Taiwan, they say, is shaped like a teardrop. At the tip is the island's biggest city, Taipei. And the "provisional capital of the Republic of China" is truly a city to make you weep.

Since it became a bolt-hole for deposed Chinese nationalists fleeing the march of Mao in 1949, Taiwan has been performing economic miracles. But when you step off the bus in Taipei, the biggest miracle is that anyone would live there. Achieving rapid economic growth, it seems, involves spreading successive layers of grime and noise across a sprawling city of three million. The civic symbol of Taipei is the exhaust pipe.

Yet the tourist may find that a couple of days of poisonous fumes and aural anguish can bestow a series of small rewards.

Just east of Shih Lin underground station, for example, the proprietor of a statue shop has purloined designs from all over the world and strewn them across the roof of his premises: an equestrian Napoleon, a soldier raising the US flag after the battle of Okinawa, not forgetting a larger- than-lifesize Michelangelo's David. You can't miss it: just look for the miniature (but not very) Eiffel Tower on the roof.

Close by, the National Palace Museum is the city's most imposing building and has the most remarkable contents. The Imperial Chinese art collection spent years being shunted around mainland China to evade first Japanese troops, then Communism. So a small island with 20 million people finds itself with a collection vastly disproportionate to its size. Among all the grandeur and glitter is a series of cartoons by one Lu Hung, a hermit who drew cartoons that embrace art and poetry. So ornate is the calligraphy that the division between words and images is blurred with each deft, sharp stroke.

It is similarly difficult to determine what precisely you are going to have for lunch. Owners of the noodle shops that lurk in every alley will invite you to choose your meal - and in some cases meet it. The vegetarian may not enjoy Taipei, but carnivores with more appetite than imagination may well.

Spiritual needs can be satisfied at the Lungshan temple, a tableau of serenity. The calm is shattered intermittently by the shriek of a mobile phone, whose owner immediately stops communing with deities and starts dealing. Taipei is a city of percentages, and no one wants to miss out on theirs.

Simon Calder