Science Advances

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• Fig. S1. Hierarchical self-similar scales enable error correction.
• Fig. S2. Noninteger scale ratios imply that the decoding algorithm must be able to rotate population vectors.
• Fig. S3. The lengths of the population vectors K_l along the hexagonal grid’s axes are correlated.
• Fig. S4. Possible distributed representations of the position vector estimate μ of eq. S6 across a population of readout neurons.
• Fig. S5. Comparison of different decoding schemes for a single module in two dimensions.
• Fig. S6. Comparison of different decoding schemes for multiple modules in two dimensions.
• Fig. S7. If the grid scales are not organized into discrete modules, population vector decoding is no longer straightforward.
• Fig. S8. Continuum decoding requires multiple population vectors.
• References (46–50)

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