By a fortunate coincidence, I’m presenting my lattice Labyrinths paper at Bridges Seoul 2014 on August 15th., which is Gwangbokjeol, 광복절 , 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.
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:
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.