Does art compute?

A decade ago, a number of physicists and astronomers, an occasional mathematician, and even an interloping engineer or two (shhh…) here at the University of Nottingham started to collaborate with the powerhouse of pop sci (/pop math/pop comp/pop phil…) videography that is Brady Haran. I was among the “early adopters” (after the UoN chemists had kicked everything off with PeriodicVideos) and contributed to the very first Sixty Symbols video, uploaded back in March 2009. This opened with the fresh-faced and ever-engaging Mike Merrifield: Speed of Light.

Since then, I have thoroughly enjoyed working with Brady and colleagues on 60 or so Sixty Symbols videos. (Watching my hairline proceed backwards and upwards at an exponentially increasing rate from video to video has been a somewhat less edifying experience.) More recently, I’ve dipped my toes into Computerphile territory, collaborating with the prolific Sean Riley — whom I first met here, and then subsequently spent a week with in Ethiopia — on a number of videos exploring the links between physics and computing.

It’s this ability to reach out to audiences other than physicists and self-confessed science geeks that keeps me coming back to YouTube, despite its many deficiencies and problems (such as those described here, here, and here. And here, here, and here [1].) Nonetheless, during discussions with my colleagues about the ups and downs of online engagement, I’m always tediously keen to highlight that the medium of YouTube allows us to get beyond preaching to the converted.

Traditional public engagement and outreach events are usually targeted at, and attract, audiences who already have an interest in, or indeed passion for, science (and, more broadly, STEM subjects in general [2].) But with YT,  and despite the best efforts of its hyperactive recommendation algorithms to corral viewers into homogeneous groupings (or direct them towards more and more extreme content), it’s possible to connect with audiences that may well feel that science or math(s) is never going to be for them, i.e. audiences that might never consider attending a traditional science public engagement event. The comment below, kindly left below a Numberphile video that crossed the music-maths divide, is exactly what I’m talking about…


There’s still a strong tendency for a certain type of viewer, however, to want their content neatly subdivided and packaged in boxes labelled “Physics”, “Chemistry”, “Biology”, “Philosophy”, “Computing”, “Arts and Humanities Stuff I’d Rather Avoid” etc… Over the years, there have been comments (at various levels of tetchiness) left under Sixty Symbols, Periodic Videos, Computerphile etc… uploads telling us that the video should be on a different channel or that the content doesn’t fit. I hesitate to use the lazy echo chamber cliché, but the reluctance to countenance concepts that don’t fit with a blinkered view of a subject is not just frustrating, it narrows the possibilities for truly innovative thinking that redefines — or, at best, removes — those interdisciplinary boundaries.

Some physicists have a reputation for being just a little “sniffy” about other fields of study. This was best captured, as is so often the case, by Randall Munroe:

But this is a problem beyond intellectual arrogance; a little learning is a dangerous thing. As neatly lampooned in that xkcd cartoon, it’s not just physicists who fail to appreciate the bigger picture (although there does seem to be a greater propensity for that attitude in my discipline.) A lack of appreciation for the complexity of fields that are not our own can often lead to an entirely unwarranted hubris that, in turn, tends to foster exceptionally simplistic and flawed thinking. And before you know it, you’re claiming that lobsters hold the secret to life, the universe, and everything…

That’s why it’s not just fun to cut across interdisciplinary divides; it’s essential. It broadens our horizons and opens up new ways of thinking. This is particularly the case when it comes to the arts-science divide, which is why I was keen to work with Sean on this very recent Computerphile video:

The video stems from the Creative Reactions collaboration described in a previous post, but extends the physics-art interface discussed there to encompass computing. [Update 08/06/2019 — It’s been fun reading the comments under that video and noting how many back up exactly the points made above about the unwillingness of some to broaden their horizons.] As the title of this post asks, can art compute? Can a painting or a pattern process information? Can artwork solve a computational problem?

Amazingly, yes.

This type of approach to information processing is generally known as unconventional computing, but arguably a better, although contentious, term is lateral computing (echoing lateral thinking.) The aim is not to “beat” traditional silicon-based devices in terms of processing speed, complexity, or density of bits. Instead, we think about computing in a radically different way — as the “output” of physical and chemical and/or biological processes, rather than as an algorithmic, deterministic, rule-based approach to solving a computational problem. Lateral computing often means extracting the most benefit from analogies rather than algorithms.

Around about the time I started working with Brady on Sixty Symbols, our group was actively collaborating with Natalio Krasnogor and his team — who were then in the School of Computer Science here at Nottingham — on computational methods to classify and characterise scanning probe images. Back then we were using genetic algorithms (see here and here, for example); more recently, deep learning methods have been shown to do a phenomenally good job of interpreting scanning probe images, as discussed in this Computerphile video and this arXiv paper. Nat and I had a common interest, in common with quite a few other physicists and computer scientists out there, in exploring the extent to which self-assembly and self-organisation in nature could be exploited for computing. (Nat moved to Newcastle University not too long afterwards. I miss our long chats over coffee about, for one, just how we might implement Conway’s Game Of Life on a molecule-by-molecule basis…)

It is with considerable guilt and embarrassment that I’ve got to admit that on my shelves I’ve still got one of Nat’s books that he kindly lent to me all of those years ago. (I’m so sorry, Nat. As soon as I finish writing this, I’m going to post the book to you.)

