Yes, the Welsh have one, too. And, unlike the white elephant in London, it's thriving

Like Xanadu and London, Tywi Valley now has its very own stately pleasure dome. Unlike its Greenwich counterpart, however, the Welsh Millennium dome has no known detractors, and is exceeding all attendance forecasts by almost 40 per cent.

Like Xanadu and London, Tywi Valley now has its very own stately pleasure dome. Unlike its Greenwich counterpart, however, the Welsh Millennium dome has no known detractors, and is exceeding all attendance forecasts by almost 40 per cent.

The dome, the world's largest single-span glasshouse, is the centrepiece of the recently opened National Botanic Garden of Wales at Llanarthne. Designed by Sir Norman Foster's firm, this giant glistening dewdrop that appears to have been distilled on the Carmarthenshire countryside was intended to echo the gentle contours of the surrounding hills. Never can concrete, steel and glass - those ubiquitous components of modern architecture - have been employed more effectively. It won an award last week from the Royal Institute of Chartered Surveyors, while the London dome did not make the shortlist.

Twenty-four tubular arches support almost 800 panes of glass which help to create a year-round Mediterranean climate in the 300ft arena beneath. As you browse among its parched screes and sandstone terraces or descend into man-made ravines between lake and waterfall, platoons of computer-controlled windows are gently opening or closing above your head to maintain the desired temperature. Fans suspended around the dome's circumference simulate tropical breezes.

Though the great glasshouse is, understandably, the prime attraction for visitors, it is only part of the £44m garden project. Executives here are naturally wary of being drawn into comparisons with the London dome which might prove odious, but the director of horticulture, Ivor Stokes, does venture one telling observation. "We knew from the beginning what we wanted to put in our dome," he said firmly.

What that involved was the creation of five ecosystems to mimic those of Australia, California, Chile, South Africa and the Mediterranean basin. Many of the trees and shrubs here are threatened with extinction in their native environments. One section features a burnt landscape with trees charred as though by some recent forest fire - a common enough event in many regions.

This, then, is Britain's most popular leisure activity - gardening - served up with an ecological message for the 21st century. It is the latest symbol of Welsh identity, among such established national institutions as the Assembly, National Library, the University of Wales and the hallowed rugby shrine of the Millennium Stadium.

Like most successful ventures, it began as the inspiration of a single individual: William Wilkins, a former Greater London Council exhibitions officer-turned-artist. There would be time later for steering committees and business plans, but the initial idea was his.

It is only four years since we waded through thigh-high grass on a neglected Carmarthenshire hillside and Wilkins talked somewhat fancifully, it seemed then, of restoring the 18th-century Middleton Hall estate and transforming its 568 acres into the first large-scale botanic garden to be built in Britain for two centuries.

Scepticism was misplaced, however: thanks to a £21m Millennium Commission grant, the Wilkins dream is now rapidly becoming a reality. In its first three months 140,000 people paid to enter the grounds, not far short of the attendance estimate of 175,000 for the entire year. Like any other garden, of course, it will take time to reach maturity, a good enough reason for return visits.

But staff are already planning for the moment when the public's initial curiosity wears off. Among the garden's strategies for luring visitors from around Britain and abroad are performances of suitable music by the National Orchestra of Wales String Ensemble, beginning on 4 November with 'Autumn' from Vivaldi's Four Seasons. The first of two editions of Gardeners' Question Time has just been recorded there.

The estate was once owned by Sir William Paxton, a former master of the Calcutta Mint and agent for the East India Company. He returned to Britain with sufficient means to pursue a parliamentary career and a number of more commendable ambitions, which included the supply of piped water to Carmarthen town and the development of Middleton. To assist him in the latter enterprise he employed Samuel Lapidge, a former colleague and admirer of Capability Brown. The result was a distinguished garden created in the contemporary manner, with water running through it as a natural thread, creating no fewer than seven lakes.

Sadly, after Paxton's days the estate deteriorated. Lakes were drained and in 1931 the mansion he had commissioned as his family home was burnt down.

Eventually the site was bought by Carmarthenshire County Council, which, before giving the land for its present use, leased it as smallholdings. This proved to be no bad thing for the present occupants, according to Stokes. "Tenant farmers did not have the cash or inclination to lavish fertilisers and pesticides on their land, which consequently remained unspoilt," he said.

We started our tour at the circular gatehouse. Another Foster creation, the timber construction was based on that of ancient Welsh roundhouses, some of which have been reconstructed at Castellhenllys in nearby Pembrokeshire.

The building's flat roof slopes gently inwards to channel rainwater down into a central pool. At first sight, the gleaming copper-and-silver floor of the pool appears to be some attractive Modernist mosaic, but on closer inspection turns out to be the result of the British compulsion to throw coins into any patch of standing water.

The spine of the garden is a broadwalk shaped like an ammonite to commemorate the life of a 17th-century Welsh scholar and founder of palaeontology. From a pebble-lined fountain the path climbs more steeply to the summit, where the greenhouse and administrative buildings stand. (Buggies are provided for the elderly and disabled.)

Lined by vividly coloured herbaceous borders, our path skirted a unique double-walled garden which remains from Middleton's past. It will not open to the public until refurbishment is complete. This corner of Wales enjoys - if that is the word - an annual rainfall of 72 inches: even on the driest summer day, water gurgles through a pebble-lined rill that meanders down the broadwalk.

Middleton Hall's former coachhouse and stables now house an exhibition space, shop and a self-service restaurant. A former barn has been turned into a replica of a late-19th-century pharmacy called Apothecaries' Hall, a reminder of times when most medicines were extracted from plants.

It was not far from here that the popular legend of the Lady of the Lake was set. The tale is a simple one: young man meets fairy maiden, marries her, then loses her, after what might now be termed serial domestic violence. Before disappearing finally into the lake from which she had emerged, the fairy commends to her sons a healing mission. They should, she says, treat the sick with remedies derived from herbs collected on the surrounding mountains.

Strangely, there is a real-life tradition hereabouts of plant medicine administered by the Physicians of Myddfai, whose descendants practised into modern times. Perhaps, if Wales had had its national garden then, they would be doing so still.