The Geometry of Failure

On the black beach of Reynisfjara, on the southern coast of Iceland, a series of gradated columns loom over starkly dark sand. Resembling the pipes of an organ, the hexagonal flutes of Reynisdrangar are unsettling, the regularity alien enough that the whole scene could be taken from the surface of another planet. In local Icelandic folklore, the stacks were once two trolls dragging a masted ship to shore. When day broke, their bodies splintered and turned to needles of rock. Closer to home, the path of the Giant’s Causeway spills over the coastline of Antrim, disappearing to stagger out of the water at Fingal’s Cave on the Scottish island of Staffa. The story is as childlike as it is familiar: Fionn MacCumhaill built the pathway across the North Channel to challenge the giant Benandonner. Again, the Causeway shows this repeated pattern of six-sided rocks.

But nothing inexplicable is happening here; no mythological beast is required to explain these strange landscapes. As ancient lava fields cooled and contracted, cracks formed in the rock to relieve the strain. These fissures spiderwebbed out, meeting at 120° angles to form hexagons, the shape that most efficiently fills a space with the least amount of material. This creates an orderly pattern, one that comes from points of weakness: breaking, splitting, cracking, failing.

This world of angles and calculations seems unrelated to the warm, fleshy world of nature, chaotic as it is. But these patterns are all around us, spontaneous architecture that shares mathematical and physical principles with the finest of abstract equations. Veins will diverge into a floodplain of capillaries. Windblown sand creates an undulating sea. Microscopic crystals branch into pin-sharp order. Scales form tessellating patterns on snakeskin. Nature is geometry dressed in fur.

Circling the landscapes contained in Sonia Shiel’s Medusa in Pieces, I found myself losing hold of perspective. A distant, arid desert leaped into the foreground; a mountain peak became the twisting of an ocean wave. I was reminded of an open world video game, where anything beyond the horizon is yet to be created. A gaming algorithm, given rules and parameters, can procedurally generate an endless landscape for the player to explore. Resources, enemies, goals and checkpoints reveal themselves from the horizon as the player makes progress. The pixels that make up these objects have been used before, and once the attention of the player falls on them, they reform into something new: complexity emerging from possibility. Similarly, the wooden boards making up Shiel’s installation have past lives – “a magician’s rig, a music box, a terrain, a portal, a roulette wheel” – and have been shaped into another form, given meaning only through attention.

This idea of attention as catalyst is familiar to anyone with even a pop-science understanding of physics (I very much include myself here). The observer effect is the disturbance of an observed system by the act of observation. The cat is both alive and dead until we look inside the box. Success and failure exist simultaneously.

As I watched, a member of staff adjusted the installation, unfurling the wooden slats into a new shape, and it had all changed again. Now there were claws, and talons, and jutting tufts of hair. As the physical shape of the pieces moved, so too did the painted patterns and outlines, creating new levels of complexity. Another diversion into amateur physics: a fractal is a mathematical structure that is infinitely complex regardless of scale. A coastline is an example of a natural fractal – the section of a rocky coast at our feet looks just as jagged as a stretch that can be seen from space. Plants like broccoli and pineapple grow according to the laws of fractals, and ice crystals form in similar shapes.

Procedurally generated fractals produced by algorithms are just as striking. Three single pixels in MS Paint is enough to generate a fractal pattern – repeated, rotated, and mirrored to create an image that quickly becomes more and more complex. Advanced programs can generate high-definition fractal patterns that surge and shapeshift as the camera zooms in. It is theoretically possible to calculate an infinite sequence by zooming continuously and indefinitely within a finite space – our current computing power is the main barrier to this. On YouTube, hours-long videos displaying colourful fractal patterns have millions of views; it is reassuring to see that I am not the only one hypnotised by this dance of angles. The word fractal comes from the Latin frāctus, meaning “broken” or “fractured” – again, the geometry of failure creates beauty, worlds within worlds within worlds.

I admit I struggle with the mathematical principles behind much of this and am tempted to attribute it to magic. To me this is supernatural: a minute, self-similar, hierarchical world; as familiar as the outline of a coastline, as foreign as an alien tentacle. The constant unfolding of an orderly infinity, an abstraction so unwieldy that I have fleeting moments of understanding before it becomes too heavy and it all tips out through my ears. Boat-hauling trolls and feuding giants seem more comprehensible in comparison.

But this marriage of the natural and mathematical, geometry and myth satisfies something in me. Humans are storytellers as well as scientists, searching for order and meaning. We wrap things we don’t understand in a neat parcel of words; invoke giants and trolls – and snake-headed women, full of chaos and rage. In Sonia Shiel’s exhibition, Medusa lurks in botanical, amphibious, fiery, desert landscapes. Collecting all the pieces seems tempting, but pointless. She is broken and disembodied, but through the breakage, comes alive.

Sheila Armstrong is a writer from the northwest of Ireland. She is the author of a novel, Falling Animals (2023), and a collection of short stories, How To Gut A Fish (2022).

Medusa in Pieces by Sonia Shiel is at VISUAL Carlow from 30 September 2023 – 14 January 2024.