This year, elegantly peppering the perfectly proportioned walls of the Georgian gallery building in neat, colour-saturated silk panels - and throwing a contemporary light on the historic collections - it is the turn of Glasgow-based artist Corin Sworn, a woman who, she tells me, now knows the wonder hidden in the leaves of the common or garden cabbage.
It almost wasn't to be. Sworn's exhibition was originally scheduled to run earlier in the year, but when the artist found that the work she had to do for last year's Scottish installation at the Venice Biennale meant that time was very much an issue, Inverleith curator Paul Nesbitt suggested she swap dates and fill the Botanical slot.
"I've worked with plants in the past, so it seemed like it was logical. There seemed to be potential there," Sworn tells me from Rome, where she is midway through a residency after winning the prestigious biennial Max Mara Art Prize for Women last year.
Born in London in 1977, Sworn was brought up in Canada, studying psychology at university in Vancouver before moving on to a BFA and then the MFA at Glasgow School of Art. Her work, conceptual in character, has encompassed textiles, sculpture and film, and has an interest in the narratives that can be constructed - or that we imbue in random objects - from fragmented information. Her strength has been her storytelling, something which the judges of the Max Mara Prize pointed to when awarding her the 2013 residency.
In Edinburgh, Sworn spent some time researching in the Botanics' Herbarium, where plant specimens collected by botanists since the 19th century have been taped carefully onto card, notated and archived with a technique that has changed little in the past 200 years. But there was no "destructive sampling" by the artist for the natural dyeing process that resulted in her subtly intense monochrome works, Sworn collected all her own specimens - from purple cabbage to goldenrod and indigo - from Edinburgh to Aberfeldy and far beyond.
The result may seem intriguingly simple, a clarified mix of infused plant colour and scientific research. But there is more to Sworn's dye-work than serene aesthetics. Upstairs, silk panels of subtly ranging colour are grouped sparsely on the walls, occasionally interrupted by a large-scale photograph of flora or specimens from the Herbarium, protected by covering "shrouds" which visitors must lift to reveal the dark, dried plant beneath, as if in a kind of botanical peep-show.
Each colour-soaked panel, glowing on the walls, is made from silk dyed with Sworn's plant specimens and either water, acid, alkaline, copper and iron, using a natural process. The plant choice is diverse, the colours resulting from a single specimen wide-ranging. In the process, Sworn discovered interesting - and infuriating - things, such as that the colour of gorse flower changes from winter to spring. The results, Sworn reminds us, are erratic, and a few "mistakes" are displayed too.
In this display in the central ground-floor room all the elements of Sworn's displays relate to one plant, the gorse, while elsewhere the strands are mixed. Dye colours obtained from the purple cabbage might be found grouped in a room on the ground floor, but the botanical specimen is found on the floor above. Titles too, are designed to intrigue, from a set of Fustic dye panels labelled "He didn't think twice about taking on the project himself" to a photograph of Goldenrod entitled "Felling the pine trees on the plot".
That disconnected narrative is echoed in the film in the basement, The Rag Papers (2013), originally conceived as two works for two closely spaced yet unconnected exhibitions, one for Inverleith and one for her recent show at London's Chisenhale Gallery. "In the end, it made more sense to put the two works together," says Sworn.
And it does, the carefully interleaved strands installed in a darkened room, book-ended with an audio narration of a chance encounter between two women, emphasised and subverted by a series of lamps in the room that flash on and off. If the video itself contrasts a man and woman in the same room searching, at different times, for the same unknown thing, the experience too has the sense of the exploratory.
"I think that in the same way that the video is a little like a detective film, so is the work upstairs," explains Sworn. "Somebody pieces together the clues and there is a pleasure in finding relationships across space, rather than being given them very immediately."
Sworn's approach to her video and writing work has evolved recently, and she has deliberately cut down on the amount of writing "to allow the viewer to find space to think through things". The Rag Papers is testament to this, although the narrative is in some ways the most immediately compelling part.
And, indeed, it is towards the end of this 20-minute work that the artist's manifesto - perhaps any artist's - is briefly revealed. "If you find something, you should use it. I don't suppose everybody works that way. But I do."
Corin Sworn, Inverleith House, Royal Botanic Garden, Edinburgh (0131 248 2971 (2849 at weekends), www.rbge.org.uk) until June 29. Part of Generation: 25 Years Of Art In Scotland