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.
That 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.