Saturday, April 15, 2017

Permutation cardi



There's some maths behind this one!  The idea here is that there are exactly 6 ways to permute 3 elements, and each of the cable represents one of these two permutations.

We can describe a permutation by writing down what it does to the elements 1, 2 and 3 - so the two cables on the front represent (1, 3, 2) and (2, 1, 3).

The ones on the back are slightly more complex - these ones represent (2, 3, 1) and (3, 1, 2), but in these cases you've got one element moving two places, which distorts the knitting a little more, so I've broken these into two steps each containing a single crossing.

The arms are the bit I'm most excited about - of the 6 possible permutations, there are two pairs which are mirror images (the ones we've seen), but the remaining two are their own mirror images, so they don't have a relationship - (3, 2, 1) and the trivial permutation (1, 2, 3), which leaves everything unchanged.  These give this nice asymmetry between the two arms.  (3, 2, 1) again has elements moving two places, but it's hard to break this up into two steps, so here I've added an extra chain stitch to extend the cables.

Also exciting, the length of the repeats varies between permutations -  this gives their order in the symmetry group: (1, 3, 2), (2, 1, 3) and (3, 2, 1) all have order 2, (2, 3, 1) and (3, 1, 2) are order 3, and (1, 2, 3) is order 1, so the lengths of their repeats is different.  It's cool too that these all divide 6, so if you could fit in exactly 6 repeats, all the cables would end up in the right place after the same number of rows.

You could go much further with this too!  These permutations are at the heart of bell-ringing, although taken much further - for example here.  I love the intricate patterns this gives, but I would be wary of doing this with intarsia cables - as much as I love the colours, this ends up with the yarn getting crossed and needing to be constantly untangled.  Still, imagine that beautiful scarf with rainbows weaving together!

Saturday, March 4, 2017

Foxtato pattern!

Also!  I should have mentioned here, I finally got around to posting my Foxtato pattern - you can see this on Ravelry here, and it's available for free download: Ravelry download

Looking forward to seeing other people's projects, and to see them Doing The Thing!

Hugh.

Data structures

Hi folks!  (I aten't dead)
I was thinking recently that I haven't made nearly enough things to do with computer science, the same way I did for maths, and it's time to fix that!
So this project is to knit a family of data structures.  The idea will be to take a bunch of plastic toy balls to represent data items, and knit wrapper cups, connected together in different ways, to represent the data structure itself.
I've got ideas for a few of these:

  • Linked list - each node has a link to the next node.
  • Doubly linked list - each node has forward and backward links.
  • Binary tree - each node has two children.  I'd like this to be unbalanced, so some of the branches will be longer than others.
  • Red-black tree - another binary tree, but with coloured nodes (and this one will be balanced).
  • Hash table - a single parent has a bunch of child nodes, each with a coloured rim to represent the hash value of the objects to place in it.  Some of the child nodes will also form (small) linked lists, of the same colour.
  • Array - a string of references, only some of which have a node attached.  (It might be more accurate if he nodes are all there, but only some of them are filled, but I think this would make it harder to distinguish from the linked list.
I'm planning to write up a pattern for this one - it should be pretty simple since the only components are the cups and the references.  But I'd love to see people knitting some other structures too, and maybe they'll be useful as teaching aids at some point?  The one drawback is this means I need to knit a *lot* of identical cups, I think the whole project will need about 40 of them.

Happy knitting,
Hugh.

Sunday, November 1, 2015

Ace-cephalopods

 The aim here was to make an ace-cephalopod, an asexual octopus, after seeing these awesome LGBT marine animals.

They're modelled on the giant pacific octopus, the main features are the head part, which leans backwards and has a slight fold where it attaches to the body.  There's then a bit of a waist, before it separates out into the arms.


The first one turned out a little more cute and cartoonish than I'd hoped - its body is too big and round, and the tentacles are too short.  I think the big problem though is that the eyes don't point outwards, so it's natural to see it as just having a big face, rather than seeing the eyes pointing sideway.  Regardless, it's pretty cute, and reminds me a lot of the dumbo octopus.  I really like how it stands up too - I'd consider adding a suction cup to the underside so it can be attached to things.

The second one I'm much happier with!  He has a real angry glare to him, and his features look great.  The main differences here are the tentacles are much longer, the head is a bit narrower and the waist more pronounced, and I've reworked the colours to give a bit more emphasis to the head.  And of course the eyes now come in little capsules so they protude and point outwards properly.

I had great fun wandering around out local docks taking pictures of them (and explaining to passersby what I was doing) - you can see the rest of them here: http://s12.photobucket.com/user/griffiths_hugh/library/Ace-cephalopods

Knitting these did make me realise quite how often the things I knit seem to end up having tentacles.  Going to try knitting a few more land-based things next!

Happy knitting,
Hugh.

Saturday, October 24, 2015

Getting ready for winter


 With winter coming, it's getting a little colder, and we're all keen to wrap up warm.  But among all the snug jumpers and mittens, let's not forget about our chlorophyll-bearing friends.
 (This comes from a suggestion from Facebook.  The hats are for the Innocent Smoothies campaign, and have been sitting in a box waiting to be sewn up for an embarrassingly long time.  No plants were harmed during the making of this.)

Enjoy,
Hugh.

Monday, August 31, 2015

Beethoven Mittens finished!

The Beethoven mittens are finished!
The basic design aims to be quite simple, with a single colour and minimal shaping. 
The flip tops are a little more involved - the fingers and the thumb both flip back, which I find really useful when moving in and out of cold places, and for fiddling with phones and things.  Making the thumb flip back is slightly unusual, but I find you need that too, particularly for smartphones.
I was expecting the openings to be more of a problem - with two layers of rib, they're quite thick, which I thought might be a bit awkward, but seems fine.


I changed the text from what I had planned, so the final two lines are:
"Alle Menschen werden Bruder"
"Und der Cherub steht vor Gott"
I decided that I liked the contrast between the two statements.
The font is aiming to be a little gothic, so the letters are tall, narrow and angular, and the heights are a little quirky.
This was quite fiddly, and took a few goes at it.  The problem with writing is that you have to figure out coherent rules and principles for all the letters, so they have a consistent look and feel.
I was amazed how much space they took too - I thought this would fit easily, but it was pretty close.

So, I'm pretty happy with how these turned out!  I'm enjoying wearing them, and they're a great reminder to be joyful all the time :)

*edit - realised later that I'd missed an "n" from "Menschen".  I went back and corrected that, but forgot to take a photo afterwards.  Ah well.*

Happy knitting!
Hugh.

Acephalopod

Just a quick project today:

I came across this, and thought it was pretty cool, being a fan of diversity, cetaceans and also terrible puns.  I'm quite tempted to make all of them, but have made a fair few whales before.  So in the meantime, I thought I'd continue the theme by making an acephalopod. 

This will be quite a small and simple octopus, in the colours of the asexual flag.  In the spirit of sexuwhales, I'll make the colour appear in bands (I did consider having tentacles of different colours, but think that would be harder to balance overall).  I'll also start with the head being the purple side, since this will show up the features better, but does mean it's technically upside down.

I think it needs saying too that if you think this is a terrible pun, Taylor Swift is even worse:
http://internet.gawker.com/taylor-swift-to-nick-jonas-in-alleged-leaked-dms-are-1682093508

You're whalecome.
Hugh.