The Art In Science

Quite a few months ago now, I was scrolling through Facebook, as I usually do, and an article published by Quanta Magazine caught my eye. I paused in my fervent morning scroll because the cover image was a high-resolution photo of a slime mould; its network of moist yellow veins stretching intricately across the screen immediately piqued my interest.  Clicking on the article proved to be a brilliant decision because it contained a collection of exquisite gifs showing slime moulds growing and undulating as they fed. Perhaps this doesn’t sound spectacular but I assure you that it is.

The text of the article was interesting too; author John Rennie described the slime moulds as having a sort of ‘intelligence’ which allows them to choose the most efficient path between food sources. While I admit the initial fascination was purely aesthetic, this ‘intelligence’ is actually a very interesting topic in itself, with links to of all things, computing. In fact, a quick search of the good old uni library catalogue turns up numerous articles about how slime moulds are being used to inform computational models regarding path-planning. This is compelling because slime moulds are a relatively simple organism.

As an initial primer, let’s introduce the basics of slime moulds. The name is misleading, as slime moulds are in fact not a mould at all, but an amoeba, and they come in two main types: plasmodial and cellular.

Plasmodial slime moulds are one huge, individual cell which contains a single cytoplasm and many nuclei. This ‘cell’ can become as large as several feet in size, pretty incredible! Cellular slime moulds on the other hand spend most of their life-cycle as single cells, but upon the secretion of a chemical signal, they aggregate together and act as a single organism in which each of the individual cells fulfils a specific role. 

Scientific research is often conducted using the plasmodial slime mould Physarum polycephalum, which is easy to grow under lab conditions. It has vegetative and dormant forms, which are each activated by the presence or absence of a food source. When there is food about and times are good, the slime mould will grow larger, in its vegetative state. But, if the food source dries up, maybe a complacent lab technician forgot to replenish its oat flakes, Physarum polycephalum will grow a tough protective shell, in which it can wait for that lab tech to bring more sustenance.

But what might you do with this squishy friend? Well, as I mentioned earlier, the slime mould is used as a model for some unconventional computing problems. Unconventional computing is a broad area of cutting-edge research which aims to develop new methods of computing, often borrowing concepts from nature. The natural world has had millions of years to perfect its problem-solving skills, so it seems reasonable that we could borrow some of it for our own use.

A lot of the complex behaviour in the natural world is what we call ’emergent’. That is, from very simple local interactions between basic components, there emerges highly sophisticated behaviour that we wouldn’t have been able to predict without witnessing it ourselves. If we can model this behaviour and recreate it, we might be able to understand the intricacies of biological systems, as well as using these techniques to solve other pressing problems.

Physarum polycephalum exhibits this emergent behaviour when it grows to fit the characteristics of its environment. Like any organism, it seeks new and delicious food sources, while steering clear of repellents such as toxic chemicals, light, and temperature or humidity extremes. It turns out that it is quite efficient at doing this in the best possible way, to the extent that it can even consistently solve a maze!

Given that it is a very simple organism, without what we’d consider a brain, how is it capable of such exceptional path planning? Well, it’s all due to that emergent behaviour. Basically, the plasmodium grows to fill the entire space of the maze, and then, once the tasty treats have been located, all unnecessary plasmodial tubes are retracted leaving only those connecting the two feeding points.

To determine which tubes to retract, pulses originating at a food source are sent into the plasmodium, these then propagate through the rest of the cytoplasm. If the wave passes sections of the plasmodial tubes that lie perpendicular to the direction that the wave is travelling, then these tubes will decay. Tubes which lie parallel to the waves remain, and eventually there will be a single path connecting all available food sources. This wave acts on each section of the plasmodium separately, without an overall ‘plan’, giving it an emergent quality.

The slime mould’s ability to create the most efficient path between points makes them quite interesting to computer scientists who want to solve the ‘travelling salesman problem’. This is a long-standing problem which remains to be solved using an exact mathematical method. Instead, there are numerous computational alternatives which can solve it approximately. The essence of the travelling salesman problem is this: ‘if I’m a salesman who needs to visit a number of cities before returning home, what is the shortest path to take?’

Now you might think this seems like a very easy problem, but consider the number of potential paths you can take between your house and work. Chances are there are many, many routes you could take. Once you extend that to a trip with multiple stops, you can see the scale of the problem, and why no-one has identified a method that will give the exact solution in all cases. The numerous computational methods each have pros and cons, and the slime mould method has the benefit of being relatively simple.

The computational model which has been developed using the slime mould method is very similar to how it solves a maze. The entire map is filled with a virtual plasmodium consisting of individual particles. Then, bits of the virtual plasmodium is retracted if they do not lie on a direct path. Retraction is determined by applying a simple rule to each of the particles. Essentially, the particles move towards areas closer to the virtual cities or food sources and away from areas that are defined as repellents, but each decision happens at a local scale. It is only when you take a step back that a useful picture emerges.

This is an interesting example of how natural systems can be used to inform how we approach computing problems. However as it currently stands, this isn’t the best method for solving the travelling salesman problem. On average, this technique does about 6% worse than the best computational method. Still, further work can be done, and it begs the question, how many organisms can we look to for help with novel solutions to everyday questions?