Finished alchemy mittens

Ok, first finished object for a while - the alchemy mittens are done! I tried to keep the pattern reasonably simple, which probably helped a lot. Also there was a lot of snooker on tv, which is ideal for knitting along to!


I'd intended to make this in the round using two circular needles(I've just come across this technique, and it's awesome), but ran into some problems - because of the way the stranding works, with independent bands on the front and back, it would be difficult to work this in the round, you would need to carry the green yarn too much. So I decided it needed to be based on intarsia in the round, which meant a switch to dpns(because I'm using interchangable needles rather than "real" circulars, and they don't handle purl rows well).
The intarsia in the round gave me some trouble - I'm not sure if I'm remembering it being easier than it was, but I ended up with some loose stitches at the join. This might mean I was somehow wrapping the yarns wrong, or possibly just that you shouldn't try to join the intarsia pieces at the end of a needle? I suspect the latter, since the stitches just looked loose rather than wrong. This seemed to get even worse when the shaping started to get involved at the top of the mitten.

Pattern-wise, I may be able to explain the design a bit better now I have visual aids. The left mitten represents antimony and the right is tin- I chose these elements because they had nice alchemical symbols and roughly the right atomic numbers to make the patterns work and fit nicely onto a mitten.
The symbols on the back are alchemical signs for the respective elements, although I suspect noone would actually recognise them without looking them up. The number of spots on the back of the hand give the atomic number of the element(51 for antimony, 50 for tin), and they're arranged to show how the electrons are divided up into shells(or, I suppose it's position in the periodic table?).
The spots on the front represent the number of neutrons in the most common isotope, so that the total number of spots on both sides gives the atomic weight. They're also supposed to give them a slightly checkered look. I'd planned to make the front kinda textured based on a pair of gloves I saw made by the mighty Juliana, which gave them a wonderfully grippy look, but chickened out cos I wasn't sure how the texture would interfere with the stranding and was too impatient to do the swatching first.

So yeah, I'm very happy with how these turned out, the dots give them a nicely complicated look and the symbols came out just about the right size that they dominate without overpowering the rest of the design. I'm curious how it would have looked if the symbols were a different colour, but I think I prefer it this way in the end. They could maybe have been done on smaller needles to make the fabric denser and warmer, but this was rather a "what I had to hand" project.

Yay!
Hugh.

Alchemy mittens

Right, continuing Operation Catch Up With Knit-Designing, I thought I'd post about the alchemy mittens I have underway.
So, what's the idea? I wanted to make a pair of mittens which would encode alchemy symbols and chemical information about certain chemical elements in a subtle enough way that they will look a bit arcane, while actually being entirely about chemistry.
Each mitten will represent a chemical element- I've picked antimony and tin for these ones, but others could be fairly easily substituted. It'll have the alchemical symbol for that element on the back, along with a pattern of spots which represent the atomic number of the element, arranged in a series of bands representing the number of electrons in each electron shell. On the front of the had there will be another collection of spots representing the number of neutrons in the commonest isotope of the element, so that the total number of spots on both sides gives the atomic weight of this isotope.

Why is a little harder to explain, but it has something to do with the different attitudes we have towards alchemy and chemistry. I think we have a tendency to see science as a bit dull and safe, as very *normal*. Alchemy, on the other hand, is a kind of magic- it's crazy and mystical and occult. I think we'd do better to see science a bit more that way - after all, it contains dragons(see also), time travel and guns that shoot lightning. And the really amazing thing is that science can *prove* that all these things exist(well, 'prove' isn't quite the right word in the last case, but hey).
So that's kinda what I'm aiming for with these mittens, that they will be based on chemistry, but in a slightly magical/arcane/alchemical sort of way.
Also, because alchemy symbols are neat.

I've done most of the knitting for them now, so hopefully will have some finished objects to show in the near future(and hopefully my explanation will be a little more coherent then).
Hugh.

Bell-ringing(ish) cardigan

Hey folks!
Well again I've failed to update this for way too long, despite having a couple of projects I should've mentioned. So without further ado - the bell-ringing cardigan. Sort of.

The idea for this cardigan grew out of a discussion of bellringing with Mair, and how this might be expressed in knitted cables. As I understand it, a bellringing pattern is produced by repeated applications of a pair of permutations (subject to some constraints), and the aim is to run through every ordering of a collection of bells(usually four, five or six). Some quick calculations suggest that a full 'peal' with five bells would involve 120 changes and would run roughly the full height of a jumper.

