Posts tagged Counting

Growing Alan Turing's legacy

Wednesday 18 May 2016 Tagged inAround the world, Counting, Weird & Wonderful

We’re proud to share exciting news about the Turing’s Sunflowers project, a citizen science experiment celebrating the legacy of Alan Turing in the centenary of his birth.

Thousands of sunflowers were planted by families, schools and community groups in honour of Turing as part of the study to explore number patterns in sunflowers and to help solve a mathematical riddle that Turing worked on before his death in 1954.

Famous for his code-breaking skills, which helped to crack the Enigma Code during the Second World War, and as a founder of computer science and artificial intelligence, Alan Turing later became fascinated with the mathematical patterns found in stems, leaves and seeds - a study known as phyllotaxis.

The spirals in sunflower seed heads often conform to a Fibonacci number (0,1,1,2,3,5,8,13,21,34,55, and so on, where each number is the sum of the two numbers before it). Turing was one of a number of scientists who tried to explain ‘Fibonacci phyllotaxis’, but he died before the work was complete.

Professor Jonathan Swinton who led on the study has now re-checked all of the sunflower pictures and data sent in by growers and, with the project coordinator, Dr Erinma Ochu, published the findings and the dataset in the academic Journal, Royal Society Open Science, which anyone can download.

Excitingly in addition to finding sunflowers with Fibonacci numbers, in a few cases, seedheads with non-Fibonacci numbers or ‘nearly’ Fibonacci numbers were discovered.

This paper, not only includes sunflower pictures submitted by you, the growers, but also provides a new dataset, which will allow theoretical explanations of Fibonacci phyllotaxis to be tested.

The challenge now, will be to create mathematical models of how sunflowers grow to take into account the rare exceptions to Fibonacci patterns.

We really want to thank every single grower who submitted data, pictures, cake  and photographic exhibitions.

To download the paper visit:

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Janet's picture of Samsun

Son of Vincent

Thursday 25 October 2012 Tagged inCounting, Meet the growers


You might remember Penelope Nyau's blog post about sunflowers and bees, here's her update after counting sunflowers.

The Turing Sunflower project has been a wondrous and fulfilling journey – cutting down the blooms with my colleagues only extending the thrilling adventure. We discovered how to count the spirals and learned about the Fiboancci sequence, which served only to deepen my admiration for nature.

Vincent and the four STEMs (the names of our sunflowers) were ripe for counting at different times. STEM 4 was an anomaly and unfortunately closed up like a clam so could not be counted. STEMs 2 and 3 have just been picked and not yet counted; but Vincent I am pleased to confirm, proudly featured spiral numbers of the Fibonacci sequence (55 clockwise, 89 counter-clockwise). STEM 1, somewhat smaller than Vincent, but no less impressive, unfortunately did not (44 clockwise, 55 counter-clockwise).

Seeds of Vincent

The point to my post is this – growing and counting done, data entered, photo-diary complete, what to do with Vincent now? Not being able to let the story end here I have patiently plucked every last one of Vincent’s seeds (soon to be doing the same for STEMs 1, 2 and 3!) and lovingly packaged them up to distribute amongst my colleagues, friends and family to grow again next year. Vincent, your legacy will live on.

Penelope Nyau is an administrator based at MOSI and amateur photographer. Follow her on twitter and flickr.

Counts away...

Friday 5 October 2012 Tagged inCounting

A little girl practices measuring her sunflower

Inspired and ready to count? You're only a few steps away from experiencing the wonder of maths in nature and honouring Turing's legacy at the same time!

It's been fantastic hearing about counting events happening around the country, like the one held by Glyndon Bloom and Berry community group in London and the ones planned for Daresbury and Manchester City Library.

sunflower harvest at MOSI

We've been busy counting spirals at MOSI too. So far, we have nearly 200 sunflowers counted but we need data from at least 1000 and preferably 3000 to build on Alan Turing's legacy.

Professor Swinton who came up with the idea for the experiment always marvelled about the wonder of maths in nature. Counting the spirals in sunflower seed heads gives us citizen scientists the opportunity to discover this ourselves.

Indeed, it's a truly wonderful feeling to follow in the footsteps of Turing and discover for yourself whether you get Fibonacci numbers in the sunflower seed heads that you've grown.

