Introducing Weaves and Insets

Weave mazes

A weave maze is a maze in which passages weave over and under one another, like noodles in a bowl of spaghetti. An example is shown below:

We can’t really draw these with our existing to_png method because our existing method does not draw any space between adjacent corridors. Without that space, there is too much ambiguity—we can’t tell if a passage has dead-ended or gone underneath another passage. The following figure shows the same maze as the previous figure but without any gaps between corridors.

Messy! And even worse, it's not very accurate. Our existing to_png implementation only draws the east and south walls for each cell, assuming that neighbors will improve the situation on the other walls. This doesn’t work with these over/under mazes. Something's got to change.

Our first task, then, is to level up our to_png method in order to support gaps between corridors. Fortunately, it’s not hard—it just requires a bit of extra measuring. We need to figure out how far each wall is inset from the original edge of the cell. Once we have this new way to draw mazes, we can look at what it takes to make the passages weave over and under one another.

Let’s look at a single cell on our grid drawn using these insets. From the diagram below, we’ll be able to infer the measurements we need in order to draw our mazes this way.

Here, the cell is linked to its neighbors to the north and east, with corresponding passages in those directions. The insets are highlighted in yellow, and the ...