A Birthday Card for the 1 in 1500 of us born on 29th. February

My eccentric friend Evan Rutherford, the Professor and Potter of Green Hill, Wirksworth, newspaper boy and contrarian scourge of the Chattering Classes, informs me that he is at a loss for a present for his brother, who is celebrating his 21st birthday soon, despite being around 80 years old. An increasing number of my friends are around 80 years old, requiring me to recruit relative youngsters in order to maintain a balanced outlook on unbalanced Life.

A good excuse to spend a morning discovering a Diamond Lattice Labyrinth (29,2) tessellation of the plane, and here are just six supertiles of it, based on a simple and elegant construction that I’ll keep under my hat for now,though you could reverse-engineer it. (Supertiles are what I call the assemblies of equilateral triangular tiles that tessellate, or tile, the infinite plane, with neither gaps nor overlaps)

I’ve shown the hexad (6-fold), triad (3-fold) and dyad (2-fold) axes with little hexagons, triangles and diamonds and have changed one of the red supertiles to black so that it can be picked out and its symmetry relished. In order to help make sense of the above, here is an illustration of Diamond Lattice Labyrinth (3,0), the lowest-order but one member of the Diamond family.

The six supertiles corresponding to those of the Diamond (29,2) figure have been given  tile boundaries, and the corresponding red supertile changed to black.

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

AND you may be interested in the powerpoint presentations given as Lightning Talks at the recent MathsJam Gathering 2019 at Yarnfield Park, Staffordshire, UK. You can click on any of the talks, including my own in Session 1b, The Brothers Fibonacci, which I’ve yet to post in full on this site. Nottingham MathsJam welcomes new members; last Tuesday but one in the month, 7 p.m. in the Crafty Crow pub, Friar Lane.



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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