Baku’s contemporary art scene is booming like never before and this special exhibition showcases two of the country’s brightest talents. Aida Mahmudova, the driving force behind the Yarat! collective’s tireless work in nurturing the emerging generation of talented artists in Azerbaijan, displays her hazy, moving canvases exploring the contrasts between the city’s fast-modernizing landscape and its semi-derelict hinterland. Faig Ahmed, shortlisted for the Jameel Prize in 2013, takes his country’s colourful carpet-making tradition and turns it into a dialogue between past and present as he subverts the genre and reinvents it as something completely fresh.

Aida Mahmudova and Faig Ahmed have been brought together for this show to explore the intersecting territory on which their body of art is built. When viewing their works independently, there don't appear to be commonalities in their concepts, either visual or theoretical. However, if you place their artworks side by side, an unframed seascape by Mahmudova and the gravitational carpet by Ahmed can radiate the same spirit, the same mood.

That mood is of an explorer. Their work possesses the robust power inherent in any explorer, whether of distant lands, an astronomer investigating the universe, or a scientist searching for what lies within. There have always been those who explore inwards – for instance, miners in the earth's core, or the early twentieth-century psychologists who claimed that the deeper you investigate the unconscious, the closer you get to the truth. Looking inward will lead you to discover what lies beyond the surface.

Aida Mahmudova and Faig Ahmed both explore inwards. This is what unites their work: the phenomenon of the explorer's curiosity, of one who travels in search of knowledge, who digs into the past to find a future. This constant journey present in their work brings them together, joined by the eternal question: 'What lies within?'

Faig Ahmed, who was shortlisted for the Jameel Prize in 2013, a biannual award supported by London's V&A Museum, demonstrates his experimental work through Azerbaijani carpets. For the Baku-based contemporary artist, tradition is merely a starting point: his works subvert the genre. It is impossible to stroll through the lanes of lcheri Sheher, Baku's medieval quarter, without encountering people selling traditional carpets. Their intricately woven patterns have been at the root of Azerbaijan's visual arts for centuries, with each region creating its own distinctive styles.

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Ahmed’s carpet patterns melt, Dali-like, over their edges. His piece Carpet Equalizer erupts into sculpted pinnacles, gushing from the ground in the manner of a mixing desk, or perhaps even an untamed oil well. He transforms the medium: instead of a warm, welcoming fabric, those inviting patterns appear on cold aluminium, upsetting expectations with one touch. Other works steadily reduce the carpets to large blocks, a pixelated view for the Internet generation. But the artist himself insists that he is not seeking to merely juxtapose ancient and modern. He breaks the stereotypes of what Azerbaijani weaving is all about.

"By spoiling carpets I add new three-dimensional patterns but I'm not interested in any kind of merging between past and present", he commented in a video clip produced for the Jameel Prize in 2013. "l'm just interested in the past because it's the most stable conception of our past. By using the modern pixel on the old carpet we just hear the voice of past times."

Faig Ahmed was one of 10 artists from the Islamic world nominated for the Jameel Prize and his works were included in an international touring exhibition. He was also among 12 artists chosen to represent Azerbaijan when the country made its first appearance at the Venice Biennial in 2007.

Aida Mahmudova, a graduate of Central Saint Martins College in London, is one of the driving forces behind Baku's burgeoning contemporary art scene. She runs YARAT Contemporary Art Space, a non-profit contemporary art collective in her hometown, staging intriguing exhibitions since 2011 and increasingly active in bringing the best of Azerbaijan's young artists to an international audience.

But Mahmudova's own art is also worthy of attention. Like many people she has been struck by Baku's position at the crossroads of East and West, while much of her work has drawn her to explore the contrasts between the city's fast-modernising landscape and its semi-derelict hinterland. That world, half-forgotten and caught between eras, evokes the sense of longing that informs much of her work.

Speaking about the Internal Peace show that was displayed in Zurich in 2013, she said, "Our physical world is shifting at a pace so rapid that our memories are frequently blurred, and our 'remembered' past is often forgotten or altered by our subconscious. This confuses our identity. These un-modernised locales function as a 'missing link’."

Mahmudova's artwork has been shown in important exhibitions in Europe, including the MAXXI Museum in Rome, in the Multimedia Art Museum in Moscow and at Philips de Pury & Company in London.