We're going to talk about
Can we compute with art?
can paintings compute and it's it's a broader theme in terms of
What are the links between physics and chemistry and biology and computing and indeed art?
So I worked with somebody called Linda Jackson who's a local nottingham artist
She'd started to play with something called acrylic pouring where basically you take different types of paint
You put them down onto a canvas you let them mix and you let them dry and you end up with what I think
Incredibly striking an incredibly beautiful patterns like this sort of foam
like what we
Scientifically called cellular networks where you can see these cells on different lens scales and right across the board in terms of different colors
Etc. Those types of patterns are absolutely ubiquitous in nature right across very very large scale and scales
in fact
The large-scale structure the universe in terms of our galaxies are distributed
best thought of his in terms of a cellular network or this type of
Foam like structure all the way down to the really really really small and we're in nanoscience group
So we're very very keen on the really really small
We took a droplet of this which are nanoparticles five nanometers across
Tiny tiny particles of gold drop them onto a surface and let the solvent
evaporate
Left us with patterns like this. So these are not the individual particles themselves
This is what the particles do in terms of how they collect together and how they dry and you end up with these
incredible cellular type patterns which are
something like if you compare this with this in terms of the length scale, this is on a length scale about
25,000 times smaller. This is a microscope emits an atomic force microscope image
So you're sitting there as a computer file if you were going
Okay, that's nice who's talking about science and he's talking about art. When's he gonna start talking about the computing?
There are strong links here in terms of the physics and the chemistry of these patterns
But the question is can you compute with curtains?
can you compute with art the question here is not can we you know generate something that does much much better than
Silicon technology CMOS technology in terms of the speed or the processing power, etc
so it's about thinking about different main sets and it's a broader and I would say more philosophical question what is information and
How do we process information?
It's a lovely piece of art what sort of computational problem can a piece of art like that solve?
I mean is this to do with colors?
Not really to do with colors much more to do with patterns in that we could just take all strip all the colors from this
And just make it black and white or even to a certain extent almost binary I said, but what's remarkable?
Is that the physical process which is underlying the art here?
Can be used to do a computation
Let's say you've got a set of schools
across a district or a county or indeed across the country and you
Want to think about the catchment area for those skills?
What's the best way of?
Dividing up the land in terms of catchment areas the fairest way and to do that we use an approach from computational geometry
called the Verona tessellation and
so to compute that which you can
Compute pretty straightforwardly, in fact, a lot of languages MATLAB included basically have the command built-in
So there's a distribution of points. It's fairly ordered
What we want to do is for each one of these points on here. We want to find the region that is
Closest to that particular point basically we want to divide this up as fairly as possible
So mathematically this is actually an geometrically is actually straightforward problem. So what we do is we connect up
One of the points to all its nearest neighbors and then what we do is we take the
Perpendicular bisectors, let's do that. So ones there
Ones here. So we're bisecting these lines and ones there
Ones there if you'll excuse the wobbly drawing
So what we have is that this area or the points within here are the closest to that point? Okay?
This is like numberphile stuff come on, it does feel like numberphile, but we're going to do a computation
I promise at the end and we're going to do a physical computation
I promise what you'd end up with then as you can see is just a set of hexagons
So that was an example of a very ordered
Let's take a less ordered set and a somewhat more
Natural set perhaps this is actually from a paper by Meredith P Richards and what she did was look at
distribution of schools in a district or
neighborhood in
Washington, I believe if I remember correctly
This is what it actually looks like the black dots are where the schools are and the question then is how would you divide up?
this area
to be the fairest in terms of the
Neighborhoods or the areas of the district that is served by each school
The algorithm is exactly as we've just done for that ordered set is you connected up
You connect a given point to its nearest neighbors
You take the perpendicular bisectors and you divide up the plane that way that's the fairest way of
Dividing up the land as it where I found being kind of picky here
I'm gonna suggest that perhaps some of those are more densely populated than others
Is that too complicated for this? So that's a really good point Sean
So yes
We're making a number of different assumptions here or assuming that the density of the population is the same right across the board
Obviously there are complications in terms of even transport links etcetera. There's a wide range of different contributions
we're going to do what all good physicists do even computational physicists and
approximate cows a large sphere PI's around three
Density population density is even across the board. We can set up a computer program to solve this. It's relatively straightforward
Let's take an example
Here's Nottingham. That's probably - higher density of points for schools. But I don't know. Let's say it's coffee shops
Well, what wanted to do is to try and work out was your closest coffee shop, which is the closest coffee shop to you
so the way to solve that is
Actually to do a Verona tessellation and so here's our points
Just taking away the map and we can calculate the Verona tessellation and it looks like that so again
It's not an ordered distribution of points. Therefore. We see a range of different polygons ranging from adult
See if we can see a triangle in there. I don't think so
I think the smallest is four-sided maybe up to seven or eight sided cells
Okay, so where is the physical computation well we can do it on a computer
or what we can do is we can
Take this as our computer
This is now a computer. This is a physical computer. And what we're going to do is going to take a droplet of these particles
Put it on a surface let the solvent evaporate
And what's going to happen? Is that those?
