Botanica Mathematica

a textile taxonomy of mathematical plant forms


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Fibonacci Tree

Last week I got chatting to Étienne Ghys, a wonderful French mathematician who was in Edinburgh showing us his new films about Chaos. We told him about Botanica Mathematica and he said “You could knit a Fibonacci tree!”.

And I thought, “Why haven’t we already knitted a Fibonacci tree??” The idea was so obvious and its execution so easy that it seemed silly not to have done so already. The Fibonacci pattern is also an excellent model for how plants actually grow, so it was perfect for the Botanica Mathematica project.

How does the Fibonacci model work? Well, you start with a branch, and after a certain period of time it splits into two smaller branches: a main one and a sapling. In the next time period the sapling stays the same size as it grows to adulthood, while the main branch once again splits into two. (We had a discussion of this in a previous post.) Here’s a picture of the resulting tree:

Fibonacci treeThe black numbers to the right indicate how many branches there are at each time step. This sequence of numbers is known as the Fibonacci sequence, and the next number is the sum of the previous two.

The small blue numbers next to each branch indicate how wide the branch is – in knitting terms this is the number of stitches you are knitting with (in the round) for that branch.

So, start at the bottom of the tree by casting on 21 stitches. Join in the round and knit for 21 rows (the blue numbers also indicate the height of each branch!). Then put 8 of the stitches onto a stitch holder while you knit with the other 13 (joined in the round). After 13 rows, put 5 stitches onto a stitch holder while you knit (in the round) with the other 8, continuing in this way until you reach the top of the tree. Then go back to the last set of stitches being held, pick up the stitches and knit in the same way as before to the top of the tree. (It’s exactly the same technique as for the binary bonsai.)

There’s Fibonacci numbers everywhere in this tree: in the number of rows you do at each stage; in the size of each branch; and in the number of branches at each horizontal cross-section. The ratio of successive Fibonacci numbers gives (an approximation to) the golden ratio, and indeed the finished tree has a pleasing dimension and appearance to it. I think it looks more realistic than the binary bonsais.

Here’s a picture of my finished tree:

Knitted Fibonacci TreeDo you like it? Do you have more ideas of what we could make, or ideas of how to adapt the Fibonacci tree? Let us know!


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Binary Bonsai Workshop on 15 March

Botanica Mathematica at Coburg House Art Studios, August 2013

Botanica Mathematica at Coburg House Art Studios, August 2013

We’ve got a workshop set up for anyone who can make it to Edinburgh to knit trees with us. We’d really love to meet as many of our supporters as possible.  All trees delivered to us by 31 March will go on display in the Science Festival Art Trail so this is an ideal chance to get started.

Date 15 March
Time 11am for a couple of hours
Location Summerhall Cafe, Summerhall Arts Centre, 1 Summerhall Place, Edinburgh (that’s a lot of Summerhall!) Here’s a map Summerhall is also the venue for the exhibition and hopefully by then we’ll know exactly where our work will be sited.

Julia and I will both be there with our big bag of wool (kindly donated by McAree Bros and by an anonymous knitter) to hand out. Bring your favourite dpns or crochet hook. We’ll give you the yarn and talk you through the process of making a binary bonsai that you can add to to the specimen collection for the exhibition in April. I’ll also have some felt and embroidery floss to get people making a stitched version. I haven’t had time to write up yet but it’s on its way. We’ll have tree stuffing stuff too!

Please spread the word. Tell members of your local knitting group. Bring/send along anyone who’s interested in contributing – basic knitting in the round or crochet skills required.

If you’ve made a tree or hyperbolic flowers or fungus this would be a good time and place to hand them in too.

Hope to see you there!


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Edinburgh Events Annouced!

EISFCover2014

This morning the Edinburgh International Science Festival launched their programme.

We really pleased to announce that Botanica Mathematica will be part of the Science at the HeART of Things art trail. It will take place from 5th to 20th April in Edinburgh’s Summerhall Art Centre which has been getting lots of media attention for its adventurous programmes of exhibitions and performances.

I’d like to take this opportunity to ask knitter or crocheter who reads this to contribute a Binary Bonsai or a Fibonacci Flower or a Hyperbolic Chanterelle to help put on a really great show. In particular we need more trees to have a good sample size for species classifications. We could hold a workshop (with free yarn from our sponsors, McAree Bros :-) ) one Saturday in March if it looks like people are interested. Email madeleineshepherd[at]gmail.com (replacing [at] with @ – of course) if you’d like to come along and we’ll take it from there.

Botanica Mathematica will also be taking part in Botanics Late in the Royal Botanic Gardens Edinburgh on 17 April. For this event we’ll be showcasing the results of our new collaboration with Naomi Nakayama from Institute of Molecular Plant Sciences, University of Edinburgh. Naomi is helping us make new designs based on lichens, mosses, liverworts and other lower plants indigenous to Scotland. We’ll have more to say about these in the near future.

