In statistics, the notion of \emph{exchangeability} provides a grip
on large alphabet scenarios. An important line of work has developed
this direction, starting with Kingman's study of population genetics,
and includes paintbox processes of Kingman, Dirichlet processes and
its generalizations.

From an information theoretic point of view, to handle the large
alphabet setup, we look for a statistic that is: (i) universally
compressible regardless of the alphabet size, and (ii) captures all
the information present in the data.  In a series of
papers~\cite{OSZ03,OSVZ04:lim}, one such candidate statistic
emerges---the \emph{pattern} of the sequence that abstracts out the
actual symbols appearing in the sequence.

In this paper, we examine patterns in the context of exchangeability,
making connections between these two lines of work. We connect
patterns to Kingman's paintbox processes, and consider alternate
representations of patterns in terms of graph limits.