  Nottingham algebras are a class of just-infinite-dimensional, modular,
$\mathbb{N}$-graded Lie algebras, which includes the graded Lie algebra
associated to the Nottingham group with respect to its lower central series.
Homogeneous components of a Nottingham algebra have dimension one or two, and
in the latter case they are called diamonds. The first diamond occurs in degree
$1$, and the second occurs in degree $q$, a power of the characteristic. Many
examples of Nottingham algebras are known, in which each diamond past the first
can be assigned a type, either belonging to the underlying field or equal to
$\infty$.
  A prospective classification of Nottingham algebras requires describing all
possible diamond patterns. In this paper we establish some crucial
contributions towards that goal. One is showing that all diamonds, past the
first, of an arbitrary Nottingham algebra $L$ can be assigned a type, in such a
way that the degrees and types of the diamonds completely describe $L$. At the
same time we prove that the difference in degrees of any two consecutive
diamonds in any Nottingham algebra equals $q-1$. As a side-product of our
investigation, we classify the Nottingham algebras where all diamonds have type
$\infty$.