Last week we counted the Dig the City sunflowers grown by Manchester City Council and were thrilled to discover that occasionally you don't get Fibonacci numbers!

lucas numbers

This sunflower has 47 anti-clockwise spirals. Those are not fibonacci numbers - they are actually part of a related number sequence called Lucas numbers. The sequence is 2, 1, 4, 7, 11, 18, 29, 47, 76 - you still add the last two numbers to get the next number in the sequence but the starting numbers are different.

We also found a sunflower with 42 clockwise and 64 anti-clockwise numbers. These numbers are a sequence of double Fibonacci numbers ie 21x2 = 42 and 34x 2 = 64.

Whatever you get, it's always worth double-checking and re-counting your spiral counts and of course taking a photo that show the spirals clearly.

It's a bit like finding a four leaf clover. Generally if you count 10 sunflowers, you're likely to find one sunflower with non-Fibonacci numbers. So, excitingly, a few of you will have sunflowers that don't have Fibonacci numbers and we are really interested in how often that happens and of course what numbers you get instead.

Don't delay, put the kettle on, download the counting guide, flyers and event poster and invite your friends round to get counting!

Blooming Marvellous! Register your sunflowers now.

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sunflower harvest at MOSI

Harvest (& Count) Festival

Thursday 4 October 2012 Tagged inCounting, Sunflower Diaries

A couple of weeks ago we had a bit of a counting fest harvesting 20 sunflowers from the batch grown as part of Dig the City.

Mel from City Council with his sunflower heads

We got a call from the City Council that their sunflowers were ready for harvesting and I went down to measure the heights and collect the heads to count later.

Mel Kirby (see pic above) is the customer & community engagement manager at Manchester City Council who grew these Russian Giants from seed, initially at home in a planter and later transferred to a greenhouse in Warrington. Here's his sunflower diary giving an insight into how he felt about getting involved and cutting off the heads...

What's been interesting is that there are different ways you can measure your sunflowers and indeed count the spirals.

sunflowers laid out

With the city council sunflowers they were all in large pots which meant that I could lie the sunflowers down and measure their height in cms on the ground.

We then cut off the heads about half a metre from the top of the head so that I could also measure and record the spiral direction of the leaves. This leaf data is a bonus but really good if we can get it because it tells us something about the direction the spirals are running throughout the plant.

I labelled each seed head with a number so I could identify it later and wrote the height and left spiral direction on a label stuck to the plant too so I wouldn't mix them up.

Multiple counting sheet

With the MOSI sunflowers, they are in planters in soil, so I measured the heights with a tape measure whilst they were still in the planters, labelled them, added the spiral direction date (ie right or left) and then cut them about half a metre from the head.

I went home with a swag of about 20 seed heads from Mel and 20 from MOSI, half of which I counted over the weekend. Seeing as I had lots of seed heads to count I created a table with columns for all the data I was collecting.

  • Column 1: sunflower name #no.
  • Column 2: height (cms)
  • Column 3: seed head diameter (cm)
  • Column 4: no. of bracts
  • Column 5: clockwise spiral count
  • Column 6: anti-clockwise spiral count
  • Column 7: leaf direction (left or right)

After I'd counted (go here to download counting sheet showing how to count) each item of data I recorded it in my table and took a picture of each seed head on my iPad or iPhone (easier to capture the big sunflowers on an iPad and smaller ones on iPhone). I then emailed these files to myself with the name of the sunflower in the subject line so I could download it and save it to a folder using that name to upload later when it came to adding the data.

Next I registered my sunflowers by putting in my email address which sent me a personalised link to add all my sunflower data individually to a dashboard.

I found it easier separating the harvest, counting, data collection and data upload into separate stages.

Often I'd count a few sunflowers in my spare time til the table was full then I'd add the data all in one go, one sunflower at a time.

It's really great to watch the countometer on the front page of the website shoot up by 20 sunflowers!

One thing to watch out for is that your seed heads don't go mouldy - count them as soon after you have cut them down as is possible.

Only 2850 to go! Come on citizen scientists!

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Mel from City Council with his sunflower heads

The first count from france!