This book, Reaction-Diffusion Computers by Andy Adamatzky, Ben De Lacy Costello, and Tetsuya Asai, is a fascinating and comprehensive discussion of how chemical reactions — in particular, the truly remarkable BZ reaction — can be exploited in computing. I hope that we’ll be able to return to the BZ theme in future Computerphile videos. But it was Chapter 2 of Adamatzky’s book, namely “Geometrical Computation: Voronoi Diagram and Skeleton” — alongside Philip Ball’s timeless classic, The Self-Made Tapestry (which has been essential reading for many researchers in our group over the years, including yours truly) — that directly inspired the Computerphile video embedded above.

The Voronoi diagram (also called the Voronoi tesselation) is a problem in computational geometry that crops up time and again in so very many different disciplines and applications, spanning  areas as diverse as astronomy, cancer treatment, urban planning (including deciding the locations of schools, post offices, and hospital services), and, as discussed in that video above, nanoscience.

We’ve calculated Voronoi tesselations extensively over the years to classify the patterns formed by drying droplets of nanoparticle solutions. (My colleagues Ellie Frampton and Alex Saywell have more recently been classifying and quantifying molecular self-assembly using the Voronoi approach.) But Voronoi tesselations are also regularly used by astronomers to characterise the distribution of galaxies on length scales that are roughly ~ 1,000,000,000,000,000,000,000,000,000,000 (i.e. about 1030) times larger than those explored in nanoscience. I love that the same analysis technique is exploited to analyse our universe on such vastly different scales (and gained a lot from conversations with the astronomer Peter Coles on this topic when he was a colleague here at Nottingham. )

As Cory Simon explains so well in his “Voronoi cookies and the post office problem” post, the Voronoi algorithm is an easy-to-understand method in computational geometry, especially in two dimensions: take a point, join it up to its nearest neighbours, and get the perpendicular bisectors of those lines. The intersections of the bisectors define a Voronoi cell. If the points form an ordered mesh on the plane — as, for example, in the context of the atoms on a crystal plane in solid state physics — then the Voronoi cell is called a Wigner-Seitz unit cell. (As an undergrad, I didn’t realise that the Wigner-Seitz unit cells I studied in my solid state lectures were part of the much broader Voronoi class — another example of limiting thinking due to disciplinary boundaries.)

For less ordered distributions of points, the tesselation becomes a set of polygons…


We can write an algorithm that computes the Voronoi tesselation for those points, or we can stand back and let nature do the job for us. Here’s a Voronoi tesselation based on the distribution of points above which has been “computed” by simply letting the physics and chemistry run their course…


That’s an atomic force microscope image of the Voronoi tesselation produced by gold nanoparticles aggregating during the drying of the solvent in which they’re suspended. Holes appear in the solvent-nanoparticle film via any (or all) of a number of mechanisms including random nucleation (a little like how bubbles form in boiling water), phase separation (of the solid nanoparticles from the liquid solvent, loosely speaking), or instabilities due to heat flow in the solvent. Whatever way those holes appear, the nanoparticles much prefer to stay wet and so are carried on the “tide” of the solvent as it dewets from the surface…


(The figure above is taken from a review article written by Andrew Stannard, now at King’s College London. Before his move to London, Andy was a PhD researcher and then research fellow in the Nottingham Nanoscience Group. His PhD thesis focused on the wonderfully rich array of patterns that form as a result of self-assembly in nanostructured and molecular systems. Fittingly, given the scale-independent nature of some of these patterns, Andy’s research career started in astronomy (with the aforementioned Peter Coles.))

As those holes expand, particles aggregate at their edges and ultimately collide, producing a Voronoi tesselation when the solvent has entirely evaporated. What’s particularly neat is that there are many ways for the solvent to dewet, including a fascinating effect called the Benard-Marangoni instability. The physics underpinning this instability has many parallels with the Rayleigh-Taylor instability that helped produce Lynda Jackson’s wonderful painting.

