Knitters and Coders: separated at birth?

People often say that computers are all around us, but you could still escape your phone and iPod and go out to the park, far away from the nearest circuit board if you wanted to. It’s a lot more difficult to get away from the clutches of computation itself though. For one thing, you’d have to leave your clothes at home. Queen Mary Electronic Engineer Karen Shoop tells us about the code hidden in knitting, and what might happen when computers learn to read it.

Boy with wool hat and jumper on snowy day

If you’re wearing something knitted look closely at it (if it’s a sunny day then put this article away till it gets colder). Notice how the two sides don’t look the same: some parts look like a raised ‘v’ and others like a wave pattern. These are made by the two knitting stitches: knit and purl. With knit you stick the needle through and then behind the knitting; with purl you stick the needle in the other direction, starting behind the knitting and then pointing at the knitter. Expert knitters know that there’s more to knitting than just these two stitches, but we’ll stick to knit and purl. As these stitches are combined, the wool is transformed from a series of waves or ‘v’s into a range of patterns: stretchy stripes (ribs), raised speckles (moss), knots and ropes (cable). It all depends on the number of purls and knits, how they are placed next to each other and how often things are repeated.

Knitters get very proficient at reading knitting patterns, which are just varying combinations of k (knits) and p (purls). So the simplest pattern of all, knitting a square, would look something like:

’30k (30 knit stitches), finish the line, then repeat this 20 times’.

A rib would look like: ‘5k, 5p, then repeat this [a certain number of times], then repeat the line [another number of times]’

To a computer scientist or electronic engineer all this looks rather like computer code or, to be precise, like the way of describing a pattern as a computer program.

How your jumper is like coding

So look again at your knitted hat/jumper/cardi and follow the pattern, seeing how it changes horizontally and vertically. Just as knitters give instructions for this in their knitting pattern, coders do the same when writing computer programs. Specifically programmers use things called regular expressions. They are just a standard way to describe patterns. For example a regular expression might be used to describe what an email address should look like (specifying rules such as that it has one ‘@’ character in the middle of other characters, no full-stops/periods immediately before the @ and so on), what a phone number looks like (digits/numbers, no letters, possibly brackets or hyphens) and now what a knitting pattern looks like (lots of ks and ps). Regular expressions use a special notation to precisely describe what must be included, what might possibly be included, what cannot be, and how many times things should be repeated. If you were going to teach a computer how to read knitting patterns, a regular expression would be just what you need.

Knitting a regular expression

Let’s look at how to write a knitting pattern as a regular expression. Let’s take moss or seed stitch as our example. It repeats a “knit one purl one” pattern for one line. The next line then repeats a “purl one knit one” pattern, so that every knit stitch has a purl beneath it and vice versa. These two lines are repeated for as long as is necessary. How might we write that both concisely and precisely so there is no room for doubt?

In knitting notation (assuming an even number of stitches) it looks like: Row 1: *k1, p1; rep from * Rows 2: *p1, k1; rep from * or Row 1: (K1, P1) rep to end Row 2: (P1, K1) rep to end Repeat these 2 rows for length desired.

piles of woollen clothes

All this is fine … if it’s being read by a human, but to write experimental knitting software the knitting notation we have to use a notation a computer can easily follow: regular expressions fit the bill. Computers do not understand the words we used in our explanation above: words like ‘row’, ‘repeat’, ‘rep’, ‘to’, ‘from’, ‘end’, ‘length’ and ‘desired’, for example. We could either write a program that makes sense of what it all means for the computer, or we could just write knitting patterns for computers in a language they can already do something with: regular expressions. If we wanted to convert from human knitting patterns to regular expressions we would then write a program called a compiler (see Smart translation) that just did the translation.

In a regular expression to give a series of actions we just name them. So kp is the regular expression for one knit stitch followed immediately by one purl. The knitting pattern would then say repeat or rep. In a regular expression we group actions that need to be repeated inside curved brackets, resulting in (kp). To say how many times we need to repeat, curly brackets are used, so kp repeated 10 times looks like this: (kp){10}.

Since the word ‘row’ is not a standard coding word we then use a special character, written, \n, to indicate that a new line (=row) has to start. The full regular expression for the row is then (kp){10}\n. Since the first line was made of kps the following line must be pks, or (pk){10}\n

These two lines have to be repeated a certain number of times themselves, say 20, so they are in turn wrapped up in yet more brackets, producing: ((kp){10}\n(pk){10}\n){20}.

