A mega egg in Paris, a hovering hotel in Machu Picchu, an hourglass tower in New York, a pleasure island in Baghdad … we reveal the architectural visions that were just too costly – or too weird

Did you know that, if things had gone differently, the Pompidou Centre could have been an egg? In the 1969 competition for the Paris art centre – ultimately won by Richard Rogers and Renzo Piano, with their inside-out symphony of pipework – a radical French architect called André Bruyère submitted a proposal for a gigantic ovoid tower. His bulbous building would have risen 100 metres above the city’s streets, clad in shimmering scales of alabaster, glass and concrete, its walls swelling out in a curvaceous riposte to the tyranny of the straight line.

“Time,” Bruyère declared, “instead of being linear, like the straight streets and vertical skyscrapers, will become oval, in tune with the egg.” His hallowed Oeuf would be held aloft on three chunky legs, while a monorail would pierce the facade and circle through the structure along a sinuous floating ribbon. The atrium was to take the form of an enclosed globe, like a yolk.

Le Corbusier called grain silos ‘the magnificent first fruits of the new age’. But what can be done with these soaring industrial cathedrals when they’re redundant? A Norwegian tycoon has the answer

If you’ve ever wondered what it would feel like to be as insignificant as a kernel of corn, you can now get a good idea in Kristiansand, a city in southern Norway. Standing on the fourth floor of its new Kunstsilo art museum, carved out of an old 1930s grain silo, you can peer down a vertiginous concrete tube that plunges towards huddles of ant-like people below. Or you can look up, through more concrete shafts, towards tiny circles of sky. You can mimic the journey of a grain by climbing a spiral staircase inside one of the cylinders, or test your nerves by walking on a glass-floored terrace suspended over another shaft, floating above a tubular abyss. It’s a dramatic spatial spectacle – and we haven’t even got to the art yet.

Once home to 15,000 tonnes of grain, this mighty concrete mountain is now a repository of the most important collection of Nordic modern art in the world. It is a 5,500-strong haul spanning paintings, drawings, ceramics, sculpture and full-size architectural installations, telling the story of the past century of abstraction, surrealism and expressionism across Norway, Sweden, Finland and Denmark – inside one of the ultimate symbols of modernity itself.

In the middle of the Mojave desert, the US army has built a huge set to prepare its soldiers for combat, filled with actors, tanks, explosions – and even fake news

In the middle of California’s Mojave desert, down a long, bumpy track that winds past barren hills and arid ravines, there is a town like no other. The first unusual sight is a golden onion dome poking up on the horizon, crowning a pale blue minaret. It rises above a cluster of boxy, tan-coloured buildings that form a network of narrow alleyways around a central street where a lively market is in full swing. Some of the buildings are topped with decorative crenellations, others have big plastic water butts on their roofs, some are adorned with plaster columns with a faintly Middle Eastern air. The buildings become simpler as they get farther from the centre of town, fading into blank grey boxes with window-shaped cutouts in the hazy distance.

It looks as if it could be a film set for Hollywood’s latest Arabian epic, or a new live-action Disney show, ready for Aladdin to swoop in on his carpet. But this is a theatre of a very different kind. It is not Aladdin but an Apache helicopter that suddenly appears overhead, its blades narrowly missing the minaret as a rapid volley of gunfire echoes through the streets. A tank rumbles around the corner, aiming towards a building on which armed figures patrol the roof. There’s a big bang, and clouds of smoke engulf the street. A human body starts convulsing on the ground, spurting with fake blood.