Mr. Palsson, who used to sell Iceland as a place to see the Northern Lights, employs an astronomer in his hotel. He has also invested in three expensive telescopes that are powerful enough for guests to see the rings on Saturn or the fuzzy glow of a distant dying star.

Landsbref, a fund management company that was spun off from one of three failed Icelandic banks, set up a $37 million tourism fund.

Reykjavik looks like a Scandinavian version of Singapore: compact, clean, orderly, and rich. Streets are lined with Crayola-color houses and Mercedes cars. Chic coffeehouses sell kale-and-date sandwiches, and play Ethiopian jazz. Restaurants offer inventive Nordic cuisine using local ingredients like puffin and shark. (One chef also proudly announced that Iceland now grows cucumbers, albeit in a greenhouse.)

The 101, a boutique hotel that was once an exclusive hangout for bankers (101 is also the city’s richest postal code), is now filled with tourists. In a possible dig at the hotel’s former denizens, a sculpture of what looked like a gray-suited banker hung on one wall, with a cryptic instruction, “Disconnect the battery, remove the rear hood and hinge brackets,” inscribed beneath it.

Tourists come from as far as Hong Kong. They chase the Northern Lights. They scale glaciers. They dive in the Arctic Circle with puffins, go horseback riding or take helicopter tours listening to ethereal, whale-like sounds by the Icelandic band Sigur Ros. Fans of “Game of Thrones” flock to filming locations around the island, some, apparently, genuinely in search of Wildlings.

Outside the capital, thick white plumes of steam, which are harnessed for Iceland’s energy needs, rise in the sky, as if the earth were vaping. Hot springs are everywhere, even in people’s backyards.