Monday, March 29, 2010

Hyperbolic crochet book

Hey folks, I just got sent a link to this book. I only know what I've read from the description there, but it seems pretty cool. The aim is to explain mathematical and geometrical concepts through crochet, to give a new hands-on perspective on what are usually quite abstract ideas. So yeah, I'm very happy to see crochet being used as a way to promote maths and make it more accessible to a wider audience!
I also think it's awesome that it's reviewed by Dr. Hinke Osinga :o)

Happy knitting, and/or reading!

Wednesday, March 24, 2010

Ada Lovelace Day!

Hey folks, it's Ada Lovelace Day again! (Their website seems to be down at the moment, Google has a cached version).
Ada Lovelace Day is a day to celebrate and promote the achievements of women in science and technology, by writing a blog post about a woman working in a scientific or techie field you find inspirational.

So, I'd like to talk about Kate Ho. Kate is originally a computer scientist, and is currently a PhD student working in the sociology of computer systems, in between starting up companies and enterprises.

Specifically, Kate studies "requirements engineering", the process of figuring out what an organisation really *wants* from their computer systems, and how to build the system to provide this. This matches Kate's vision for computer science pretty well -- not just technology for technology's sake, but technology fitted to people's needs, making a real difference to how they get things done.

Kate's other main passion is entrepreneuring. She is constantly looking for new business opportunities, and while I've known her has usually been involved in at least 3 start-ups at any given moment. Now that her thesis is submitted, she has had the chance to move into entrepreneuring full-time and has started Interface3, a company specialising in developing multi-touch surface systems.
Again, her aim in this is to find new applications for technology, to find new ways in which it can improve people's lives, and to make them a reality. I think this is what she is really passionate about -- trying to work out ways in which technology can change the world.

She does lots of other awesome stuff too -- she set up Edinburgh University's Hoppers group, and helps organise Edinburgh's Girl Geek dinners, not to mention running Scottish Women's Rugby. She also knits!

So, Kate -- social entrepreneur, innovator, geek, knitter!

Happy Ada Lovelace day, everyone!

Monday, March 15, 2010

More on Cellular Automata

Hi again!
So, ages ago I talked about the possibility of using cellular automata to generate lace patterns. A key step in this is to interpret the cellular automaton as a collection of rules for interactions between chains of digits, travelling left or right, or remaining stationary.
On closer inspection it turns out this is rather more complicated than I'd expected. The problem is that these interpretations can be influenced by neighbouring digits, so:

looks like it should to be a left-travelling chain, but if the neighbouring digits are:

then we need to see this as a chain bifurcating into left-travelling and stationary chains. Worse, if it was

we would probably want to see this as two left-travelling chains running alongside each other.
Because of these problems, I think it is impossible to interpret general cellular automata as chains in this way -- what's needed is a non-local approach. What can be done is to come up with a procedure to read through the pattern and divide each of the `1' digits into chains travelling left, right, or remaining stationary (and some `orphan' digits left by themselves). This is then fairly straightforward to convert into a lace pattern.
I feel this is cheating a bit, it's not really in the spirit of cellular automata and there are a lot of arbitrary decisions to be made. There are further complexities I haven't dealt with -- how do you deal with chains bifurcating? Or colliding? So far my chains are just left hanging.

Still, it generates some very nice patterns with some interesting features. Mostly though I'm just enjoying the idea of computer-generated lace, there's something magical about putting in a set of logical rules and generating a pattern.
So, applying this to rule 30, generating the pattern starting from a single `1', I get something like this:

(not sure how that'll turn out, but it's just to give an impression)

So, this turns out to be rather more complicated than I'd expected, and very much less canonical than I'd hoped. It does produce viable patterns though, and makes me rather keen to try to elaborate this method.

Pictures of the finished shawl soon!