You can probably imagine that, considering the climate, demand for fountains isn't too high in Greenland. In fact, when it was completed in 1932, Mindebrønden (Memorial Fountain) was the only fountain on the entire island.
Construction on the Qaqortoq fountain, forged out of distinctive Igaliku sandstone, began in 1927. The subject matter is also endemic to Greenland. Several whales squirting water out of their blowholes are mounted at the top of the lantern-like base - a nod to the island's whaling tradition (you'll likely see some living ones in the fjords surrounding the city). Several smaller spouts arranged around the circular stone basin shoot delicate arcs of water towards the fountain's center.
Mindebrønden is hard to miss, as it's right in the middle of the very tiny square that makes up Qaqortoq's very tiny city center. Locals and tourists alike often gather here for lunch on the surrounding picnic tables. The fountain also shares the space with the Qaqortoq Museum, formerly a blacksmiths' shop, which now showcases both modern art and Greenlandic handicrafts.
The only other fountain in Greenland can be found further to the north, in Sisimiut.