A Lattice Labyrinth for Gwangbokjeol – Independence Day of Korea 광복절

By a fortunate coincidence, I’m presenting my lattice Labyrinths paper at Bridges Seoul 2014  on August 15th., which is Gwangbokjeol  , the day in which the Republic of Korea (South Korea) celebrates independence from Japan. This generates the separation parameter pair (15,8), specifying a labyrinth on the square lattice in the Chinese family.

A standard version of the Chinese Labyrinth (15,8), (a,b) being co-prime, can be found by the standard algorithm but is a little dull perhaps. I have found a much more labyrinthine version (after the usual struggle); perhaps it suggests some symbols of the Korean alphabet (Do any of the latter tessellate? – must investigate).

Here is a three by three portion of the infinite tiling in an attempt at Korean flag colours.

KoreanFinalyChinese(15,8)darker Each supertile contains 225  + 64 = 289 squares, which rather pleasingly equals 2×144 +1, 144 being dear to me as the climax of the times table as learned in primary or even infants’ school. Multiplying by 13 is such a slow business for me, they should have driven us on to 20×20.No doubt they do that in Korean schools (North and South).

(15,8) also specifies a Trefoil labyrinth on the triangular lattice, which I may try to construct later -success being by no means a foregone conclusion. Each supertile would contain 225 + 15×8 + 64 = 409 triangles; quite a whopper.

Postscript:  I did manage to design and demonstrate Trefoil lattice Labyrinth (15,8) in time for my Bridges talk in Creation Hall at the GNSM on August 15th. Here it is:

A Tessellation in Honour of Korean Independence Day, August 15th.

A Tessellation in Honour of Korean Independence Day, August 15th.

P.S. Links to the how-to-do-it workbook: From the publisher, or via you-know-who , better,  from a good independent bookshop or just Google.


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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