Time magazine has identified a new demographic for our times: the locavore.

It named Rene Redzepi, chef-patron of Noma in Copenhagen, the world's No.1 restaurant, as its locavore hero, and put him 11th in its list of the world's 100 most influential people, ahead of famous sportspeople and fashion designers.

Locavores are interested in eating food that is locally produced, in season and fresh. The term was coined in the US, where the movement is ideologically coupled with sustainability and the word itself has entered the Oxford American Dictionary.

Many foodies regard Redzepi as the man who sparked this culinary revolution by sourcing only ingredients that are indigenous to his native Norway and Scandinavia. He eschews the classic Mediterranean cooking style of most double-star Michelin chefs in favour of foraging and reinventing his country's natural larder.

The philosophy has growing numbers of devotees in Scotland, where the innovative Fife Diet movement, which began in 2007 as a project to persuade people to eat only food from Fife for a year, has developed into a network of thousands of people who are re-localising their eating. It is organising Blasda, a series of "food feasts" across Scotland in September.

Now the locavore movement has taken hold of the eating-out scene in Edinburgh. Many restaurants are expanding their local-seasonal-Scottish repertoires of beef, lamb, chicken, fish and shellfish to embrace a mind-blowing choice of locally sourced fresh and foraged produce, the likes of which have never been seen in such quantity and variety in Scotland before.

Grasping the grow-your-own zeitgeist, Edinburgh's chef-proprietors are either planting out their own kitchen gardens, or bypassing the traditional fruit and vegetable wholesale markets to buy in fresh produce daily from their local market garden.

The big surprise is that in addition to carrots, turnips, cabbages, peas and potatoes, cutting-edge Scots cuisine is encouraging the production of exotic and interesting vegetables. Step forward uber-trendy turnip tops, flower sprouts, pak choi, cavolo nero, coloured beetroot, black and red kale, and gorgeous-looking squashes to name but a few. Consquently, the variety of flavours, textures and colours on our plates is unprecedented. The revolution starts here.

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Carina and Victor Contini, chef-patrons of two central Edinburgh restaurants, are spearheading the locavore movement. In January, they bought a run-down Georgian mansion in Midlothian that had a huge, overgrown one-acre garden – with the intention of fulfilling their long-held dream of establishing a large kitchen garden that would yield enough fresh fruit and vegetables, eggs, chicken, ducks and honey to supply not only themselves and their young family, but also their kitchens at the Scottish Cafe at the National Galleries and Centotre in George Street.

The Herald Magazine has been following the progress of the garden since March, when its old crumbling stone walls were covered in ivy, a huge copper beech tree had crashed to the ground, and the earth was covered in deep-rooted, widespread weeds.

At the time, there was nothing to see but the work that lay ahead. However, there was enthusiasm by the spade-load and an unwavering vision for the place they rechristened Casa San Lorenzo, after the patron saint of cooks. "In Italy, as in other European countries like Spain and Poland where we got some of our chefs, there is an ancient culture of smallholding and growing your own which means they're more connected with raw ingredients. We don't see so much of that with people of Scots or Irish ancestry," says Carina. "We want to cut food miles and deal only in fresh Scottish produce. It's like slowing down in some respects, but speeding up in other ways."

Last week, we visited for the third time. Even after months of unremitting rain, what they have achieved, with the help of Erica Randall, their newly appointed head gardener, and students from the Edinburgh Royal Botanic Garden, is astonishing. All the more so is the fact that they've done it without the assistance of the polytunnel they intend to build in August or September.

The old stone walls have been cleared of ivy and repointed, the earth has been dug over and enriched with manure from a neighbouring farm – and four large raised beds are covered with an abundant display of vegetables, salad leaves, peas and beans. There is red orach, chop suey greens, flat leaf parsley, pea shoots, mazuna, bronze arrow, reddy spinach, lollo rosso bronze, calendula, Cobra French beans, Scarlet Emperor runner beans, Peewee petits pois and mustard frills. Fat green courgettes and their distinctive orange flowers will be picked for the first time next week in the morning, to be delivered to the restaurants and on the menus by lunchtime. Purple sprouting broccoli, leeks, chard, kale and others will follow in a rotational planting scheme.

When the pond at the centre of the plot is infilled and earthed over they will plant soft fruit bushes, and espalier pear, apple and plum trees will take root by the old walls.

This week they will take delivery of 24 laying hens, a gift from Patricia Stephen of Phantassie Organic Growers in East Lothian. Apart from providing eggs, the chickens will help combat the slugs, snails and aphids that have emerged in the damp weather.

"Having our own eggs makes sense when we buy thousands of them every year for fresh pasta, bacon rolls with egg, and other dishes. When you have London-based Italian chains coming to Edinburgh the independents need to be able to offer something different."

When they eventually move into the renovated house, Victor and Carina plan to do the deliveries personally each day.

"Speed is of the essence when it comes to fulfilling our ethos of fresh, simple, Scottish," says Carina. "Our chefs tell us that as a rough guide they will require about 25kg of produce each week for each dish on the menus, which change every month. Erica's planting is geared towards meeting that target. It's a tall order but we're really up for it."

They don't intend to become a commercial market garden; planning permission restricts activity to their own restaurants and, in any case, they have enough work on their hands to keep them going.

Neither do they plan to drop all their existing suppliers; on the contrary, they are working with them. For example, Sandy Pattullo of Eassie Farm in Perthshire will help with planting asparagus, and Peelham Farm in the Borders has offered to supply them with piglets. Robert Wilson of Scotherbs is also on board, as is Graham Stoddart of Cuddybridge Apple Juice at Innerleithen.

"This whole project is more about learning about the seasons, the land and the challenges of growing the food we take for granted when we buy it off the supermarket shelf," explains Carina.

"We have the feeling that we're going back in time to the era of our ancestors, who grew their own and were connected to the land. I have been involved in some great projects in my life though they are all building related. To see something coming out of the ground ... it's a completely different emotion. I've got goose bumps all over. This is spiritual."