There’s also a Mini Maker Faire on 20 April at Summerhall. We will both be around in one capacity or another. More on this as it gets finalised.

I hope you’ll all be able to contribute to/take part in/visit these and other events during the Festival this April. Please share your thoughts and photographs if you do.


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Public lecture – with free mince pies!

BotanicaMathematicaTreesAs we reach the end of 2013, it’s time to pause and take stock of all the wonderful things Botanica Mathematica has produced over the year. Join us at ICMS for a public lecture about the project, including the mathematical ideas behind the patterns, the classification of all the specimens we’ve been sent, and all the crazy directions that people have taken the project in!

The talk is 6-7pm on Tuesday 10 December, at 15 South College Street. Tickets are free but limited, so book yours today at Eventbrite: https://botanica-mathematica.eventbrite.co.uk/. The event will be followed by drinks and mince pies, and a chance to see the full Botanica Mathematica collection.

This lecture is actually the third in a trilogy of talks celebrating Maths for Planet Earth. As this year draws to a close, we will be starting to think about 2014 and what new projects might be in store. 2014 will be the International Year of Crystallography and also the 400th anniversary of the invention of logarithms in Edinburgh by John Napier. Tell us what ideas you have for a new maths/textiles science communication project!


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Natural Knits!

Natural Knits! by MadeleineS
Natural Knits!, a photo by MadeleineS on Flickr.

Back in February we met the organisers of the Midlothian Science Festival at a networking event. They were looking for some science and knitting input for their programme so we stuck our hands up and said “pick me please!” – and they did!

The festival takes place in October in the towns and villages of Midlothian. Roslin village is one of them. They have an active knitting group called Knit, Knot and Sew who exhibit in the local library from time to time. The idea was for them to try out some of our patterns over the summer and then come to a public workshop during the festival.

Roslin Library hosted the workshop on 12 October and very friendly hosts they were too. The Knit, Knot and Sew group had dropped off a lovely basket of hyperbolic knitting chanterelles and some came along to try out the binary bonsai pattern on the day. Once the trees started to take shape there was a lot of enthusiasm for making more as presents for friends and family.

We left a little display of trees and fungus, pattern leaflets and yarn with the library for the rest of the festival and to inspire the local knitters. I’m really looking forward to collecting the results.

IMG_2308


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Doors Open Display.

Doors Open Days is a project that encourages buildings not normally open to welcome the public in for a nosey around. The focus is architecture but most have some more exhibits and activities. On 28 September my Day Job at the International Centre for Mathematical Sciences involved taking part, so they asked me to bring along Botanica Mathematica.

We set up the entire collection in the glass walled room that houses the library. Around 200 people came along and from the way I was croaking by 4pm, it felt like I spoke to most of them! I know i didn’t because I lurked in corners to take photos.

One of the 200 visitors was a schoolteacher I met in Orkney. She’d taken a few of the kits I had there to try and get some of her pupils interested and dropped in with the results. Out of her bag came lots of lovely hyperbolic crochet algae and flowers.

Katy's Hyperbolic Flowers

Katy’s Hyperbolic Flowers

A special thanks go to Katy from Kirkwall Grammar School who I understand learned to crochet in order to take part with her red and lilac flowers!

Hyperbolic Crochet Laminaria by Jean from Kirkwall

Hyperbolic Crochet Laminaria by Jean from Kirkwall

The algae included a lovely specimen of Laminaria sp. complete with holdfast attached to a felted pebble covered in fleece from a local pet lamb.

It really makes the project feel worthwhile when I see how people can take the ideas we’ve set out and make them their own. I hope we get some equally good feedback from the people who visitied ICMS on Doors Open Day.


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Island Hopping!

It’s been quiet on this blog for the last couple of months but that’s because we’ve been doing so many things! A trip to the Orkney Isles was the first of these activities.

The Orkney International Science Festival team made Julia and I very welcome in the first week of September. Julia gave several talks about different aspects of mathematics while I got to show the ever-growing collection of trees and fungus to 250 visitors on the Family Day. I arrived the day before and collected some locally made trees from the library in Kirkwall – the delicate little peach tree in the pot on the table and the magnificent green specimen with the hanging red fruits. Many thanks to the Orkney Library Service for co-ordinating this and the Orkney knitters for their excellent work.

All the binary and trinary trees were on display along with all the the hyperbolic flower and fungus creeper, which is becoming quite encrusted! Click here to see more of the event and some tourist photos from around Kirkwall.

More trees and fungi arrived later in the day and lots of yarn and pattern kits were handed out. If you picked up a kit, we’d love to see what you’ve made. Contact me using the details on the leaflet.

Some lovely flowers, fungi and kelp have arrived from Orkney since I got back to Edinburgh, but they’re destined to be part of the next post…

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