Moscow Art Theatre was founded in 1898 by Konstantin Stanislavski, the godfather of theatrical acting technique. But when Brian Cox talks about the 'great lineage' passed down through the company and school over the years, he could just as easily be talking about his own family.

Brian first saw the company perform when he was a student in London, and was later invited to Moscow to teach at the school in the late 1980s. 'The work ethic and methodology these young Russians employed was incredibly impressive – their movement was astonishing,' he recalls. 'Then I did a TV programme called Brian Cox's Russia for BBC Scotland a couple of years ago, and met up with the students again, who are now running theatres and starring in films.

'And because theatre and ballet are so fundamental to Russia, there's always been an edge to it – the way it reflects society is really quite unique. The tradition of "going to the bottom of your soul", as one young Russian student described it to me, is what the Russian theatre and ballet is all about.'

Like father like son, Brian's son Alan was also bitten by the Russian theatre bug as a young man. 'I think it's because it was an enthusiasm of my dad's when I was at a formative age,' says Alan. 'It was a culture I was exposed to and responded to. I did a summer school with people from Moscow Art Theatre and then a student exchange scheme. There was always a sense that they were the keepers of some mystery, and had an approach to acting and theatre that I became fascinated by.'

Meanwhile, Brian's daughter Margaret was studying Russian at university in St Petersburg and is now fluent in the language. Which has come in handy as she, brother Alan and dad Brian, have helped bring recent Moscow Art Theatre graduates, now part of the Brusnikin Studio theatre collective, to this year's Fringe with Forest.

As the name suggests, Forest is set in a woodland and while Alan has been scouring the woodyards of Perthshire to secure timber for the show's Fringe set, the performers in Moscow have been polishing up the production they originally created in 2017. Back then, the show's director Dmitry Melkin discovered that most of the young actors had little connection with the natural environment – so took them into an actual forest for a month-long preparation period.

'With our eyes blindfolded, we walked barefoot with an escort for 30 minutes through the forest,' recalls actor Nikita Kovtunov. 'We were trying to feel a unity with the forest, to feel the forest inside of us. We were really overwhelmed with the result and it opened up a lot of emotions and feelings. And we'll try to transfer that experience to the audience, to offer them the possibility to stop and think about the natural things that are inside all of us, to feel that connection and harmony with nature.'

The performers rehearsed using the Meyerhold system of biomechanics, in which an actor uses gestures and movements to express emotions. 'It's a universal language,' says fellow actor Eva Milgram. 'We don't have any lines, we don't use words – we just have movement. In rehearsals we would take an object, discover it, find all the possibilities of how to use it – then put the object away and continue to move as if it was still in our hands.'

Speaking to the young graduates, it's clear their experience of working with director Melkin has been illuminating. 'In regular theatre, the director tells you what to do – and at the beginning of our rehearsals for Forest, I expected it to be like that,' says performer Dmitri Severin. 'But this is actually much simpler, you're not an actor but you are a performer. You inhale and exhale with the rhythm of the show, hear the atmosphere with your own ears, operate with a new vocabulary, it's all about being natural.'

All three performers speak with enthusiasm about sharing the work with an international audience. And when the Moscow performers arrive in Edinburgh, the Cox family will be here, too – welcoming them to the UK, just as they were all welcomed to Russia.

'Forest is quite astonishing and dazzling in many ways,' says Brian. 'One of the things that struck me when I first went to Moscow, is that theatre there very much reflects society – it was the one way that the truth of society was being told. And the performers in Forest are reflecting what's happening now, how the natural world is being disturbed and their concerns about that.'

Forest, Assembly Checkpoint, 2–11 Aug, 4.40pm, £12–£14 (£11–£13). Previews 31 Jul & 1 Aug, £10.