modelled on Constantinople, capital of the Eastern Roman empire.
From Wikipedia:
Caernarfon's appearance differs from that of other Edwardian castles through the use of banded coloured stone in the walls and in its polygonal, rather than round, towers. There has been extensive academic debate over the interpretation of these features. Historian Arnold Taylor argued that the design of the castle was a representation of the Walls of Constantinople. The conscious use of imagery from the Byzantine Roman Empire was therefore an assertion of authority by Edward I, and influenced by the legendary dream of Magnus Maximus, a Roman emperor. In his dream Maximus had seen a fort, "the fairest that man ever saw", within a city at the mouth of a river in a mountainous country and opposite an island. Edward interpreted this to mean Segontium was the city of Maximus' dream and drew on the imperial link when building Caernarfon Castle.