Wednesday 26 September 2012 Tagged inCounting, Weird & Wonderful

Well, if a field of sunflowers in Worcester wasn't enough, our first sunflower counts came in from France! Peter Elliott and his wife, Maddy, live very close to the city of Carcassonne in the Aude, about an hour from the Meditterranean, at Narbonne, and a couple of hours from the Pyrenees, and the Spanish border. The sunflowers in the picture are from last July...

Here's Peter's story...

Sunflowers in a field in france

I read about the Sunflower seed head count in an article that appeared in the Times earlier in the year.

Until the end of last year I was a corporate lawyer in a city of London law firm and although I have no farming background, my wife comes from farming stock and we produce a sunflower seed crop of about 14 tonnes annually. It was not difficult therefore to take a few sample seed heads from the fields and enter them in the count.

We purchased our property in the Massif de Malepere (literally "bad stone") in 2005, and are in a farming area that is devoted either to cereal crops or vines (the local wine cooperative is in the nearest village) . We bought an agricultural holding with a small house already on the land, as this enabled us to extend the house, and create a contemporary Languedoc house in an agricultural zone where there are strict controls on building. So we found ourselves with an additional acreage on which cereal crops had always been grown (we have 45 acres in total). We simply continue growing the crop by employing the same agricultural contractor to do the work as had done this prior to our purchase. We sell the crop either to the local Farming Co-Operative or to an independent cereal trader. Annually we rotate the crop between the two halves of our land. On the one half we have winter wheat (seeded in November and cropped in July) and on the other half sunflowers (seeded in mid April/May and cropped in September/October). It is a sensible rotation, as neither crop requires any irrigation (and it would be totally uneconomic to irrigate the crop) and the sunflowers require no additional fertilizer, as they "live" off the feed of the previous year's winter wheat.

Most of my seed heads are large, but I did include 2 smaller seed heads in the sample. I uploaded my sample of 6 sunflower seed heads successfully, including photos, in about 30 mins. I found the questionnaire quite straightforward, and the online experience was good. Only 1 of the 6 seed heads failed to produce a Fibonacci number on one of the spiral counts. Otherwise the results were all consistent.

Thanks to Peter for kickstarting the count with six sunflower seed heads, testing out our counting sheet (and spotting an error that's now updated!) and for putting a question to Professor Swinton about the relationship of the length of the spirals to one another...

Peter is interested in the relationship between the clockwise and anti-clockwise spirals both in terms of the fibonacci numbers and their length. He noticed, for example, that the clockwise count is  usually one Fibonacci number higher than the anti-clockwise count. This is something we are interested in testing out... which has the higher fibonacci number the clockwise or the anti-clockwise spirals?

If you have any more questions about the experiment for Professor Swinton, let us know and we'll get him to answer them in a blog post.

If you want to write a blog post about your counting experience - do get in touch!

Measure and Count

Saturday 8 September 2012 Tagged inCounting

To prepare for counting here's a few of the things that you will need:-

What you'll need

  • measuring tape
  • pen
  • pair of tweezers
  • scissors
  • a camera or camera phone
  • a ladder and an adult to help if your sunflower is really tall

We have made a special counting guide and videos to help you count the spirals in sunflowers. Why not watch the video to familiarise yourself with seeing the spirals and learning how to count them.

Have a look again at your sunflowers to check when they are ready to count. Here's a video to show you when they are ready.

If you're sunflowers are ready to count - why not host a counting event - you can use our flyer and event poster, to spread the word and invite your friends. Why not put a date in the diary now?

Finally in the meantime, why not swot up on why we are doing the experiment, what we hope to find out and why we need lots of sunflowers.

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Janet's picture of Hammerhead

Dig The City

Saturday 28 July 2012 Tagged inCounting, events

Sunflower corner stand

Come and visit us this Saturday and Sunday at inaugural Dig the City where we have an especially grown sunflower corner and stand where we are showing people how to count spirals in everything from pineapples and pine cones. We've had a fantastic week here at the heart of the festival and were even mention in this article. We were visited by Royal Horticultural Society judges who were doing the rounds. There is much to see here, in addition to counting spirals, including a 'living street' and Cathedral full of flowers, and a replica of the Jubilee gardens when the Queen visited. I even hear this weekend there will be some urban pigs on site!

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Chris's picture of home-largest Chris's picture of home-largest