This was a collaborative project with artist Fiona Gannon and architect Sorcha Murphy. We were looking at how mathematical ideas may be used in finding forms and began exploring cellular automata, which are visual rules that determine the next step in building a structure based on its state. The structure may initially be very simple but as a rule is repeatedly applied it can grow in complexity. A good example of this is cellular automata rule 30. The fact that they’re visual and their behaviour may be unpredictable made them a good place to start. Physicist Stephen Wolfram’s book A New Kind of Science has many examples of cellular automata but as we looked through the book it became apparent that many algorithms covered in it would need to be implemented in software. Would it be possible to find interesting rules that could be made by hand? The snowflake algorithm in the book uses a hexagon as the basic building block, but a cube is similar in that it has six faces. We adapted the rule to work with cubes and went from there.

As a shoal of fish moves it can seem to respond to its environment as a single entity, particularly when a predator approaches. This behaviour puzzled biologists for some time, but behavioural biologist Iain Couzin among others recently began to unlock some of the mechanics behind their movement. A model of it can be made by setting out the movement of individual members – no overarching mechanisms across the shoal are needed. Members of the shoal will roughly move as follows:

1) Each member tends to keep a set distance from their neighbours.

2) Each member keeps a similar orientation of their neighbours.

3) Each member is only aware of their closest neighbours.

There are many places around buildings that are easy to overlook and walk by. They tend to be spaces that aren’t all that social, often linking those that are. I started exploring these spaces to see what goes on in them and found a rather strange inhabitant that I missed all those times I’d simply passed by. Those odd sounds that are sometimes heard around the place or that occasional glint of light that almost catches your eye may, it turns out, be caused by a Shoal Thing. Not much is known about Shoal Things or where they come from, however they can occasionally be found lurking in these obscure places around buildings. There’s usually a drain on the electricity supply wherever they happen to be and it is thought that this is what attracts them. They have come to be regarded as pests for this reason by those building officials who are aware of them, which may go some way towards explaining their wariness of people and their habit of moving around overlooked spaces, never staying in one place too long.

Objects in the man-made world are usually consciously designed by someone or by a team of people. Computation may be used to aid in the design process, particularly where complex calculation is involved, however this is usually to assist in realising preconceived ideas. Increasingly though, computation is edging further into the design process, particularly with techniques such as evolutionary algorithms and emergent systems. In using such techniques, a designer might set out a basic structure and some instructions that allow it to evolve towards a solution to a problem or a finished design. Few assumptions are made about the end result, and this can allow novel structures to emerge that bypass any preconceptions of the designer – the structures may even be beyond their comprehension. A third year project took some tentative steps into exploring evolutionary algorithms and attempted to bring some of the ideas behind them to the fore in a novel way.

A basic addressable structure like the one below was used as a starting point. It’s a surface composed of many triangles and the position of each vertex can be changed independently.

The same structure is seen below after each vertex has been moved a small amount in a random direction.

If this process was applied to the structure repeatedly then it would be become chaotic since there’s nothing guiding the progress of the vertices. However, if a decision is made about which changes to keep and which ones to discard then this brings the possibility of the structure converging on something more organised. This decision is known as a ‘fitness function’ and can be used to allow the structure to evolve towards an end guided by it.

The image below shows the addressable structure as a flat surface without any changes.

Then a light source is placed above its centre and it starts to evolve towards a structure reflecting this light back towards the source. Each vertex is changed randomly and the triangles affected by the change are tested to see if the reflect more light back towards the source. If they do then the change is kept, otherwise it is discarded. This process is then repeated for each vertex and the resulting structure will reflect a little more light back towards the source when it is finished. Each one of these cycles is known as a generation.

More commonly known as logarithmic spirals, these can be found in both the natural and man-made worlds as a simple solution to the problem of growth. The nautilus shell above is good example of such a spiral. These structures were examined for a third year project that aimed to look a little deeper than their immediate appearance and into the mechanics behind them. The spiral can be described using polar coordinates by:

$r = ae^{b\theta}$

where $a$ and $b$ are arbitrary constants. A simple plot of such a spiral might look like this one:

Pushing this idea a little further and moving into three dimensions, a structure like the following one can be produced, seen here from the top and from the side: