A Truchet tiling is a tiling made of the same square tile repeated over and
over in a square grid with different orientations.
See
Wikipedia article. There are very many Truchet pages on the web.
Here is an example made from the tile below left.
The sequence of tiles 0-12 shows a sequence of explorations leading up to
the fractal construction explained later. I discussed these in my talk at
GA2021.
I added tiles from -1 to -6 after my talk,
with a few more controls.
These are just to explore a different joining of edges, similar to the
Smith Truchet tile and tile 6. In tile -5, I add dots moving on the paths.
To have one dot per path, they need to take the same time to move along each
path. However, that means moving at different constant
speeds, so they won't match up nicely at the boundaries. So tile -5 is
not quite right.
In tile -6, instead of considering the center of the dot to move across
each path on a tile in the same time, I use a local coordinate system for
each path with coordinates Y from -1 to 1, and X from 0 to 1, but on the
straight path, from 0 to 2, because this path is much longer than the others.
The local coordinate system is distorted, but means less work in matching up
where tiles meet. There are plenty of other ways to get dots to match up
at the boundaries, but they would involve more work.
Click the "change tile" button to decrease the tile number, and click the
tile on the left to increase the tile number.
This program is written in JavaScript and Webgl, and has only been tested on
Chrome on a MacBook.

Tile number and description: 0, as in
Truchet's original
investigation
change number of tiles in
tiling=
Pattern -3... options:
path width:
path position:
dot position:

Click or on the tiling to change the orientations of the tiles in
the tiling. This alternates between being random or else repeating the first
2x2 block.
Click here to change the tile image in option 2 to your own file:
Click here for more examples of Truchet tilings.
My goal for this talk
is to understand the relationship between the different scaled
Smith/Truchet quarter circle tilings.