Town spacing

Why do towns on an open plain space themselves out at surprisingly regular distances?

Drive across the flat middle of a large country and the towns arrive with an odd regularity: small ones every so often, a bigger one every several of those, a city every several of those. Nobody surveyed the plain and laid them out; each was founded by people acting for their own reasons, centuries apart, mostly in ignorance of one another. So where does the spacing come from — and is it as regular as it looks, or is that the eye inventing a pattern?

Start with something smaller than a town: a single shop. What does it need to exist at a given spot? Enough customers within reach to cover its costs — call that minimum catchment the threshold. And customers only come from so far, since past some distance the journey costs more than the errand is worth — call that the range.

Two numbers, and immediately a rule: a service exists only where its range encloses enough people to meet its threshold. If nobody travels more than four kilometres for bread and a baker needs a thousand customers, a baker appears wherever a thousand people live within four kilometres, and nowhere else.

Now notice that the two numbers differ by service. A bakery has a small threshold and a small range. A cardiac unit has an enormous threshold, needing hundreds of thousands of people, and a correspondingly large range, because people will travel far for heart surgery and not for a loaf. Everything else lies between.

What follows for a whole plain? Bakeries can be dense, their threshold being met often; hospitals must be sparse. And a place supporting a hospital supports everything with a smaller threshold too, since the people are already there. So services do not scatter independently — they stack, and settlements sort into levels: many small places carrying only low-order services, fewer medium ones carrying those plus mid-order services, a handful of large places carrying the full set.

Why should spacing within a level be regular? Ask what happens if it is not. Two bakers three hundred metres apart split a catchment neither can live on, and one closes. A stretch of plain with no baker in range is an unserved market, and someone opens there. Both deviations are corrected by the same pressure — too close and you starve, too far and you leave money uncollected — and its equilibrium is an even scatter, at a separation set by the range of that level's goods.

One geometric step remains, and it gives the theory its picture. If every place serves customers within a radius, market areas are circles, and circles either overlap or leave gaps — neither an equilibrium, since overlaps are contested and gaps unserved. The shape that tiles a plane completely while staying as close to circular as possible is the hexagon. So the idealised map is a lattice of hexagonal market areas, nested at each level: Walter Christaller's central place theory, worked out from the settlements of southern Germany in the 1930s, with variants depending on whether the arrangement suits markets, transport routes, or administration.

The theory is an idealisation, and its assumptions are exactly where reality departs from it. It supposes a flat featureless plain with population and spending power spread evenly; transport cost proportional to distance and equal in every direction; consumers going to the nearest centre offering what they want; and no lasting excess profit, so entry continues until the pattern settles.

Take away any of those and the lattice deforms. A coastline halves market areas, so ports sit at the centre of semicircles. Mountains and rivers make travel cost depend on direction, stretching cells along valleys. A railway or motorway lowers cost along a line and pulls centres onto it. Mines, fords and defensible hills put towns where the resource was. And history is sticky: a place that grew for a reason since evaporated usually stays.

So the honest claim is narrow. Central place theory does not predict where towns are; it describes one force among several, most visible where the competing forces are weakest — which is why it was tested most convincingly on agricultural plains such as southern Germany, the American Midwest and the Dutch polders, and fits mountainous or heavily industrial regions poorly.

Two refinements. The regularity people notice is partly statistical rather than geometric: city sizes across a region tend to follow a steep rank-size pattern whether or not their positions form a lattice, which is a different regularity from spacing. And the structure is dynamic. Cars lengthened ranges enormously, so the smallest centres lost their threshold and their shops closed. Online retail has collapsed the range of many mid-order goods to nothing, which is why medium towns have hollowed out while the largest centres, holding services that still require presence, have not.

• Why city sizes within a country tend to follow a rank-size or Zipf-like distribution, a separate regularity from spacing.
• How agglomeration economies pull activity into a few large centres, against the even spread this argument predicts.

Every term the collection defines is gathered in the glossary.