A collaborative artwork by Daksha Patel and Dr Silke Henkes. The piece involved construction of an interactive active matter system, consisting of moving chalks driven by a circular vibrating blackboard. The traces left by the chalk leave a visual imprint of their journey across the surface.

Below is a picture of the initial working prototype produced by the School of Engineering fabrication department:

‘Active matter’ systems classify materials where the individual elements can move on their own. The most famous examples are flocks of birds and swarms of fish, but so are herds of sheep, or even crowds of people! At the smaller scale, cells working together to close a cut in your skin are active matter and so are many of the components inside a cell that make it move in the first place.

The final piece was a much larger construction, inspired by a real active matter experiment that recreated active motion at a table top scale (Collective motion of vibrated polar disks, J Deseigne, O Dauchot, H Chaté, Phys. Rev. Lett., 2010).

It consists of a large thin plywood plate, vibrated at carefully chosen frequencies (pitches) by playing a humming sound through speakers placed directly below. Chalks are prepared by slipping rubber bands many times over one end, then scattered atop the plate (see video below). When the plate vibrates upwards, the chalk momentarily loses touch with the surface and can bounce in any direction. Without the rubber band, the bouncing directions are random, and on average the chalks will go nowhere. However, when the rubber band is attached at one end only, this side bounces more easily due to the bigger coefficient of restitution (bounciness) of the rubber compared to the chalk at the other end. At every bounce, the piece drops down just a little bit more towards the rubber side than the chalk side. Over many bounces, it will start to move forward, leading with the rubber side. Every bounce also leaves a bit of chalk on the board, creating the tangle of chalky trajectories left by the active particles.

The artwork was on display to the public during Bristol’s Creative Reactions Exhibition 2019. Later, a standalone video artwork was produced using time-lapse photography.

The artwork was recently selected for the interdisciplinary conference Drawing Conversations 3: Drawing Talking to the Sciences, Lancaster University, The Ruskin
16th–17th January 2020.

Daksha will be presenting her recent project Misprints during the conference, and showing the video Active [Drawing] Matter in the accompanying exhibition Drawn to Investigate.

A piece by Rose Vickers, using her collection of reclaimed rulers and yardsticks, reflected on by Dr Mark Hagen.

Dr Hagen’s comments on the artworks mathematical language and structure may be downloaded in pdf format.

A collaborative artwork by Paul Nano Skawinski and Dr Shibabrat Naik. It was inspired by research in applied dynamical systems and draws specifically from results in a recent paper: https://arxiv.org/abs/1804.05363.

See two more videos of Paul’s work here:

https://vimeo.com/244557520

For more mathematical details, feel free to contact s.naik@bristol.ac.uk.

A collaborative artwork by Zoë Power and Dr Rachel Bennett. The piece is inspired by the theory and application of research into very viscous fluids.

For very tiny organisms like bacteria, when they swim through water, the size of the difference forces they encounter mean they experience the water in the way we would experience a very viscous fluid like honey. The types of flow patterns that emerge in a fluid depend on the viscosity and the size and speed of objects within the fluid and can be characterised by the Reynolds number.

“Low Reynolds number” flow (often called Stokes flow after physicist Sir George Stokes) is smooth and mathematically predictable. Many of its properties are described in the following lecture due to the celebrated fluid dynamicist Sir G. I. Taylor:

In this low Reynolds number world where bacteria live, various non-intuitive phenomena are at work. For example, flapping a tail like a fish does not actually propel a microorganism and symmetry in the swimming stroke must be broken to achieve propulsion. Some of Dr Bennett’s research involves theoretical modelling of bacteria swimming close to a surface and understanding how the bacteria interact with the surface via the fluid. The goal of this project is to gain a better understanding of the initial stages of biofilm formation and design strategies to prevent formation of biofilms that lead to infections.

Dr Bennett:

I have used this modelling to show how physical features of the bacteria, such as the body shape or friction created by hair-like structures called pili, affects the way bacteria move close to a flat surface. Currently, I am investigating whether the shape of a surface can be used to modify the interactions between the bacteria and the fluid, with the goal of using the flow created by a swimming bacterium to push it away from the surface.

Further reading:

• https://en.wikipedia.org/wiki/Stokes_flow
• https://phys.org/news/2019-04-patterns-bacteria-surfaces.html
• https://en.wikipedia.org/wiki/Biofilm
• https://en.wikipedia.org/wiki/Pilus

A collaborative artwork by Lucy Ward and Dr Karoline Wiesner, inspired by research in complex systems and network theory. Complex refers to a system that has very many interacting components. Examples that may be considered complex systems are diverse: bee colonies, democracies, the human brain and the climate. Though complicated, complex systems may sometimes be reduced to a few simple rules, from which global order or patterns can emerge.

The piece is shown below.

Its title refers to a stochastic process — a mathematical term for a process involving many random events. Such processes typically underlie complex systems.

Lucy Ward:

I was keen to investigate ideas in Complex Systems using the methods and processes of drawing. There are many different facets to the Theory, many of them we discussed, and some of these are included as conversations between the people in the drawing. Using the process of drawing to think about Complex Systems took a number of forms: Some were material – I worked repeatedly from left to right, laying down layers of marks, so as not to smudge the ink. This, in it’s own way, was my set of rules for the system (or drawing). I also wanted to consider the ideas around the appearance of order from apparently random actions. In making the drawing, I knew there would be some sort of formation of the hexagonal grid pattern by the marks, but I did not plan this out, or draw a guide on the paper. It just emerged as I drew more and more people and tried to make a sense out of their distribution. The connecting lines between the people are there to represent the ‘communication’ that occurs between the units of a Complex System. I tried to make these instinctively, imagining the interactions of the people on the page rather than considering the image or composition.

Further reading:

• https://en.wikipedia.org/wiki/Complex_system
• https://taylorpearson.me/complexity-science/
• https://en.wikipedia.org/wiki/Network_theory

A pair of collaborative artworks by Patrick Brandon and Dr Lynne Walling.

A collaborative artwork by Brendan Lancaster and Dr Florian Bouyer. It shows very many hand-drawn visualisations of K3 surfaces, on a large roll of wallpaper. Some examples are shown below.

These structures are of interest in the mathematical field of algebraic geometry, where they can be used to help mathematicians prove facts about whole numbers, using a geometric perspective. The surfaces that we encounter in our day-to-day lives are 2-dimensional. An example would be the wallpaper used in the pair’s artwork. If we imagine ourselves shrinking and standing at a corner of the wallpaper, we can move in 2 orthogonal directions: one for each edge of the paper. (We assume that the thickness of the paper is negligible, so we cannot really travel down, through the paper.) In contrast to this, the K3 surfaces used in Dr Bouyer’s research are 8-dimensional. While this sounds complicated, we must simply have the guts to imagine being able to head off 8 different directions rather than 2!

That said, if we wish to visualise these surfaces, it is challenging, because they do not really exist in our 3-dimensional world. Consequently, we can only glimpse sections of them at a time, called projections. This is for the same reason that we can only ever see the part of an object that faces our eye — it appears to us as a 2D picture, or projection, from the ambient 3D space that we live in.

The collaborators’ drawings use projections of their K3 surfaces, that may be obtained using computer software. They then interpret these on paper, effectively reprojecting them, through their own visual sense and aesthetic intuition.

A collaborative artwork by Dail Behennah and Dr Fatemeh Mohammadi.

Photograph by Jo Hounsome.

A collaborative artwork by Huw Richards Evans and Professor Andrew Hogg.