ART THROUGH TOPOLOGY ART THOUGH KNOT THEORY
ART THROUGH TOPOLOGY ART THOUGH KNOT THEORY
Welcome
My work is derived from the wonderfully strange world of topology and knot theory. I hasten to say I leave the mathematics to the experts! I find beauty, really challenging ideas and even mystery in amongst surfaces ducking in and out of 4-space. There millions of knots with no loose ends. It is where the Moebius strip lives and where coffee mugs can shape-shift to become doughnuts, where spheres can be knotted and where surfaces can move through one another without intersecting.
If you are interested in buying one of my pieces, please contact me at
hocking.reid@gmail.com
Crypt Gallery exhibition 2025
Big knot, 11_34
The Conway knot as a ribbon.
Black and white Pastel
Smooth Slice, a counter offering.
The black swirls and curves are taken from the solution to the long standing problem in knot theory. Lisa Piccirillo, an american mathematician solved the problem, finding that knot 11_34, the Conway knot, was not smooth slice. (Don’t ask!!) I emailed her and asked if we might meet on zoom sometime to talk about her work. I did not hear back from her. So I decided to have a bit of fun. I inserted a smooth slice into her solution. My slice is in no way mathematical, it is purely humorous.
Pastel, pencil and siberian charcoal
Two studies for Smooth Slice
Pencil and pastel
Blue Knot 10-15
Giclee print
Three Knots
7_6, 8_6 and 9_4
Pencil
8-6 Emerging
This is a plaque 30cm by 20cm by 8cm. It is a 3D version of the centre knot in the Three Knots drawing above. It is cast in plaster. It can be cast in almost any material
Zero, Three, Four.
Pencil
Crypt Gallery exhibition 2024 Braids
Five, Six, Seven
Pencil
Copper Knots
3,4,5,6,7,8
These knots are made from 3mm copper bar and are mounted on a lovely piece of cherry wood which was an extension leaf from my mother-in-law’s dining table.
White 5-2 knot
Giclee print
Knot 5_2
Suspended on an Idea.
Pencil
Mystery Knot
Giclee print
Braids are basically knots that are flattened into 2D diagrams that show how the knot strand crosses over and under itself, as in the image below.
On Point
The dancing braid of knot 10_54
Copper Braid of the Conway Knot 11_n 34
3 mm copper bar mounted on wenge wood
Unfurling
A braid opening and unfurling, returning to its knot form.
Pencil
Kind of Like a Quantum Computer
I drew this before I learned that quantum computers employ braiding through fine sheets of rare earth minerals to perform computations.
Pastel and coloured pencil
Crypt Gallery exhibition 2024
Continuous Deformation
Curtain
An imagined diaphanous curtain, depicting changes in surface of a two-twist spun trefoil knot diagram
Coloured pencil and pastel
Reidemeister Moves
These are the three moves which allow for the continuous deformations that are at the center of knot theory and its mathematical cousin, topology
Pencil
Reidemeister Flowers
This is a decorative play on the Two Twist Spun Trefoil knot stacked diagram as a vase and the Reidemeister moves stretched and extended as colourful flowers.
Coloured pencil and pastel
Spun Trefoil Knot
The spinning trefoil knot sweeps out a surface which passes through and around itself.
Giclee Print
Spun 5_2 Knot
Giclee Print
Spun Mobius Band
Almost a Klein bottle
Giclee print
Two-Twist Spun Trefoil Knot Slices
This is the work of the mathematicians listed in the drawing. My role in the piece was to make it beautiful
Pencil
Crypt Gallery exhibition 2024
This wall was a mix of work based on fantasy and studies of the Hopf Link.
Fantasy
Hopf links drift through screens towards a mysterious light.
Pencil and Siberian charcoal
Seeking
A fantasy of Mobius band seeking the 4th dimension to unite with their other selves to become Klein bottles
Pencil
Chopped
Here I am playing with Mobius bands encountering the triangulation of the Klein bottle and being chopped into pieces. This uses mathematical idioms but is utterly unmathematical
Pencil
Help! I need advice on how to photograph drawings on white paper. Backgrounds of my photographs all come out grey!
Study for Chopped
Charcoal
Naughty Knots
four pairs of knots adapted from the online catalogue of mathematical knots; Knot Info.
Pencil and coloured pencil
The following four images are
Conversations in a Foreign language
Scott’s Secret
Three Solid Arguments
15 Statements, some a bit Fanciful
Twisting the Narrative
This series takes the Hopf link through several iterations. All the individual images represent the same two linked circles.
Pencil and coloured pencil
HELP!
I need advice on photographing drawings on white paper. My backgrounds are always grey.