But how do we program our physical computer? [3] To input the positions of the points for which we want compute the tesselation, we need to pattern the substrate so that we can control where (and when) the dewetting process initiates. And, fortunately, with (suitably treated) silicon surfaces, it’s possible to locally oxidise a nanoscale region using an atomic force microscope and draw effectively arbitrary patterns. Matt Blunt, now a lecturer at University College London, got this patterning process down to a very fine art while he was a PhD researcher in the group over a decade ago. The illustration below, taken from Matt’s thesis, explains the patterning process:


Corporate Identity Guidelines™ of course dictate that, when any new lithographic or patterning technique becomes available, the very first pattern drawn is the university logo (as shown on the left below; the linewidth is approximately 100 nm.) The image on the right shows how a 4 micron x 4 micron square of AFM-patterned oxide affects the dewetting of the solvent and dramatically changes the pattern formed by the nanoparticles; for one thing, the characteristic length scale of the pattern on the square is much greater than that in the surrounding region. By patterning the surface in a slightly more precise manner we could, in principle, choose the sites where the solvent dewets and exploit that dewetting to calculate the Voronoi tesselation for effectively an arbitrary set of points in a 2D plane.


There’s a very important class of unconventional computing known as wetware. (Indeed, a massively parallel wetware system is running inside your head as you read these words.) The lateral computing strategy outlined above might perhaps be best described as dewetware.

I very much hope that Sean and I can explore other forms of lateral/unconventional computing in future Computerphile videos. There are a number of influential physicists who have suggested that the fundamental quantity in the universe is not matter, nor energy — it’s information. Patterns, be they compressed and encrypted binary representations of scientific data or striking and affecting pieces of art, embed information on a wide variety of different levels.

And if there’s one thing that connects artists and scientists, it’s our love of patterns…

[1] And that’s just for starters. YouTube has been dragged, kicking and screaming every inch of the way, into a belated and grudging acceptance that it’s been hosting and fostering some truly odious and vile ‘content’.

[2] On a tangential point, it frustrates me immensely that public engagement is now no longer enough by itself. When it comes to securing funding for engaging with the public (who fund our research), we’re increasingly made feel that it’s more important to collect and analyse questionnaire responses than to actually connect with the audience in the first place.

[3] I’ll come clean — the nanoparticle Voronoi tesselation “calculation” shown above is just a tad artificial in that the points were selected “after the event”. The tesselation wasn’t directed/programmed in this case; the holes that opened up in the solvent-nanoparticle film due to dewetting weren’t pre-selected. However, the concept remains valid — the dewetting centres can in principle be “dialled in” by patterning the surface.

Rhapsody in Q

While digging through my e-mail archive to find a completely unrelated e-mail from years ago, I unearthed the following wonderful parody progress report (for the month of January 2012) from Julian Stirling, a PhD student researcher in the Nottingham Nanoscience Group at the time.  I just couldn’t leave it languishing in the archive so have released it into the wild here. Julian’s PhD project was focussed on various aspects of the qPlus variant of atomic force microscopy (described by its originator Franz Giessibl in the video below).

At the time of writing his Jan 2012 monthly report, Julian had been working on an analysis of the tip geometry in qPlus AFM which was later published in the Beilstein Journal of Nanotechnology.

Over to you, Julian…

Is this a real force?
Is this just fantasy?
I am not sure if they
Line up with reality

Open a book,
Look up at the maths and see…

It’s not a good guess, look at condition three.
Tips are, rather big, rather long
Rather like, other prong,
Any way the tip moves, all this matters to me.

To me…

I just solved the math,
Put a pen against board,
left no solution unexplored

Da-dah… This has just begun,
Because now I got to work out what it means

Da-dah woo-hooo,
Didn’t mean to stop and cheer
If I’m right there is work to do tomorrow
Carry on, carry on as if nothing’s really finished

Look now, simulation’s done:
Sends vibrations down the tine
Oscillating all the time
Hey look, ev’rybody, the way it moves,
Gotta see the graph and try to face the truth

Da-dah woo-hooo,
I don’t want to stop,
I sometimes wish I’d never solved this at all

I see a little simulation of a tine,
Look at that! Look at that! Do you see the lateral motion?!
Eigenmodes and vectors, simulate detectors! Gee!
Galileo, Galileo
Galileo, Galileo
Galileo, Figaro – magnifico

Its just a theory, no one believes me
Its just a theory, why should we believe thee?
Just take a look at a this spectroscopy!
In it comes, out it goes, will you watch it go?
Bismilah! No, we will not watch it go
(Watch it go!) Bismilah! We will not watch it go
(Watch it go!) Bismilah! We will not watch it go
(Watch it go) Will not watch it go
(Watch it go)(Never) Never watch it go
(Watch it go) Never watch it go (Watch it go) Ah
No, no, no, no, no, no, no
Oh mama mia, mama mia, mama mia, watch it go,
Beelzebub had a simulation put aside for me
For meeeeeeeeeeeeeeee!

So you think you can model me and predict how I scan?!?!
So you think you can simulate all that I am?!?!
Oh, Euler- can’t do this to me Euler,
Just gotta derive, just got to derive it in full

All this really matters, Anyone can see,
All this really matters,
All this really matters to me…

Any way the tip moves…