Burns Night 2015. Single Malts, Tessellated Tartans and a Hexed Honeycomb for the Bard

Aberlour, Ben Nevis, Glen Moray, Jura, The Macallan, Monkey Shoulder – where’s the Laphroaig? One in fifteen guests brought a bottle of single malt whisky  to my latest decadal birthday party. And tomorrow the 25th of January is Burns Night, traditionally celebrated with a Burns Supper, Whisky and Poetry.

As Robert Burns was a Lowlander, writing in the Scots dialect of English, us English Britons are as entitled to celebrate his birthday with cock-a leekie soup, haggis, tatties, neeps and Scotch as are the Scots, most of whom are of course English dwelling on the wrong (or right) side of the Border. So, the number pair is (25,1), which can generate a Serpentine Lattice Labyrinth with each supertile comprising (25^2 + 1^2)/2 = 313 squares or (among other possibilities) a Honeycomb Lattice Labyrinth with 2(25^2 + 25×1 + 1^2) = 1301 equilateral triangles. But how to colour the designs? The Scottish flag is azure and white only, which amounts to only one colour unless seen against a darker background. A Burns Tartan doesn’t really exist which is why the Scottish Register of Tartans lists no less than twelve contending for the honour, but all of designs apparently dating from the 20th. Century or later. the colours I employ can be found in the Burns Family Tartan and also in the Burns Legacy Tartan and Burns Heritage Tartan. Do visit the beautiful  Memorial Gardens, Burns Monument Auld Kirk and Brig o Doon at Alloway. Robert Burns retells the legend of Tam o Shanter pursued over the auld brig by the witches he surprised in the Auld Kirkyard of Alloway and you can see an ingenious weathercock depicting the pursuit.  Here it is, with one supertile of Honeycomb (25,1) superimposed. Appropriately this displays HEXagonal rotational symmetry.

Tam o ShanterSingleSupertileand below, Ive added the six surrounding supertiles and depicted them in the spurious tartan colours, 1301 equilateral triangles per supertile.

Honeycomb (25,1)BurnsTartanFinally, here is a whimsical version of Serpentine (25,1).


Just two supertiles are shown in each orientation, each comprising 626/2 = 313 squares.

Finally (maybe), here is another Serpentine (25,1) design, arguably more attractive than the above,extended to the smallest square area which will encompass all of four supertiles, two in each orientation. This could be a design for a Burns Night placemat, a carpet, a floor-tiling or even  the paving of a public open space dedicated to the Bard. If you use the design I would be grateful for, or even entitled to, a royalty or fee ……. I hope.

Serpentine (25,1), inbetweenFinal


Here are some links to the inexpensive how-to-do-it  Lattice Labyrinths workbook which is available from the publisher or you-know-who , or from a good independent bookshop or via Google.


About davescarthin

After terminating academic and local government careers, long an independent bookseller/publisher at Scarthin Books, Cromford, Derbyshire, UK. An antiquarian bookseller in two senses, I now have more time to be an annuated independent post-doc, developing the long dormant topic of lattice labyrinth tessellations - both a mathematical recreation and a source of compelling practical tiling and textile designs. Presenting a paper and experiencing so many others at Bridges Seoul 2014 Mathart conference was a great treat, as were the spirited MathsJam Annual Conferences in November 2016 and 2017. I'm building up to a more academic journal paper and trying hard to find practical outlets in graphic design and landscape architecture. I submitted 8 ft square tiling designs to the Wirksworth Festival Art and Architecture Trail in 2016 and 2017. I love giving illustrated talks, tailored to the audience. Get in touch to commission or to collaborate.
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1 Response to Burns Night 2015. Single Malts, Tessellated Tartans and a Hexed Honeycomb for the Bard

  1. abyssbrain says:

    Hey, those patterns are beautiful.


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