In a previous post we experienced what a Truchet tiling looks like. This time, the animations above show what it might be like to look down on a Truchet tiling, but while moving along it in a straight line.

In each of the animations the tiling is really only shifting in one direction (the direction corresponding to “down” when viewed on your screen) as made apparent in the following simple Truchet tiling:

For an increased dramatic effect, the rate of this downward movement in the animations is made to correspond with the frame rate of the GIF in such a way where precisely one row of the tiling leaves our view every frame. This makes the smoothly translating tiling just shown look like this instead:

This explains why the individual tiles seem to be changing orientations in place, and why there appears to be a static grid of horizontal and vertical lines outlining the tiles. Together with the geometry of the configurations in the tilings, this also explains why there seems to be motion in several different directions for any given tiling. Perhaps one might be able to realistically create a similar effect if they manage to run along such a tiling at a rate which corresponds to the "frame rate" of human vision.

Mathematica code:

T[r_, x_, y_] :=
Translate[
Rotate[
{EdgeForm[Thickness[0]], Polygon[{{1, 0}, {0, 0}, {0, 1}}]},
r, {.5, .5}],
{x, y}]

Manipulate[
Graphics[
Table[
T[Mod[a*x + b*y, m] Pi/2, x + h, y + v],
{x, 1, X, 1}, {y, 1, Y + 60, 1}],
PlotRange -> {{1, X}, {1, Y - .1}}, ImageSize -> 500],
{{X, 23}, 1, 100, 1}, {{Y, 23}, 1, 100, 1},
{{m, 11}, 1, 100, 1},
{{a, 18}, 1, 100, 1},
{{b, 14}, 1, 100, 1},
{h, 0, 14},
{v, 0, 14}]
 
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