  Looking at incidence matrices of $t$-$(v,k,\lambda)$ designs as $v \times b$
matrices with $2$ possible entries, each of which indicates incidences of a
$t$-design, we introduce the notion of a $c$-mosaic of designs, having the same
number of points and blocks, as a matrix with $c$ different entries, such that
each entry defines incidences of a design. In fact, a $v \times b$ matrix is
decomposed in $c$ incidence matrices of designs, each denoted by a different
colour, hence this decomposition might be seen as a tiling of a matrix with
incidence matrices of designs as well. These mosaics have applications in
experiment design when considering a simultaneous run of several different
experiments. We have constructed infinite series of examples of mosaics and
state some probably non-trivial open problems. Furthermore we extend our
definition to the case of $q$-analogues of designs in a meaningful way.