If we want to provide a more general pattern, not fixing the number of kps in a row or the number of rows, the 10 and 20 can be replaced with what are called variables – x and y. They can each stand for any number, so the final regular expression is:


How would you describe a rib as a regular expression (remember, that’s the pattern that looks like stretchy stripes)? The regular expression would be ((kp){x}\n){y}.

Regular expressions end up saying exactly the same thing as the standard knitting patterns, but more precisely so that they cannot be misunderstood. Describing knitting patterns in computer code is only the start, though. We can use this to write code that makes new patterns, to find established ones or to alter patterns, like you’d need to do if you were using thicker wool, for example. An undergraduate student at Queen Mary, Hailun Li, who likes knitting, used her knowledge to write an experimental knitting application that lets users enter their own combination of ps and ks and find out what their pattern looks like. She took her hobby and saw how it related to computing.

Look at your woolly jumper again…it’s full of computation!

– Karen Shoop, Queen Mary University of London, Summer 2014

The ping pong vaccination programming challenge

Vaccination programmes work best when the majority of the population are vaccinated. One way scientists simulate the effects of disease and vaccination programmes is by using computer simulations. But what is a computer simulation?

Lots of multi-coloured ping pong balls

You can visualise what a simulation is with ping pong balls bouncing around a crowd. Imagine having a large room full of people. A virus is represented by a ping pong ball, bouncing from person to person, infecting each person it touches. Each person who is hit by a ping pong ball and not already infected becomes infected. That means they toss that ping pong ball back into the crowd to infect more people, but they also toss an extra one too (and then they sit down: dead). Start with a few ping pong balls. Quickly the virus spreads everywhere and lots of people sit down (die). You have run a physical simulation of how a virus spreads!

Now start again but ‘vaccinate’ 80 per cent of the people first: give them a baseball cap to wear to show who is who. If those people get a ping pong ball, they just destroy it: they infect noone else. Start with the same number of ping pong balls. This time, the virus quickly dies out and only a few people sit down (die). Not only are the vaccinated people protected but they protect many of the un-protected people too who might have died.

Now (if you can program) you can write a program to do the same thing, and so simulate and explore the spread of infection, which is easier perhaps than getting a thousand people to chuck ping pong balls about. Create a grid (an array) of 1000 cells. Each represents a person. They can be infected or not. They can also be vaccinated or not. Start with five random cells (so people marked as infected). Run a series of rounds. After each round, a newly infected cell randomly chooses two others to infect. If not infected already and not vaccinated, then they become newly infected. If already infected or vaccinated, they do not pass the infection on.

You can run lots of different experiments with different conditions. For example, experiment with different proportions of people infected at the start or explore what percentage of people need to be vaccinated for the virus to quickly die out. Is 50 per cent enough? You could also change how many people one person infects, or for how long a person can infect others before dying. Perhaps they each keep causing new infections for three rounds before stopping instead of only one. In what situations does the virus infect lots of people and when does it die out quickly?

What you are doing here is computer modelling or simulating the effects of the virus in different scenarios, and that is essentially how computer scientists make the predictions that governments use to make decisions about lockdowns and mask wearing, if they are “following the science”. Of course, such models are only as good as the data that goes into them, such as how many other people does each person infect. In reality, this is data provided by surveys, experimental studies, and so on.

– Paul Curzon, Queen Mary University of London, Spring 2021

Download Issue 27 of the cs4fn magazine on Smart Health here.

This post and issue 27 of the cs4fn magazine have been funded by EPSRC as part of the PAMBAYESIAN project.

A recipe for programming

By Paul Curzon, Queen Mary University of London

How is a computer program like a recipe? Let’s see, and as a bonus, here’s how to cook a quick pasta dish (for International Hummus Day).

Virtual Table Setting

Programmers are the master chefs of the computing world – except the recipes they invent don’t just give us a nice meal, they change the way we live.

Programs are very similar to recipes. They both give instructions that, if followed, achieve something. There is a difference between them, though, and it has to do with language. When chefs invent recipes they write them out in human languages like English. Programmers write programs in special languages. Why’s that? It’s all about being precise enough to be sure exactly the same thing happens every time. Recipes are often ambiguous which is why when I follow one it sometimes goes wrong. Programs tie down every last detail.

Let’s apply some ideas from programming languages to making meals. One of my favourite recipes is a hummus-based pasta dish (see box) so we’ll use that.

Structure it!

The first thing to notice about a recipe book is there is a clear structure. Each recipe is obviously separate from the others. Each has a title and a brief description of how it might be used. Each has an ingredients list and then a series of steps to follow. Programs follow a similar structure.

Cookery books use page layout to show their structure. Programmers use language: grammar, symbols and keywords. A keyword is a word that means something special. Once you have decided a word is a keyword you only ever use it for that purpose.

