These images are notes and sketches that come from the many, many hours of exploring how to translate topological ideas into art.
My topologist father in the centre of my pin-board
The Line-up
This illustrates the elements of the Klein bottle. The bottle has one continuous surface only, like the two Moebius strips that join to make it. There is no real inside, you can’t fill it up. Topology doesn’t allow surfaces to intersect so instead of the neck of the bottle poking through the belly, it has to step into 4-space to bypass an approaching intersection. The idea is quite mind-boggling. It’s not the fourth dimension of time and space, which is also mind-boggling,. Topologists tell me 4-space is a dimension at a right-angle to our 3-D world.
Sketchbook
Braids are really a single continuous thread that describes the order of the crossings. each knot has. Topological knots are closed. Unlike a shoelace you can tie a knot in and then undo, these knots have their ends fused together. In a braid you can follow the thread all the way around and end up where you started.
Notebook ; from braid to knot
I was trying to figure out how to turn the braid diagram of knot 10_32 in to its knot. I believe topologists do this the other way around but I was really proud of myself for succeeding.
Braid diagrams and their knots
Blue mesh knots waiting for their time in the limelight.
Each knot has its identification number sewn to it so that I don’t forget which one is which.
A screenshot of the many, many knots I have yet to attend to
Studio shot
The 6 paper knots are those that appear in several of my finished photographs
Studio shot
Sketchbook braid for knot 10_79
A braid is a diagram indicating the crossings and the order of the crossings of a knot. Each knot has a number which indicates how many times the knot crosses itself and a second underscored to indicate its unique number. So this braid is of a knot with ten crossings and it is the 79th in the ten crossing category. I believe there are 179 knots altogether with ten crossings.
braids for knots 10_15, 10_33 and 10_32
I frequently use the device of planes dividing the image. It locates the subject firmly in the space and give a counterbalancing rigidity to the flowing imagery.
braids for knots 10_32 and 9_7
I am trying to find a way to represent topological braiding that accords with my sense of the rogue tendencies of living things when confined by structure.
Notebook
