Drawing Truchet Tiles

In continuing my interest in geometric art, I've gotten interested in tiles and tiling patterns.  One of the simplest patterns is called the Truchet tile.  It consists of 4 types of tiles, each with one corner filled in with a right triangle.  Below is a picture of the 4 tiles that make up the Truchet set.

I wrote a small python function that draws Truchet tiles using the matplotlib plotting library.  I've put it in my GitHub repository.  If you run the code it produces a bunch of Truchet tile patterns (below). Also you can clone the python functions and play around with them and make up your own tiles.

Here is the first pattern.  Just a 20x20 grid of random Truchet tiles.  I've added in blue gridlines so you can see the individual tiles.

Next is an arrangement the follows a particular pattern.  This is where it gets interesting.  Imagining patterns and drawing them.  If you number the four tiles above 1-4, and start at the lower left and work across by row to the upper right, this pattern is a row of 1s, then a row of 2s, then a row of 4s, and finally a row of 3s, and repeat.

A variation on the traditional Truchet tile is the two tile set with semi-circles in the corners below.

Just sitting there those two tiles look kind of lame, but a grid of these is surprisingly cool.  Below is a random 20x20 grid, and again I've marked the gridlines so you can see what's going on.

That's pretty fascinating.  It's like a maze.

One can also apply patterns to these modified Truchet tiles.  One examples are below.  I'll leave it to you to work out the pattern.

   Finally, I invented my own new Truchet tile.  It's just a simple modification of the two semi-circle pattern, where a line is drawn that connects the semi-circles.  Below is a 20x20 random grid of these 2 modified tiles.  I think they look cool.  You can imagine all kinds of other modifications that might look neat.  My guess is that organic patterns, like things that look like leaves or flowers in the corners of the tiles might look really nice.  One day I may get around to mocking that up and posting here.