"Peas and beans! Peas and beans!" The famous Japanese architect was in his office, high in a Tokyo tower, its walls crowded with framed honours and diplomas. Assistants of exceptional beauty shimmered in with tea, but what he wanted to talk about was pulses. Rising prosperity in China would lead to rising meat consumption, and in turn a global protein crisis. It was the greatest problem, he said, facing mankind today. The solution lay in Kazakhstan, the vast former Soviet republic, for whose president the architect, Kisho Kurokawa, was masterplanning a new capital. This country, to the south of Russia, stretches from the eastern edge of Europe almost to Mongolia. For Kurokawa it offered ample opportunity for growing peas and beans, and – in a symbolic way – his plan would help. It was based on the interweaving of city and nature, with swaths of green between the buildings. It represented an idea of interdependence of which pulse-growing on an immense scale would be the practical outcome.

This meeting was in 2001, and Kurokawa died in 2007, but his city is now there, more or less following his plan. There are plenty of parks and trees. Called Astana, it is the world's latest example of a rare but persistent type, the capital from zero. It is in a line that includes St Petersburg, Washington DC, Canberra, Ankara and Brasilia and like them it provokes a question: can a city, in all its teeming complexity, really be planned? Or does the attempt lead only to a synthetic simulacrum, a kind-of city that is not quite the real thing?

To look at, Astana is so strange that it has one grasping for images. It's a space station, marooned in an ungraspable expanse of level steppe, its name (to English speakers) having the invented sound of a science fiction writer's creation. It's a city of fable or dream, as recounted by Marco Polo to Kublai Khan. Except it's not quite so magical: it's also like a battery-operated plastic toy, all whirring noises and flashing colours, of a kind sold by the city's street vendors.

Astana's ornaments include a 62-metre-high silver pyramid, designed by British architects Foster + Partners, giant gold-green cones and a gold orb resting on a structure of erupting white steel. At night its buildings go purple, pink, green and yellow. Astana's latest, most technically ambitious addition is a 150-metre-high translucent tent, also by Lord Foster. Called Khan Shatyr, a single leaning mast props its roof, which offers shelter from a harsh climate to a shopping and entertainment complex underneath. It follows a familiar Foster strategy, to be seen in the Great Court of the British Museum, or his airports at Stansted, Hong Kong and Beijing, which is to create an impressively engineered roof – a thing to be looked at and admired but not inhabited – hovering over a lower, less ordered, zone where the activity of the buildings, in this case shops and theme-park rides, takes place. This strategy, derived from the geodesic domes which the visionary American designer Buckminster Fuller once proposed throwing over whole cities, makes for striking architecture but also for awkward clashes where the two zones meet. Top and bottom seem to be different worlds.

Khan Shatyr opened last month with an extravagant celebration which coincided with the 70th birthday of President Nursultan Nazarbayev, who is the beginning and end of everything that happens in Astana. The building is there "because the idea came from the president", says its German-born manager: that there were four other malls within a square kilometre "didn't matter for him". The gold orb on the white steel tower, which signifies the egg laid annually on the tree of life by the mythical bird Samruk, was designed by Nazarbayev himself. When Nazarbayev commissioned Foster to design his Palace of Peace and Reconciliation, he told them he wanted it pyramid-shaped, which may be the first and only time a client has told the mighty Foster what a building should look like, and been obeyed.

Such cities are often the work of a single strong man. There is a museum of the founder in Astana, as there are of Kemal Atatürk in Ankara and President Kubitschek in Brasilia, pharaonic insurance against the afterlife that contains such things as Nazarbayev's grandfather's seal of office as a local judge. There is the president's palace, which stands on a long axis linking the two Foster works, the tent and the pyramid, and the golden orb. The palace is a version of the White House, improved by the addition of a blue dome. Also by its dominating location: the American original is placed off-centre from Washington's Mall, signifying a separation of powers that is not quite the Kazakh style.

