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
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.
LatticeLabyrinths 