It was the clifftop village of Catterline in Aberdeenshire which first drew Rebecca Sharp to the paintings of Anna King.

In the summer of 2011, the writer, who hails from Glasgow but has been living in Liverpool for the best part of a decade, was browsing online to see if there was any chance of securing a residency at The Watchie in Catterline, the former customs lookout point where the great Joan Eardley painted some of her finest works.

"That didn't work out," Sharp explains, "but I discovered Anna's work, which she had made in Catterline and, after looking at it online and feeling a real connection with it, I made contact with her."

King, who is still a year shy of her 30th birthday, won the first ever Jolomo Award in 2007 for her bleakly beautiful landscapes, many of which were painted during a residency at The Watchie. Sharp got in touch and the two women sparked up a friendship based on a mutual connection through their different arts.

Initially, they started trading ideas by email – each curious about the other's approach to making art. These "ether ideas" were soon replaced by a good old-fashioned hardback sketchbook, which they began to post back and forth between Scotland and England.

Both would add to sketches by King and texts by Sharp, responding to the abandoned spaces in society that retain a trace of human presence. Disused factories with no glass in the windows and a single traffic cone outside; a back court stretching out onto a cleared area where houses once stood...

The resulting Unmapped project, now on show at the Kelly Gallery in Glasgow after a successful short run at the StAnza poetry festival in St Andrews last weekend, consists of a series of paintings by King with an accompanying set of poems by Sharp. The exhibition is beautifully self-contained and thoughtful; all the work is for sale and, with each purchase, comes a small book of the same name.

Poems by Sharp, who graduated in theatre from Glasgow University in 2000, are presented side-by-side with King's paintings. The text of the poems, which are mounted on ragged-paper on board, is kept deliberately small so that the viewer has to step inside the "space" of both painting and poem. Their titles – such as Day One, Scavengers, Vespertine and White – are, like King's work, simple and resonant.

According to Sharp, sending her fragments of text back and forth in a sketchbook gave the project a pace which might not have happened otherwise. "I didn't want to complete a poem before I got the book," she says. "They were all about hidden places and the sketchbook was quite secretive, so it gave the work real resonance. It was as though you were entering something; going on a journey and leaving again.

"On first seeing Anna's work, I was immediately drawn to her understated, non-judgmental treatment of locations – places that have always fascinated me. Cool, quiet spaces often accented, with great emotional effect, by a clean line of contrasting colour."

Sharp found that she instinctively started to translate what she saw in King's sketches of these places into word choice, line breaks and spacing. "It was magical to be shown each new painting," she adds, "and to see the poem reflected in it."

For King, who graduated from Duncan of Jordanstone College of Art in Dundee in 2005, working with Sharp and forging a friendship based around their art has been a liberating experience. "With this project, there was no pressure," the artist says. "We had the time to let it grow. It was good to have the luxury of spending time on one painting. Normally, I'd be working towards a show and making a lot of work."

The result is a body of work which brings blips of simple brightness to neglected spaces that surround us all. In words and in pictures, with no added froth.

Anna King & Rebecca Sharp: Unmapped, Kelly Gallery, Douglas Street, Glasgow, www.unmapped-project.co.uk, until April 6