The common view of Nazarbayev, among those western politicians who have one, is that he is by some distance the best of the extremely bad bunch running the former Soviet republics of central Asia. Margaret Thatcher has written a foreword to Nazarbayev's book The Kazakhstan Way, praising him for throwing off "the Soviet yolk [sic]". He established himself as a reformer in the 1980s, enough for Gorbachev to ask him, unsuccessfully, to be prime minister of the Soviet Union. The west was also extremely grateful to him for giving up his ballistic missiles when the collapse of the Soviet Union left him the master of the world's fourth-largest nuclear arsenal.

Kazakhstan may rank 142nd in the world press freedom index, and 120th in the corruption perception index, and he may win elections and referendums with suspiciously high votes of 91% and 95%, but – goes the pro-Nazarbayev argument – nobody else could have stabilised his country's potentially explosive ethnic combinations, and ridden the violent post-Soviet economic storms. This argument is set out in Nazarbayev and the Making of Kazakhstan, an eloquent, if oily, book by the British former minister Jonathan Aitken. Among its gems is a description of the romance between the president and his future wife, which flourished after an accident at a steel works: "While the flames of the blast furnace were damped down, the fires of love ignited."

Aitken reports how his subject, as a young champion of steelworkers' rights, was scathing about both grandiose building projects and the decision to locate a steel plant in a site with an appalling climate. Yet he chose to build Astana, which can fairly be called grandiose, in a place that had been notable previously for its Soviet penal colonies and where the temperature runs from -40C to 40C (-40 to 104F). His logic was that the previous capital, Almaty, was too close to China, too congested, and prone to earthquakes.One can guess that, as for other rulers, building a new capital gave Nazarbayev a place he could control, made on his own terms. In keeping with his status as a better-than-average dictator, this is done subtly: Astana is not littered with statues and images of its maker, and when his followers suggested that it should be named after him, he modestly demurred. (Although the somewhat neutral "Astana" – it means "capital" – might indicate that the space is being kept open for a renaming in the future.)

Instead you hear, again and again, that things are the way they are "because the president wants it", which is delivered as a sufficient and unarguable statement. The shopping centre manager says it, as does the waiter serving horse steak. President Medvedev of Russia said that Nazarbayev "has given this city not only his work but also his soul". He wanted the city, and he specified its monuments in detail. He had his government officials, who initially left their families in more hospitable Almaty, shipped in. David Nelson, of Foster + Partners, describes long design meetings with the president: "He had thought about the building. That's what's impressive."

What he wanted he got, thanks partly to oil revenues from the distant Caspian Sea, which Nazarbayev claimed for Kazakhstan in a protracted haggle with Boris Yeltsin – closing the deal with the help of vodka and a map doodled on a napkin, which is now in the Museum of the First President of the Republic of Kazakhstan.

Like Gulf cities, Astana floats on an exhalation of petrodollars. Like Gulf cities and new Chinese cities such as Shenzhen, Astana inspires wonder that it is there at all; but while having some buildings of eye-aching ugliness, it has a greater sense of order. At street level in Dubai all is congestion. Here it is trimmed hedges, well-behaved traffic, well-kept paving and a complete lack of litter, or of visible signs of prostitution, drug-taking or beggary. It most resembles the controlled cleanliness of Singapore.

The world's most famous Kazakh is the fictional Borat, but people in Astana are nothing like him. Except, perhaps for a taxi driver who growled like a tomcat whenever he saw a woman. In general Astanans are placid and dignified. They gather in the hour or so around dusk, when the hammering heat of the day gives way to deliciously balmy air, and promenade in the city's grand avenue. Children career over the pavements in electric cars like unfenced dodgems, while everyone gasps obediently at the pre-programmed fountain displays. The avenue is decorated with topiary giraffes and elephants, and vast swirling carpets of brightly coloured bedding plants. There are artificial trees, made of steel rods, blossoming with pink or orange lights and the plastic roof of Khan Shatyr now joins the display, lit from within with a spectrum of disco colours. Sam Cooke's Wonderful World plays from the shrubberies. The place offers childish delights, laid on by the unseen hand of a benevolent daddy.

There is not, yet, much more to Astana than this. It doesn't have bohemian quarters, or a rich nightlife, or hidden surprises. It feels sedated. The striking architecture is combined with a lack of excitement in the street life, as if the design of buildings were a cipher for risk and drama. These are very early days, of course, and over the decades Astana might mature into something different.