Quaint Mazes in the Wanton Green

The 23rd.  of April is believed to have been the day of  William Shakespeare’s birth in 1564. The neglected mazes regretted by Titania in A Midsummer Night’s Dream

The nine-men’s-morris is filled up with mud
And the quaint mazes in the wanton green
For lack of tread are undistinguishable

will have been turf labyrinths, tightly wound paths that may have been trodden as a penance or an offering or to accompany prayer – but surely for youthful fun and frolics too, as I  discovered when a child taken to  Julian’s Bower on the plateau edge at Alkborough, Lincolnshire. So it is appropriate to plot a Lattice Labyrinth, sharing the convoluted appearance but simple topology of the mediaeval mazes, for the Birthday of the Bard. Trefoil lattice Labyrinth (23,4) has come out rather well. I show first of all just one trigonally symmetrical supertiles, of a playful spirit and comprised of 637 equilateral triangles, then a portion of the tessellation, showing how six supertiles interlock perfectly.


Trefoil(23,4)ShakespeareMaybe it’s time I let you into part of the secret. Here is the construction that enabled me to find William Shakespeare’s Wanton Trefoil Labyrinth.

Trefoil(23,4)ComplementaryThat in itself is pretty, and by no means straightforward to arrive at, but much easier to comprehend and discover than the final tessellation. The details of how and why to draw graphs like the above can be found in my workbook Lattice Labyrinth Tessellations bold art from modest mathematics, published by Tarquin at £7.95 and available from Scarthin Books, the Publisher, through your favourite bricks-and-mortar bookseller or most online sources including the unmentionable.


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.
This entry was posted in Birthday labyrinths, Trefoil Labyrinths and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s