  The structure and dynamics of tissue cultures depend strongly on the physical
and chemical properties of the underlying substrate. Inspired by previous
advances in the context of inorganic materials, the use of patterned culture
surfaces has been proposed as an effective way to induce space-dependent
properties in cell tissues. However, cells move and diffuse and the
transduction of external stimuli to biological signals is not instantaneous.
Here, we show that the fidelity of patterns depends on the relation between the
diffusion ($\tau_D$) and adaptation ($\tau$) times. Numerical results for the
self-propelled Voronoi model reveal that the fidelity decreases with
$\tau/\tau_D$, a result that is reproduced by a continuum reaction-diffusion
model. We derive a minimum length scale for the patterns that depends on
$\tau/\tau_D$ and can be much larger than the cell size.
