Mike’s 1994 Serpentine Labyrinth

After another extended struggle, I can reveal a construction of Serpentine Lattice Labyrinth (37,25), which has the desired repeat unit of 1994 squares, made up of two supertiles at right-angles to one another, and each comprising 997 squares. Finding this particular robust solution again involved serial attempts and failures, but the final failure revealed a passage to success. Here is the result, with one supertile in each orientation shown in black. Old Mitchell’s Almanac characterises this as an impressive tessellation. It liberates its bearers to act with flair and panache, but only after persistent and methodical footslogging.

Serpentine (37,25)3rdTryFinal

997: Here in this year the raiding-army travelled around Devonshire into the mouth of the Severn, and there raided, both in Cornwall and in Wales and in Devon; then they went up at Watchet, and wrought great harm there by burning and slaughtering of men, and after that turned back round Penwith Tail to the south side, and then turned into the mouth of Tamar, and then went up until they came to Lydford, and burned and killed everything that they met, and burned down Ordwulf’s monastery at Tavistock, and brought indescribable war-booty with them to the ships’.

(Michael Swanton, ‘The Anglo-Saxon Chronicle’ (JM Dent, 1997) p. 131)

Better to be living in these than those days I hope. DJM

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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