  We show that when cells communicate by contact-mediated interactions,
heterogeneity in cell shapes and sizes leads to qualitatively distinct
collective behavior in the tissue. For inter-cellular coupling that implements
lateral inhibition, such disorder-driven transitions can substantially alter
the asymptotic pattern of differentiated cells by modulating their fate choice
through changes in the neighborhood geometry. In addition, when contact-induced
signals influence inherent cellular oscillations, disorder leads to the
emergence of functionally relevant partially-ordered dynamical states.