Let’s invent a keyword RECIPE to mean we’re starting a new recipe. The only time that word will appear in our recipes is to start a new recipe. What follows it will always be the name of the recipe. We will also need to know when the name ends. To make that clear we will use a special symbol made up of open and close brackets ().

We also want to be absolutely sure what is part of this recipe and what isn’t. We will use curly brackets: everything between the brackets is part of the named recipe.

RECIPE Hummus and Tomato Pasta ()


No comment?

Spaghetti that looks like optical fibre

Recipes usually include a brief description that isn’t part of the actual instructions. It is just there to help someone understand when you might use the recipe. Programs have descriptions like this too. Programmers call them ‘comments’. Remove the comments and the recipe will still work. We need a clear way to show when a comment starts and ends. We will start them with a special symbol ‘/*’ and end them with ‘*/’.

RECIPE Hummus and Tomato Pasta ()
/* Serves 2
This is a very quick 20-minute after work dish.


Variable storage

What comes next in a recipe is usually a list of ingredients. The idea is to list everything you need so you can have it all ready before you start. I often have a problem following recipes, though, as they don’t list absolutely everything. Mid- recipe I might suddenly find I need a frying pan…when mine is crusted with burnt cheese sauce from last night! To avoid that, let’s list all the pans we need too. For our recipe we need a frying pan and a saucepan.

Something used to store things (like pans do) in a program is called a ‘variable’. Program variables hold things like numbers. The equivalent of the ingredients list ‘declares’ the variables. Declarations give each variable a unique name used to refer to it and also give each a ‘type’ – is it a saucepan or a frying pan we need? To be clear about when a declaration ends we add in some punctuation. Programming languages tend to use a semicolon for that – it’s a bit like a full stop in English.

Saucepan pan1;
Fryingpan pan2;

This says that in the rest of the recipe when we say pan1 (the variable name) we mean a particular pan: a saucepan (its type). When we say pan2 we mean a particular frying pan.

New assignment

Assignment does NOT move things around, it makes new copies

We will make a distinction between things to hold stuff, like pans (variables) and the actual ingredients that go in them: ‘values’. We will also follow the TV chefs and start by setting out all the ingredients in little dishes at the start so they are at hand – and make that part of the instructions.

We will need to declare a dish to hold each ingredient, giving its type and giving the dish a name. At the same time we will say what should be put in it before the recipe proper is started. We will use an ‘=’ symbol to mean put something in a variable (i.e., dish or pan). In programs, this action of putting something in a variable is called ‘assignment’. So, for example, we will declare that we need a dish to hold the hummus (called hummusDish). We assign 200g of hummus to it.

Dish hummusDish = 200g hummus;

We are now ready for the recipe proper. We can use assignment as a precise way of moving things from one place to another too. So if we say, for example:

pan2 = oilDish;

We mean empty the contents of the dish of oil into the frying pan. Programs are slightly different here, as when they do an assignment they don’t move things from one place to the other, they copy it. That would be like having a dish that automatically refilled itself whenever it was emptied.

Often we want to add to whatever is already in a pan. Programmers leave nothing to doubt and say explicitly that is what they mean:

pan2 = pan2 + onionDish;

This tells us to mix what is in the onion dish with what is in the frying pan, and then leave the result in the frying pan. We will use the + symbol to mean add together and stir.

Methods in my madness

So far all we’ve done is put ingredients in things and copied them around. To make a meal we need to do various basic cooking things like heat a pan or drain a pan. Rather than spell out every step of how you do that in every recipe, we will use a short hand. We create mini-recipes that say how to do it and just refer to them by name. They are often called ‘methods’ by programmers. Each is written out just like our recipe. In fact to a programmer our recipe is a method too. When we want to use it we just give its name followed by any extra information needed. For example to heat a pan, we need to know which pan, how high a heat and for how long. We write, for example:

Heat (pan1, medium, 12 minutes);

This format helps make sure we don’t miss something (like the time for example). We need similar methods for draining a pan and serving the meal. We won’t give the actual instructions here. In a full program they would be written down step-by- step too and not left to chance.

Time to do it right

We have come up with a language for recipes similar to the ones used for programming. We’ve used symbols, keywords and very precise punctuation – the language’s ‘syntax’ – to help us be precise. On its own that’s not enough – each part of the language has to have a very clear meaning too – the language’s ‘semantics’. Together they make sure in following a recipe we know exactly what each step involves. There is then less scope for a cook (or computer) to get it wrong. Computers, of course, have no intelligence of their own. All they can do is exactly follow the instructions someone wrote for them (a bit like me cooking).