  In this paper we introduce and study new notions of uniform recurrence in
multidimensional words. A $d$-dimensional word is called \emph{uniformly
recurrent} if for all $(s_1,\ldots,s_d)\in\mathbb{N}^d$ there exists
$n\in\mathbb{N}$ such that each block of size $(n,\ldots,n)$ contains the
prefix of size $(s_1,\ldots,s_d)$. We are interested in a modification of this
property. Namely, we ask that for each rational direction $(q_1,\ldots,q_d)$,
each rectangular prefix occurs along this direction in positions
$\ell(q_1,\ldots,q_d)$ with bounded gaps. Such words are called \emph{uniformly
recurrent along all directions}. We provide several constructions of
multidimensional words satisfying this condition, and more generally, a series
of four increasingly stronger conditions. In particular, we study the uniform
recurrence along directions of multidimentional rotation words and of fixed
points of square morphisms.
