The idea that contemporary Islamic culture is inward looking was contradicted from the word go by the invitation to IM Pei to be the chief architect of the project. The Chinese born American considered by many to be a master in his field was gently coaxed out of retirement to design the building. Most agree he has done a stupendous job. You may know him for, among many other projects, the glass pyramid outside the Louvre.
The Museum of Islamic Art in Doha, Qatar is a stunning example of contemporary architecture fused with traditional cultural sign posts. It is one of the most remarkable buildings in the Persian Gulf but sadly, not so well known out of its locale.