/u/Steelcan909 and I discussed the possible availability of exotic animals not only for the Vikings, but also medieval Europeans in general respectively in n the television show Vikings, various Medieval European courts and nobles are pictured as having a variety of rare or exotic animals such as monkeys and parrots. The leader of the Vikings is also shown petting both a rat and a python at one point. Are such portrayals historically accurate?
In short:
- Elephant: has been known to Europeans as an exotic gifts for the ruler sometimes from non-European ruler since the 9th century. Not only Charlemagne (mentioned in the linked thread), but also some European kings during the crusader period like King Louis IX of France (d. 1270) and King Henry III of England (d. 1272) had an elephant. As for the latter's elephant, we also had a illustration in the manuscript, cited in this blog entry of the Parker Library. Charlemagne's elephant even had a 'personal name' (Abul-Abbas).
- Birds (Gyrfalcons): exotic birds, especially gyrfalcons, were prized both among the Europeans and among the Muslim nobles (Cf. Takayama 2010 in the linked post) since many of them loved falconry. As I mentioned briefly in What knowledge did mainland Europeans have of Iceland, Greenland and Vinland during the Middle Ages?, Medieval Icelanders and Greenlanders in the North Atlantic were famous for the exporters of the gyrfalcons, together with the polar bear. Some of them were sent even for the Middle East as a gift from the European ruler to the Islamic Sultan in Egypt.
- Australian Parrot: Emperor Frederick II (d. 1250) of HRE, famous for his 'diplomatic crusade', in fact had another face: He authored himself a book of the falconry, showing his talents of patient observation as well as wide geographical knowledge (up to Greenland). Recently, a scholar also discovered that one of the illustration of a parrot in his book was indeed a female cockatoo, originally living near Australia. This cockatoo had probably been captured and taken first to the Middle East, then the Islamic ruler presented it to Emperor Frederick II as a gift, though we don't know what this exotic parrot was called in Europe (Dalton 2018 in the linked post).
References are to be found in the linked post above.