  An {\it omnimosaic} $O(n,k,a)$ is defined to be an $n\times n$ matrix, with
entries from the set ${\cal A}=\{1,2,\...,a\}$, that contains, as a submatrix,
each of the $a^{k^2}$ $k\times k$ matrices over ${\cal A}$. We provide
constructions of omnimosaics and show that for fixed $a$ the smallest possible
size $\omega(k,a)$ of an $O(n,k,a)$ omnimosaic satisfies
\[\frac{ka^{k/2}}{e}\le \omega(k,a)\le \frac{ka^{k/2}}{e}(1+o(1))\] for a
well-specified function $o(1)$ that tends to zero as $k\to\infty$.