This project is a baby cardigan along similar lines: if you use just three cables, any pair of transpositions will run through every ordering of the three cables. This pair of transpositions can be chosen in six different ways, so the idea is for this cardigan is to have six different cables to represent each of these choices. The cables are picked out in intarsia to make the rearranging clearer as well as to make the whole thing pretty and colourful.
The 'ish' is because not all of these transpositions is allowable in the bell-ringing problem - the position of a bell in the sequence can only move by one place for physical reasons, but we haven't included this constraint here - some of the patterns involve swapping cable 1 with cable 3. This leads to some fabricky issues too, since this is quite a big cable and distorts the fabric a bit. Some experimenting shows that this isn't too bad provided the cable rows are appropriately spaced though.
One other problem is that these patterns don't distinguish "over" and "under" crossings, so these have to be more or less made up. To make the braids (more or less) alternating(so that if a cable went 'over' on the previous cable row it will go 'under' on the next) narrows it down a bit, and I seemed to come up with the right number of solutions, but it struck me as a little arbitrary and I'm not sure if there are others. Quite possibly there are exactly six though, and I just haven't spotted the reason for it yet.

So there we go - colourful little baby cardigan with intarsia cables, group theory and possibly some bell-ringing. I actually did most of the knitting over christmas and just need to get around to sewing it all together, so hopefully it'll be all done and ready to post pretty soon!
Happy knitting,
Hugh.

Cellular automata lace

Hi folks!
This is an idea I'd been vaguely intending to develop for quite a while, but didn't get around to seriously implementing until last week.
So, a cellular automaton is a rule for taking a grid of binary numbers, and generating a new grid in which the value of each entry is determined by the previous entry in the same and adjacent squares. So, if you take a 1-dimensional cellular automaton, it takes a row of 1's and 0's, and makes a new row, and each entry is determined by the entry above it and it's two neighbours. They're extremely simple, but they can produce some suprisingly complex patterns.
My idea was to use this to generate lace patterns - the 1's represent holes, the 0's plain stitches. There are some technicalities to overcome - lace knitting has left- and right-leaning holes, and while you could just pick one and apply it everywhere, I wanted something which would reflect the way digits 'travel' in CA patterns, so that you would arrive at a pattern of left and right travelling lines, meeting, annihilating, generating new lines. You can do this in a reasonably canonical ways - by looking at the three digits on the previous row you can more or less say it's heading left or it's heading right. There are some cases where a choice needs to be made though, so I just choose these. This loses some of the generality, but isn't too bad.
Having made these choices, I wrote a short program to choose a cellular automata 'rule' at random, pick some starting conditions, and apply the rule to generate a pattern. A second program then looks through the 1's this gives, and by looking at the arrangement above them translates this into a pattern of K, YO, K2tog and SKP stitches. Putting the output of this into a spreadsheet then gives you a lace pattern, and best of all, this is all entirely automatic. One such spreadsheet is here(for now- may need to move that at some point). (alternate rows are plain)

There's a couple of problems - this particular pattern involves a lot of double yarn overs. I'm told you can manage this by working K1 P1 on the alternate row, but I suspect it may be neater to write a quick program to look through the pattern and eliminate these - I think that wouldn't obscure the pattern and might need to a nicer finished piece, as well as easier knitting. So I need to try those out and see which solution I prefer.
The other problem is that there aren't that many 1D cellular automata, 16, by my count. While CA were very much the motivation for doing this, I kind of feel that sticking with them is selling the lace pattern generating half of the programme a bit short - it could apply equally well to any binary grid. So while this is a good starting point, I'm thinking about maybe inventing some slightly more elaborate generating rules - a quick way would be to allow a block to be decide by the five blocks above it, or the previous two time steps. Another approach I'd like to try would be to replace the binary grid with trinary, which would give a much wider family of rules, then map all the 2's back to 1 to produce a grid to feed into the lacing programme.

So yes, let's to play with. I particularly wanted to mention this because there was an extremely timely xkcd comic about cellular automata. In fact, I think the CA he's talking about simulating the universe with there may well be the same one in my lace pattern, though I haven't looked too closely.

So, anyone for an extremely geeky shawl?
Hugh.

Roses

Ok, just a quick post cos I realise I haven't written anything here for months.
So, I decided to make some roses for a rose-loving friend. I had a fiddle around with a couple of rose patterns, particularly a nifty one from Knittiana which involved twisting your knitting to form petals(I love that about knitting - that whatever you can possibly do wrong, someone somewhere will have found a use for). But I couldn't make them come out how I wanted, they all looked kinda rose-ish, rather than actually like a rose.

