  Tropical friezes are the tropical analogues of Coxeter-Conway frieze
patterns. In this note, we study them using triangulated categories. A tropical
frieze on a 2-Calabi-Yau triangulated category $\mathcal{C}$ is a function
satisfying a certain addition formula. We show that when $\mathcal{C}$ is the
cluster category of a Dynkin quiver, the tropical friezes on ${\mathcal{C}}$
are in bijection with the $n$-tuples in ${\mathbb{Z}}^n$, any tropical frieze
$f$ on $\mathcal{C}$ is of a special form, and there exists a cluster-tilting
object such that $f$ simultaneously takes non-negative values or non-positive
values on all its indecomposable direct summands. Using similar techniques, we
give a proof of a conjecture of Ringel for cluster-additive functions on stable
translation quivers.
