On Saturday Alan Turing would have celebrated his 100th birthday. In his short life he revolutionised the scientific world and so 2012 has been declared Turing Year to celebrate his life and scientific achievements. You can join the celebrations by visiting the special exhibition at the Science Museum or attending the Turing Educational Day at Bletchley Park. Turing is also being honoured in this year's Manchester Pride Parade and the LGBT History Month. And here at Plus, apart from getting to work on building our own Turing machine out of LEGO, we're also celebrating with these favourites:

Alan Turing: ahead of his time

Alan Turing is the father of computer science and contributed significantly to the WW2 effort, but his life came to a tragic end. This article explores his story.

What computers can't do

Another look at Turing's life and work. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.

How the leopard got its spots

How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? The answer comes from an ingenious mathematical model developed by Alan Turing.

Omega and why maths has no TOEs

Is there a Theory of Everything for mathematics? Gregory Chaitin thinks there isn't and Turing's famous halting problem plays an important part in his work.

Exploring the Enigma

Turing is most famous for his work as a WWII code breaker. This article looks at the efforts of all the code breakers at Bletchley Park, which historians believe shortened the war by two years.

CAPTCHA if they can

A version of Turing's famous test – the "Completely automated public Turing test to tell computers and humans apart", or CAPTCHA for short – helps in the fight against the everyday evil of spam email.

Building a bio computer

Turing's scientific legacy is going stronger than ever. An example is an announcement from February this year that scientists have devised a biological computer, based on an idea first described by Turing in the 1930s.

Did a philosopher kill WALL-E?

AI has become big business in Hollywood, but will we ever see the computers reliably pass the Turing test? Or is it philosophically impossible?

Our planet is shaped by the oceans, the dynamic geology and the changing climate. It teems with life and we, in particular, have a massive impact as we build homes, grow food, travel and feed our ever-hungry need for energy. Mathematics is vital in understanding all of these, which is why 2013 has been declared as the year for the Mathematics of Planet Earth.

As well as encouraging research into fundamental questions about the Earth and how to meet the challenges it faces, there will also be many opportunities during 2013 for everyone to get involved including public lectures and workshops, competitions and exhibitions. The first such competition is now underway: the MPE 2013 competition to design an exhibit about the mathematics of Planet Earth.

Everyone is invited to design an interactive or physical exhibit, images or videos that explain how mathematics helps to understand our world and solve its problems. MPE 2013 has come up with a list of possible topics to get you started and there are several examples of what an exhibit might look like, from fractal coasts to crystal flights and subway scheduling.

The competition is open for submissions until 20 December 2012. The winning entries, as well as winning cash prizes, will be exhibited in institutions around the world, including the UNESCO headquarters in Paris in the inaugural exhibition in March 2013. All exhibitions will be open source and hosted by IMAGINARY, where anyone can download and reproduce the exhibits in their own museums or galleries.

Have you got an idea of how to explain the maths of planet Earth? Perhaps after reading about climate change and the Arctic or why we should all be nicer to one another? Then why not develop your ideas into an exhibit and share your mathematical ideas with all of us on planet Earth!

For more information visit the competition website or http://mpe2013.org/.

If you've never heard of cubic Hamiltonian graphs before then take a look at Christopher Manning's wonderful cubic Hamiltonian graph builder. No, really, do! We too had never heard of them and now we think they are the bee's knees!

But what is a cubic Hamiltonian graph, you ask? A graph, of course, is just a bunch of points (vertices) connected by lines (edges). A cubic graph is a graph where every vertex has 3 edges – that is, each vertex is connected to exactly three others in the graph. And a Hamiltonian graph is a graph which has a closed loop of edges (a cycle) that visits each vertex in the graph once and only once, (this is called a Hamiltonian cycle). So a cubic Hamiltonian graph is a graph where each vertex is joined to exactly three others and the graph has a cycle visiting each vertex exactly once.

What has made us so excited about cubic Hamiltonian graphs is watching Manning's cubic Hamiltonian graph builder in action. The builder starts from the Hamiltonian cycle in the graph. This loop of edges accounts for two out of the three edges for every vertex in the graph. The builder then starts adding in the third edge for each vertex, knitting the graph together before your eyes. The creation of a torus is particularly beautiful to watch.

Manning uses something called the LCF notation to build the graphs. This ingenious notation succinctly describes the structure of cubic Hamiltonian graphs by describing how you add the extra edge to each vertex by counting backwards or forwards around the Hamiltonian cycle. For example our torus has the LCF notation [10]¹⁵⁰. This means that every vertex is joined to another 10 edges along the cycle, and this process is repeated 150 times, once for each vertex, to complete the graph. (The 1st vertex is joined to the 11th, the 2nd to the 12th, the 3rd to the 13th, and so on...)

A graph represented by the LCF notation [10,7,4,-4,-7,10,-4,7,-7,4]² starts with a cycle of 20 vertices – inside the square brackets is a list of instructions for 10 edges, and these are repeated twice, giving the total number of extra edges, and therefore vertices, as 20. In this graph the 1st vertex is joined to the 11th (a distance of 10 edges), the 2nd to the 9th (a distance of 7), the 3rd to the 7th (a distance of 4), the 4th to the 20th (a distance of -4, or counting backwards 4 edges), the 5th to the 18th (distance of -7), and so on. This graph is knitted into a dodecahedron.

Watching Manning's program knit together these graphs is beautiful to watch. But this mathematics has many important uses as well. Not only are Hamiltonian cycles important mathematically, they also have many useful applications. You can read more about graphs on Plus, and about the role Hamiltonian cycles play in bell ringing and DNA analysis. And you can read more about Christopher Manning's work on his blog.

Today sees the launch of The Aperiodical, a new maths magazine/blog aimed at people interested in mathematics who want to read stuff. Aperiodical will post news stories related to maths, opinion pieces, maths videos, feature articles, as well as blog posts. It will also publish accounts of monthly MathsJams and host the Carnival of Mathematics, a monthly blogging carnival.

"We started the site as a shared blogging outlet, and it grew out of our desire to have a place on the web where we could keep up to date with what's going on elsewhere, and to share the mathematical things we do," says Katie Steckles, one of the editors. "We're not funded to write here, and all of the work we do on the site is in our (increasingly rare) spare time."

"We're very keen to publish reports, exposition, videos, or anything mathematical and interesting that you want to share. If you've got something you want to share, or just have an idea for something, please send it in."

Today is also the birthday of the famous mathematician Felix Klein, so Aperiodical is running a new feature article, Klein: Outside the Bottle, as well as a video about the Klein Bottle by stand-up mathematician Matt Parker and editor Katie Steckles. Aperiodical is also hosting an online Google+ Hangout today (25/4) from 6pm-6.30pm, for anyone who wants to speak to us and find out more.

The editors of The Aperiodical are:

• Peter Rowlett — Mathematician Errant, podcaster, and usually the most bearded member of the team;
• Katie Steckles — Maths Communicator, hair dye fan, and currently the most qualified member of the team;
• Christian Perfect — Group theorist, computery type, koala fan, and the tallest member of the team.

Aperidoical has RSS feeds for all the different sections, and is also on Twitter, Facebook and Google+.