Animal skin patterns take an astounding variety of forms, a result of dynamical processes at the cellular level acting as the organism grows. How cellular dynamics interact with organism growth to form skin patterns remains unclear. Here, we study this interplay by tracking the evolving cellular point pattern of chromatophores, the pigment cells present in squid skin. The arrangement of chromatophores appears locally ordered, but disordered at large spatial scales. In particular, its degree of disorder increases with spatial scales more rapidly than for a purely random system. This atypical behaviour resembles highly irregular critical systems in statistical physics. We combine experiments and theory to reveal how this exotic pattern develops through chromatophore insertion as the organism grows. The mechanism we describe may apply to a broad class of growing tissues.