Trefoil from Heaven 1807

Having posted a moderately high-order Chinese Labyrinth, here is a beautiful cousin from the TREFOIL LABYRINTH family

Trefoil Labyrinth (42,1)

This figure includes just six supertiles, each made up of 1807 equilateral triangles. Two supertiles (0ne coloured yellow, one red) make up the repeat unit of the tessellation. This example is a relatively lowly member of an infinite sub-family of the Trefoil Labyrinths, any one of which can be constructed, given enough time and paper or computer capacity, by following simple rules. As you might hypothesize after looking at this example, sub-family members bear a strong resemblance to each other. As we ascend to higher- and higher-order members, adjusting the scale of the figures to keep the area of the supertile constant, the shape will retain the family character but the length of the boundary of the supertile will “tend to infinity” , a loosely fractal-like property.


About davescarthin

After a brief academic and local government career, long an independent bookseller/publisher at Scarthin Books, Cromford, Derbyshire, UK. An antiquarian bookseller in two senses, now also has 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/paving and textile designs. Presenting a paper and experiencing so many others at Bridges Seoul 2014 Mathart conference was a great treat, as was the MathsJam Annual Conference in November 2016. I'm building up to a more academic journal paper and trying hard to find practical outlets in graphic design and landscape architecture. An 8 ft square tiling design was part of the Wirksworth Festival Art and Architecture Trail 2016. I love giving illustrated talks, tailored to the audience. Get in touch to commission or to collaborate.
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