Make the most of the many exciting cultural events taking place this weekend by exploring one of the Mayor of London’s cultural trails.

This Saturday, it’s all about South London, with activities taking place from 10am to 9pm. And it’s all free!

Start your day at the Southbank Centre where you can watch a documentary about the Diverse City – Breathe project, a unique collaboration between disabled and non-disabled performers from Dorset and Brazil.

Next, pop into the Southbank Centre’s shop on Festival Terrace, which is being curated by not-for-profit organisation Design Nation all month. Here you can see new products and showcases from some of Britain’s best design talent.

Your next cultural stop is Tate Modern. Take a look at Tino Sehgal’s Turbine Hall Commission. This live show involves choreographed movements and sounds from participants in the space – you’ll never have the same experience twice! Then check out the brand new Tanks at Tate Modern, hosting an ongoing programme of live art, performance, film and installations during the London 2012 Festival.

There’s more performance at your final stop in either Burgess Park or Peckham. Mayor of London Presents Showtime (a festival visiting all London boroughs) is collaborating with Southwark’s annual Elephant and the Nun festival. Highlights include the electrifying Lords of Lightning at Peckham Multi Storey Car Park (free but booking advised).

Download the free London Official City Guide app to guide you on the trail, and to give you more ideas along the way, or download a PDF

The leaves are turning brown, the weather’s getting chillier and it’s time for a bumper crop of autumn art exhibitions in London.

Two major shows open this week: the British Museum’s Grayson Perry exhibition, which combines new work with objects chosen by Perry from the museum’s collection, and Tate Modern’s retrospective of Gerhard Richter, marking the German artist’s 80th birthday.

Tacita Dean’s installation for The Unilever Series is unveiled in Tate Modern’s Turbine Hall on 11 October. Chinese artist Ai Weiwei covered the hall in ceramic sunflower seeds for last year’s commission. We can’t wait to find out what Dean has in store!

Frieze Art Fair returns to Regent’s Park in mid-October, bringing together 170 of the best art dealers from around the world, along with arty talks, films, music, installations and a sculpture park.

Wildlife Photographer of the Year returns to the Natural History Museum, displaying the best wildlife images chosen from 41,000 submissions. And then, in November, one of this year’s most anticipated exhibitions opens: Leonardo da Vinci at the National Gallery, which is sure to be another London blockbuster.

Which London exhibitions are you looking forward to? Let us know in the comments below.

Chinese artist Ai Weiwei today unveiled his latest work: 100 million porcelain sunflower seeds in Tate Modern’s Turbine Hall. Visitors are invited to walk on, touch and listen to the seeds.

Each seed has been individually made by craftspeople in the Chinese city of Jingdezhen, which is famed for its production of Imperial porcelain.  “It looks simple but it takes some skill to make,” explained Weiwei.

Sunflower seeds have a special significance for the artist, who remembers the sharing of seeds as a gesture of friendship during the Cultural Revolution (1966-76).

You can record a video message for Weiwei in a booth beside the installation. The videos will be published on the Tate Modern website, and the artist will respond to one each week. You can also join the conversation via Twitter, where Weiwei will reply to tweets with the hashtag #tateaww.

The Unilever Series: Ai Weiwei is at Tate Modern until 2 May 2011. Entry is free

Happy 10th Birthday, Tate Modern!

Here’s a trip down memory lane, courtesy of farnishk on YouTube. Remember Olafur Eliasson’s The Weather Project back in 2003-2004, which brought a massive sun into Tate Modern’s incredible Turbine Hall?

It was certainly one of those fantastic, unforgettable Tate Modern shows – the kind the art gallery has become renowned for over the last 10 years.

As Tate Modern celebrates a decade of fantastic art this weekend with No Soul For Sale: A Festival of Independents, we wonder if you could share your favourite Tate Modern memories with us in the comments below.

Did you love Louise Bourgeois’ giant spider? That mindbending crack (Doris Salcedo’s Shibboleth)? Carsten Höller’s incredible art-as-amusement-park slides? Or are you still in awe of the Rothko Room? Let us know!