Information tradeoffs in receptor arrays

Organisms sense the world through arrays of receptor cells, such as photoreceptors on the retina. In cases such as the compound eyes of insects, these arrays are nearly crystalline, while in others, such as the human retina, sampling is much less regular. Ordered arrays gather more information, but this comes at the cost of specifying the positions of all the cells. We explore this tradeoff between bits of sensory information and bits of positional information. This problem maps to an equilibrium statistical mechanics problem for the positions of the receptor cells, with interactions that depend on the correlation structure of the input signal. We find limits where the cost of disorder is small and where it is larger, and we try to relate these results to the diversity of structures that we find across different organisms.