Simulation of STATE cell responses in the HD cell model shown in Figure 1b with AHV self-motion inputs. For those simulations in which the model was trained, the model was trained with the agent both translating and rotating within the environment according to a random walk. Each of the four plots in the figure shows the HD tuning of several randomly selected STATE cells under different training conditions, averaged over locations in the environment (see Methodology for testing details). Top left (a): network is untrained. We observe some HD preference induced by the random initial synaptic weights, but note that this tuning is irregular and sometimes split into multiple peaks. Top right (b): after training the network with only ecological distal visual landmarks (beyond the boundary of the navigable maze but not at infinity). Each of the STATE cells has learned to respond selectively to a single, localized interval of the HD space, like real HD cells found in the rat brain. Bottom left (c): after training with both distal and proximal visual landmarks present. The STATE cells have again learned to respond to single, localized regions of the HD space, like real HD cells in the brain. The STATE cells have succeeded in developing HD cell responses anchored to the distal landmarks regardless of the presence of proximal landmarks. Bottom right (d): out of the whole population of 1000 STATE cells, we only find nine cells with weak HD selectivity. These do not cover the whole circle, and display a degree of instability in their responses not otherwise observed when distal visual landmarks are present. This demonstrates the importance of distal landmarks for the emergence of HD responses.