Then I came across a great crochet pattern for them from RS Island crafts, which was very simple and turned out really well. I haven't done much crocheting, so I was very impressed with how well this turned out, and heartily recommend the pattern.
I did have some trouble with the sewing up, particularly attaching the stems to the flowers, but that's probably me just now knowing how to sew.

So yep, there's some roses! Should be getting back to posting soon, I have a project or two underway that I've been too busy to blog yet.

Happy knitting!
Hugh.

Knitting the polar way

Hi folks.
I've been playing with some knitting-related maths lately, and after a certain amount of experimenting I've just about got a design ready to be playing with.
This kind of follows on from the ideas behind the 'science doilies', trying to knit standard shapes in non-standard ways. Particularly, I've been looking at knitting colourwork radially.
Planning colourwork when knitting flat is fairly straightforward, the lack of shaping means that the stitches obey nice easy-to-follow patterns. If you knit radially(starting at a central point and work outwards), it becomes a lot harder to judge. The reason for this is that flat knitting is based on cartesian coordinates, where radial knitting is using polars.
So to make this work, I came up with another little Maple program which will take a curve(given in normal cartesian coordinates), convert this into polar form, then use some numerical trickery to convert this into a workable knitting pattern. This seems to work pretty well, with one caveat that you need to be a little careful about spacing your increases - the calculation assumes that the increases are all entirely homogeneous about each round, which isn't possible in practice because the stitches are discrete. In particular, the standard trick of distributing increases evenly along the round(as you would for most lace doilies) isn't even enough, I think it distorts the colourwork pattern too much.
The reason I'm really excited about this though, is that the same program could also be used to work out short row patterns for knitting non-trivial shapes in the same radial way. Initially I'd hope to be making sensible rectangular pieces, but ultimately I think there's the potential for some truly mind-boggling designs from this.

I'm working on a design just now which will be a bit of a trial run for this - the plan is to make a little baby jacket for my little nieceling, the back panel of which will be knit radially with a pattern of colourwork hearts. I'll blog about that design specifically another time, because there's some nifty maths behind the heart pattern(if you're part of the 'geekcraft' group of Ravelry, you may have heard me being excited about this already). I'm not too sure how I'll do with the rest of the jacket, will have to play with it a bit more.

So yep, more about that when the actual knitting is underway, and assuming more goes well, I'll say some more about the mechanics of the radial coordinate program then too.

Happy knitting!
Hugh.

Alien surfaces

Hey! It's been pointed out to me that I haven't written anything here for ages, and I realised there's a couple of projects I haven't found the time to mention yet.

So, first off, Alien surfaces!
This project actually belongs to local mathematician Madeleine Shepherd, but I helped out with some of the maths, so I'm sure it's worth a post :o)
As part of a festival exhibition on 'alien surfaces', artwork inspired by descriptions of alien planets in science fiction, Madeleine knit a model of , the surface you get if you take the curve y=1/x and rotate it around the x-axis(for the region x>1 - although I think we took x>1/30, or thereabouts, to make the curvature show up more).
This surface has some very cool properties mathematically - it turns out that it's surface area is infinite, while it's volume isn't, which means that you could, hypothetically, fill one with paint, but it would be impossible to paint it's entire surface. Which is a bit mind-boggling. (The trick is that in comparing a volume with a surface area in this way, you're kind of assuming that you're covering the surface with a layer of paint of uniform thickness, the volume is only finite because the trumpet tapers off quickly as x becomes large.)

Since the surface has a rotational symmetry, writing down a pattern for it is relatively simple - you just need to work out the circumference at each row, convert this into a number of stitches, and work out how many stitches you need to decrease each time.
The difficulty is that the rows in this case do not correspond to the coordinate x, but the arclength - the distance you've travelled along the curve from the first row. Now, in differential geometry, this isn't really a problem, you can just change coordinates without any difficulty, but actually doing this in practice takes a bit more work because while it's easy enough to find the arclength from the position, inverting this formula is quite hard, and needs to be done numerically.
Happily though, Maple actually cooperated with this, so I now have a bit of code which is capable of doing this more or less automatically. If anyone's interested, or is keen to knit there own surfaces of revolution, I'd be happy to go into more detail on this. I was considering tidying up the code a little and convincing it to print out real honest-to-goodness knitting patterns, but I'm not sure how many people would be interested in this and have access to Maple?

And I love how the surface turned out, there's something amazing about writing down a bunch of maths and getting to see it suddenly turned into a piece of knitting! I'm quite keen to read the book it comes from too, I'd be interested to see how far the author was able to take this idea, and how this unusual geometry affected the people living there :o)
(Oh, and the tapir is because Madeleine seems to be quite keen on them)

Happy knitting!
Hugh.