Hyperdisordered cell packing on a growing surface

Abstract

While the physics of disordered packing in non-growing systems is well understood, unexplored phenomena can emerge when packing takes place in growing domains. We study the arrangements of pigment cells (chromatophores) on squid skin as a biological example of a packed system on an expanding surface. We find that relative density fluctuations in cell numbers grow with spatial scale. We term this behavior ``hyperdisordered'', in contrast with hyperuniform behavior in which relative fluctuations tend to zero at large scale. We find that hyperdisordered scaling, akin to that of a critical system, is quantitatively reproduced by a model in which hard disks are randomly inserted in a homogeneously growing surface. In addition, we find that chromatophores increase in size during animal development, but maintain a stationary size distribution. The physical mechanisms described in our work may apply to a broad class of growing dense systems.