Visualising network topologies

[User:Simon/Special_Issue_8/networked_research Networked research]

Drawing visualisations

Drawing (by hand and using vectors) became a large part of the outcomes I produced as part of my research. The drawings often shifted between "hand-drawn" and "computer-drawn", for example, I would use a .svg file made from one of my GPS walks in a vector graphics program, then print it and hand-draw with pencil over the top.

Abstraction became a key interest, and I started to think more about how these different ways of visualising all employed some level of abstraction in order to communicate. This brought me back to the typical idea of displaying network topology, as nodes and straight lines:

The drawings I made while GPS walking employed straight lines between trackpoints. However, this was just an abstraction - there are no straight lines in reality. In fact, the more accurately I would be able to map the network, the less useful it would be as a readily comprehensible visualisation. I also noticed that at points the GPS signal had become confused or obscured - this happened when I went into buildings (such as a cafe to buy a coffee) or when the signal might have been obscured by tall buildings around me. This produced knots, which I saw as analogous to nodes.

When I imported the lines I made by GPS walking into .svg format, I experimented with unraveling some of these knots, and then drew this process.

knotboard, knots and knotworks

A key reference point for my investigations into network topologies began with the klein form.

Klein forms are the basis for klein worms; illustrated in Radical Software:

The knotboard I had made in the first half of the trimester proved a useful tool for thinking with my hands. I noticed that as a physical object, it was different from my drawings as it immediately had depth, and form, and as a result was affected by light, particularly shadows:

When configured in different ways, the knotboard took on a different presence. I made drawings from this, incorporating light and shadow as well as alternative ways of imagining the three-dimensional space the knotted links occupied:

Research into knot theory (a field of mathematics which studies the topology of knots) led me to discovering mathematical knots, which are different from the usual idea of a knot. I had previously explored knots as ways to record numbers (a notable reference being Quipu from ancient Andean cultures):

Mathematical knots are different, in that they are based on the embedding of a circle into three-dimensional Euclidean geometry R3. As such, they resemble closed loops. The first of these is the "unknot":

I imagined knots as nodes, which when unraveled would reveal that the node and the link are the same:

Visualisation is a powerful tool when communicating alternative ways of thinking and "seeing" things. Through visualisation, I found another way of thinking about nodes