General: Uniform Distribution of Objects in a Homogeneous Field: Cities on a Plain

THE uniform distribution of objects in a homogenous field is familiar in all kinds of circumstances—atoms in liquids1–3, fibrils in cells4, hairs on insects5,6 and mammals7, stomata on leaves8, trees in forests9–10 and cities on plains11,12. In many of these circumstances the relative positions of the objects may be described by a radial distribution function. In what follows we shall show that such a function may be used to study the distribution of cities on a plain.