Fig. 3.

Representational capacity. The flexible representation on which the megamap is built alleviates the inherent size limitations of the single-peaked code on which the standard attractor chart is built and even improves on the large representational capacity of the upstream grid cell network. A: the single-peaked place code enforces a rigid spatial relation among place fields within a single environment, constraining a population of N place cells to support at most N unique activity patterns (blue). The representational capacity of the grid cell population is similarly linear in the number of cells, although it is exponential in the number of modules, M (green; Eq. 18). The representational capacity of the flexible representation approaches an exponential growth in the number of cells (red; Eq. 17), where p denotes the proportion of co-active cells in an activity bump. B: replication of A for N ≤ 1,000.