How to Draw a Low Place

Here is a strange fact about maps: you can’t draw a hollow by drawing the hollow. There is nothing there to draw — just air where the ground isn’t. What you draw instead is the ground around it, line by line, at the heights where it begins.

I find this oddly comforting, because a low mood works the same way. It’s very hard to describe head-on. Ask someone what it is and they’ll struggle. But ask about its edges — what they stopped doing, which small things got heavy, which hour of the day is worst — and a shape appears.

The method

The computer draws contour lines using a method with a lovely, plain name: marching squares. It goes like this:

1. Sample the ground on a grid of points. Each point gets a height.
2. Pick one height — say, 400 metres.
3. Mark every point: is it above 400, or below?
4. March across the squares. Each little square has four corner points. If all four agree — all above, or all below — no line passes through it. If they disagree, the line must cross the square somewhere between them. There are only sixteen ways that can happen, and the computer just looks up the right one.
5. Join the pieces. Where the line enters and leaves each square is estimated from how far each corner is above or below 400. Stitch all the little pieces together and you have a contour.

Try it below. Filled dots are above the chosen height, hollow dots are below, and the glowing line runs exactly between them. Press and drag on the map to dig — you’ll watch the line bend around the hollow you made.

Height 0 m Cells crossed 0 Lowest 0 m

Height Show grid points Shade terrain New ground

Slide to change the height. Press and drag on the map to dig a low place.

Three things the demo shows

A low place is defined by what’s around it. Dig a hole and watch: the amber line doesn’t go into the hole. It wraps the rim. The hollow becomes visible precisely because of the ground that holds it.

Lines never just stop. Slide the height up and down. Every line either closes into a loop or runs off the edge of the sheet. A contour cannot end in the middle of nowhere — mathematically, it isn’t allowed to. There is always more ground on the other side.

Lower the line far enough and the hollow shrinks to a point. Slide the height down towards the bottom of the hole you dug. The ring tightens, and tightens, and then it’s gone — you’re below the lowest point, and there’s nothing left to enclose. Every hollow on every map has a bottom. That’s the definition of one.

Why I like knowing this

None of this makes a low place less low. But there’s something steadying in knowing that the shape of it can be traced — that it has a rim, and a bottom, and lines that lead away from it to other ground. On a fog day, it’s something to hold on to: this has edges, even if I can’t see them from in here.