Dave Computes Ladder Doodles

Here's a kind of doodle I've been drawing for a while now. It started from the idea of tiling a grid with a single square tile.

Here's a small tiling. The tile can be rotated, and adjacent edges must be the same color.

After a while, I stopped thinking of it as a tiling. For lack of a better name, I'll call these ladder doodles. I begin with horizontal line segments across the top of a page of gridded paper. Some lines are drawn on the top row and some on the second row, chosen at random. Then I copy those lines down the page, on every other row.

Then I repeat with random vertical line segments copied across the page.

The entire drawing is uniquely determined by the choices on the top row and left column. Thus, a drawing on an n × n grid contains exactly 2n bits of information. I like drawing diagonal lines to show the paths more clearly.

The paths can get quite intricate in larger drawings.

Here I've filled in the drawing with random colors.

And here are a couple more.