Heading east out of Vik you almost immediately begin a long desert crossing - the Myrdalssandur is indeed a desert of lava stone, the result of the vagaries of Katla volcano. In fact, the further east you go the less inhabited the area becomes, because it is regularly victim to floods.
The first time I crossed Myrdalssandur, I didn't necessarily realise that all the lava stones around me had been spewed by the volcano.
The place is surprisingly empty and, of course, there is no human presence - who would want to live in a place where the volcanoes belch their rocks and where the waters destroy everything in their path!
If you want to stretch your legs and don't want to settle for a photo stop by the roadside, try to go to Hjörleifshöfdi, just outside Vik. It's the only hill of any size that offers a view of the coast. By continuing almost straight ahead toward the ocean you will arrive at Kötlutangi, the most southerly point of the island.