The Japanese Labyrinth Family

The Japanese Lattice Labyrinths (why the name – I’ll let on later) are one of several families of Lattice Labyrinth Tessellations which display the “full” 442 overall symmetry (see the Rotational Symmetry post) though the supertiles of which they are made are not themselves symmetrical. This may make some members of the Family particularly suitable for Escherisation/Escherization, the process by which an artist can transmute the purely geometrical shapes  into organic images. Actually most of the shapes in the tessellations below seem more Expressionist than Organic. Was Picasso really a Cubist, or only a Squareist?

here are some examples, Japanese Labyrinths (6,0), (6,4) and (8,2) with supertile areas of 9,13 and 17 squares respectively

Japanese(6,0),(6,4,)(8,2)And here are two more, (8,6) and (10,0) with, of course, supertiles of the same areas (thanks, Pythagoras) though very different shapes.


Note that the supertiles of the Japanese Labyrinths come in four different orientations, so that the repeat unit is four times the supertile area, 4 x 25 = 100 in the above cases.

I’ve left out the symmetry axes, but the locations of the two families of tetrads, at least, are easy to spot.



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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