  For each $\Pi^0_1$ $S\subseteq \mathbb{N}$, let the $S$-square shift be the
two-dimensional subshift on the alphabet $\{0,1\}$ whose elements consist of
squares of 1s of various sizes on a background of 0s, where the side length of
each square is in $S$. Similarly, let the distinct-square shift consist of seas
of squares such that no two finite squares have the same size. Extending the
self-similar Turing machine tiling construction of Durand, Romashchenko and
Shen, we show that if $X$ is an $S$-square shift or any effectively closed
subshift of the distinct square shift, then $X$ is sofic.
