## Dominic Hopkinson MRSS Sculpture and Mathematics

"Tiling Variations in n=3 Space"

Plywood

2018

This work was selected to be shown in the large group exhibition "Time. Space, Existence" held at Palazzo Bembo, Palazzo Mora, and the gardens as part of Venice Architecture Biennale 2018, hosted and curated by the European Cultural Centre. The image above and text below appeared in the exhibition catalogue.

“Artists realise that mathematicians have a way of looking at the world that can make them see things differently”

- Marcus du Sautoy

“Without mathematics, there is no art”

- Luca Pacioli

What creates form? What creates space? Is there a ubiquitous mechanism that underpins all physical processes? Artists, engineers, architects, and designers all create shape, form and space, yet this process also happens spontaneously in nature. The wind forms ripples in sand and water, the dynamics of the atmosphere generates clouds. All animals and plants grow, create structure, occupy space according to rules and processes defined within their DNA. Atoms align into crystals with explicit geometries, the matter in the universe is strangely evenly distributed in space, space and time are the same thing. As a sculptor I attempt to study this creative mechanism as it is relevant to different scales: is it possible to define this mechanism as mathematics, and if so, can my working process function as an algorithm in its own right, to make sculpture that follows a simple set of mathematical rules, trusting the maths to deliver a satisfying outcome?

“In mathematics, the art of proposing a question must be held of higher value than solving it.”

- Georg Cantor

Utilising traditional materials and techniques, I define a set of mathematical rules or parameters, that become my process, guiding the final outcome. All my work is handmade, eschewing the use of contemporary fabrication methods, such as laser cutting and 3d printing. I have to rely on my haptic skills and the mathematical rules to generate form that, despite being abstract in every sense, also has the ability to engage and interest the viewer. I believe this engagement is an act of self-recognition which occurs because mathematics is the fundamental basis for the creation of structure in nature.

“Mathematicians do not study objects, but relations between objects”

- Henri Poincare

Collaborative research plays a major role in my process, recently spending a year as Artist in Residence at University of Leeds, School of Mathematics, working with Prof. Alastair Rucklidge and Dr. Priya Subramanian, studying aperiodic tiling systems in 2 and 3dimensional space. The work presented utilises this tiling and is analogous to how the atomic structures of quasi-crystals are created, each “point” representing the location of an atom. This tiling system relies heavily on a particular number, 1.61803… an irrational number, known as phi(also known as the Golden Ratio) that occurs whenever nature begins to build structure. It seems to be fundamental at all scales, across a bewildering range of phenomena. It forms the foundation of most of my work.

“Where there is matter, there is mathematics.”

- Johannes Kepler