Under a star-filled sky, the silhouette of a towering alien creature, with spindly limbs and bulbous head, is cast long and looming upon a domed-roofed UFO, the green lights from the vestibule glowing eerie and luminous.

โ€œOver here,โ€ he commands, beckoning me towards four hooded figures that stand before a building, suggestive of a crown. โ€œAre you taking me to your leader?โ€ I joke, as I join the extraterrestrial (in fact, my teenage son Freddie) to gaze at Brasiliaโ€™s futuristic Catedral Metropolitana.

Catedral Metropolitana brasilia
Inside Catedral Metropolitana

Sixteen bowed ribs cradle the edifice, and inside, under a dome of undulating stained glass, hang aluminium angels. I see now that the four menacing figures are sculptor Ceschiattiโ€™s Four Disciples that guard the cathedralโ€™s entrance, and that the spacecraft heโ€™s left behind is the white cupola of the National Museum with a ramp that juts from its base and circles the building like a ring of Saturn.

Catedral Metropolitana brasilia
Inside Catedral Metropolitana

By day, the Brazilian capital gleams with bright, white, futuristic architecture. By night, it is shadowy, ethereal and encourages imaginations to soar. Taking a tour after dark leaves a lasting, surreal impression.

Brasilia was the first modern city to be protected by UNESCO for its unique, stirring, brutalist design, chiefly planned by architect Oscar Niemeyer โ€“ described as “king of the curve” and the “concrete poet” (and who was also responsible for Londonโ€™s Serpentine Gallery) โ€“ and urban planner Lucio Costa, who were tasked with creating a new capital, in place of Rio, in 1955. Itโ€™s hard to believe that 60 years ago there was nothing here but baked savannah.

Itโ€™s a city that splits opinion on whether itโ€™s the future or the past, and challenges views on what makes a great metropolis. Those who hate the place call it a botched utopia, where culture and character have been suppressed in favour of modernist planning. Those who love it (and live here) laud it as an antidote to urban chaos, where order, cleanliness and quiet reign, in stark contrast to the riot that is Rio, where weโ€™ve arrived from.

Memorial to Juscelino Kubitschek

โ€œRio is great, but itโ€™s thanks to Brasilia that Brazil is no longer considered a developing country. Niemeyer once said that architecture isnโ€™t just a matter of creating something beautiful, but of shaping space so that people feel good and can live with dignity. We have a very good life here,โ€ my guide, Lucio Montiel, tells me; Lucioโ€™s father worked as an architect directly under Niemeyer.

Brasiliaโ€™s otherworldly atmosphere wins me over quickly. I hadnโ€™t expected the charmingly retro feel of the place, which reminds me of my teenage penchant for B-movies. Itโ€™s something of an irony to realise that what was deemed a model of progress already stirs nostalgia.

“Itโ€™s hard to believe that 60 years ago there was nothing here but baked savannah.”

To appreciate the true brilliance of the cityโ€™s design, an aerial map is required. Niemeyer took inspiration from the shape of an aeroplane, placing uniform, perfectly spaced out, low-rise apartment blocks and retail outlets, known as superquadras, on arched โ€˜wingsโ€™, and government buildings, theatres, galleries and hotels on the central โ€˜fuselageโ€™, referred to as the Monumental Axis.

In the โ€˜cockpitโ€™ sits the Praca dos Tres Poderes (three powers), named for the three branches of government. A memorial to Juscelino Kubitschek, the former president who championed the construction of the city, dominates here.

Praca dos Tres Poderes

To the west, a 420-hectare park provides playgrounds, tennis courts, running tracks and football fields (when we visit, the noisy, passionate matches in play prove a reassuring sight). โ€œI feel like weโ€™re back in Brazil,โ€ comments Freddie.

At Supaquadra 702, we stumble back to the realms of the otherworldly at the Dom Bosco Sanctuary, built between 1963 and 1970. Designed by Carlos Alberto Naves, this colossal glass and concrete box, with 50ft-high archways filled with twelve shades of blue Murano glass, offers visitors the chance to bathe in heavenly light.

Dom Bosco Sanctuary

Manmade and vast, with a circumference of 50 miles, Paranoa Lake was created to reduce the effects of low humidity in drier months and is bordered by restaurants and private clubs (not all as fancy as they sound, with most built for the working masses).

Weโ€™re on the trail of wild capybaras, which patrol in buck-toothed gangs. Impossibly cute, they are a little out of control in their numbers, which creates a pleasing tension in this well-ordered city, and offers a reminder that weโ€™re in the Cerrado, a vast savannah of grasslands and forest that covers 21% of Brazil and teems with wildlife.

Capybaras near Paranoa Lake

Niemeyer believed that beauty is a fundamental necessity for the human spirit and not a luxury. What attracted him, he said, was โ€œthe free and sensual curveโ€. Within the buildings of the National Congress,
the House of Representatives, with its saucer-like roof, was designed as a symbol of Brazilโ€™s openness to all ideologies (yet serves as another reminder that this is a city built at a time of moon landings and space obsession).

Other standout buildings include the National Theatre, like a futuristic pyramid or how, perhaps, youโ€™d imagine the headquarters of a cult to be, while the Palรกcio do Itamaraty (Foreign Ministry) is
a mind-bending illusion, with a series of arches reflected in pools.

National Congress

But itโ€™s the presidentโ€™s office, Palรกcio do Planalto, thatโ€™s the showstopper, all trademark Niemeyer curved lines and epic columns, suggestive of ancient Greece. In August, this immense concrete scene is brightened by the bright yellow blooms of Brazilโ€™s national tree, the ipรช.

From a Niemeyer-designed shrine beside Paranoa Lake, I catch my first sunset over this flush, far-horizon heartland. As the heavens morph from tangerine to lavender, and finally settle upon deepest navy, Freddie and I scan the sky, agreeing that should little green men land tonight, theyโ€™d be hard pressed to find a more weirdly inviting city.

Need to know: Brasilia

Getting there: Itโ€™s an epic journey to reach Brasilia by road, but there are frequent connections to all of Brazilโ€™s other major cities by air (LATAM, Gol and Azul all fly here).

Getting around: Buses run along Monumental Axis, allowing you to hop on and off to see major sights. A limited metro system covers the south of the city, so itโ€™s often easier to call an Uber.

Best time to go: The dry season lasts from May (often considered the loveliest time to visit) to September. Rainfall can be heavy from November to February but, when the sun does shine, you will see Brasilia at its greenest.

Where to eat: Donโ€™t miss a lakeside seafood lunch at stylish Sallva (Instagram @sallvabsb). For no-frills barbecue and pizza, and ice-cold beers, head to Boteco do Juca (botecodojuca413.com.br), or to Choppao (choppao.com.br), where the star of the menu is escaldado cuiabano (chicken soup). Feast on Brazilโ€™s favourite dish of feijoada from the vast buffet at trendy Mangai (mangai.com.br).

Where to stay: To immerse yourself in Niemeyerโ€™s Modernist world, stay at the Brasilia Palace Hotel (plazabrasilia.com.br). On the Monumental Axis, the modern Windsor Plaza Hotel (windsorhoteis.com) has a great location and vast rooms.

Further information: visitbrasil.com / lata.travel. Kate travelled as a guest of Rainbow Tours UK (rainbowtours.co.uk).