Under the nearest tartans table, many pages in the Dictionary carry a small scatter — the neighbourhood map. Every grey dot is a cloth in the corpus, the red dot is the cloth whose page you are on, and the blue dots are its nearest neighbours. This post explains what the map is, and — just as important — what it is not.
Where the dots come from
ΔTartan describes each cloth by a bundle of measured features — its colour ladder, its proportions, how its sequence jogs against others — and measures the distance between two cloths in that feature space. That space has many dimensions: two tartans can differ in ground colour, in the shade of one overstripe, in the count of a band, in the order the colours cycle, in scale, each an axis of its own.
A page is flat, so the map has to squash all of that into two. It uses the standard trick — principal component analysis (PCA): find the direction along which the corpus varies most, then the second-most at right angles to it, and place every cloth by those two coordinates alone.
Half the story, by design
The caption under each map states how much of the corpus's variance the two plotted components carry — typically around half. That is not a defect to be tuned away; it is what flattening a genuinely many-dimensional space costs. The other half of the variation lives in the dimensions the picture had to drop.
Two consequences are worth keeping in mind when you read the map:
- Close on the map does not always mean close in cloth. Two dots can land near each other while sitting far apart along a dropped dimension — the projection folds distant points together, the way two towns on opposite sides of a hill can look adjacent from directly above.
- The blue dots may not look like the red dot's nearest dots. The neighbours are chosen by the full ΔTartan distance, in all dimensions — not by map distance. A blue dot that seems oddly far away on the map is usually a cloth whose similarity lives in the dimensions the picture cannot show.
The division of labour is deliberate: the table above the map ranks by the true distance and is the thing to trust; the map gives the corpus a geography — which region of tartan space a cloth lives in, whether its neighbourhood is dense (a well-trodden design) or sparse (an outlier) — at the cost of precision.
Reading it well
Treat the map as a locator, not a ruler. If the red dot sits in a tight grey cloud, the design is one of a crowd; if it sits alone at an edge, the corpus holds little like it. Follow the blue dots by clicking them, but judge their closeness by the ΔTartan numbers in the table, not by the millimetres between dots. The map is one 2-D shadow of the space the Dictionary actually searches — useful for orientation, silent about every dimension it had to leave out.