Particles are going to be carried by the tide of the solvent and get pushed together and they're going to create our own
Verona tessellation, let me show you exactly what I mean with a simulation
So the yellow dots here are the nanoparticles one question you might ask is. Well, I can't if I hold it up
oh, they're definitely nanoparticles and there are most definitely
Nanoparticles in it. In fact, we did a sixty simplest video on this some time ago. You might ask
Why does it look red isn't gold gold? Why does this look right?
There's a lot of very interesting physics as to why this is right. The yellow dots are the nanoparticles
The white is actually the solvent. So that's the liquid in which the particles are dissolved. What's going to happen?
Is that the dark bits meet you're about to see you can already see some?
Black patches that's where the solvent is evaporating. And so what's going to happen is when we run this
These holes are going to open up as the solvent evaporates the nanoparticles love to be wet by the solvent
They looked at to be dissolved in the solvent so they will track back as a solvent dee wets as a solvent
Evaporates the remaining solvent left on the surface will spread back like this carrying the nanoparticles with it
What we'll end up with in the end is a Voronoi tessellation. So let me run this
So you see these opening up?
Carrying the nanoparticles with them and you can already see the density and they collide
And so what's happening here is that you can see as these holes spread out
they force the nanoparticles together and ultimately you end up with something that looks like that those tessellations are absolutely everywhere just
Earlier this year. There was a scientific American article
On this is not a beautiful image
This is a dragonfly's wings and you see this same type of tessellation everywhere near to the large-scale structure
the universe giant's causway announced from this is the
cross-section through a cork from a wine bottle and
The point I want to try and make for computerphile audience is in each case. These are effectively physical computers you might argue about the
the universe what the large-scale structure universe, but in terms of the
Physical and chemical processes that have been weakened exploited to do a computation
Which gets me back to this? This was a distribution of coffee shops. Here's our points for our coffee shops. Here's a Verona tessellation
lots of calculated by the computer
However, this is what happens when we take a droplet of our particles put them on a surface and we look at the final stage
And if we overlay this on this the physics has done the computation force. It's not cared about
How do I join up the nearest neighbors and how to get the perpendicular bisectors?
It's fallen out of the physics and you might think hang on there seems to be a bit of a trick there
maybe there is but it's all about thinking about computation and
Information processing in different ways. This is almost
This is computation not by algorithm but computation by analogy
By trying to look at what's happening in a physical system and say well actually can we exploit that?
To do a computation for us. There must have been some kind of control in this there
You must have decided where those have operational right? So that's in this case
I've cheated a little bit shown reason the points were distributed like this is that I work backwards from the image
So cheated a little bit, but could we actually program this system? How would we program the system?
Well, what we'd have to do is control where the evaporation happens
Can we do that?
Yes
We can take our surface and what we can do is we can oxidize it using the tip of something called a scanning probe
Microscope in this case. Those lines were about a hundred
Nanometers wide something like are very very small lines
Obviously you can some some will recognize the logo at least
And what we can do is we can control how the the particles this is the real experiment
This is the simulation
we can control how the solvent evaporates from the surface by patterning the surface and so that's a couple examples and we can
put a lot of different patterns down there the next step in this is can we actually
Program the Verona tessellation. Can we put little points two four the evaporation of those points and
calculate the
tessellation that's something were
Actually is going to be stimulated by this video
can we part on a surface and drive the formation of the Verona tessellation and can we do a computation that way and
Then the values of those array elements can be whatever you want, but they might be for example
How much you spent on beer and pizza and coffee and so you could write a very simple program that would let simply say