  A long standing question asks whether $\mathbb{Z}$ is uniformly 2-repetitive
[Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an
infinite sequence over a finite subset of $\mathbb{Z}$ avoiding two consecutive
blocks of same size and same sum or not. Cassaigne \emph{et al.} [2014] showed
that $\mathbb{Z}$ is not uniformly 3-repetitive. We show that $\mathbb{Z}^2$ is
not uniformly 2-repetitive. Moreover, this problem is related to a question
from M\"akel\"a in combinatorics on words and we answer to a weak version of
it.
