This article unifies neural modeling results that illustrate several basic design principles and mechanisms that are used by advanced brains to develop cortical maps with multiple psychological functions. One principle concerns how brains use a strip map that simultaneously enables one feature to be represented throughout its extent, as well as an ordered array of another feature at different positions of the strip. Strip maps include circuits to represent ocular dominance and orientation columns, place-value numbers, auditory streams, speaker-normalized speech, and cognitive working memories that can code repeated items. A second principle concerns how feature detectors for multiple functions develop in topographic maps, including maps for optic flow navigation, reinforcement learning, motion perception, and category learning at multiple organizational levels. A third principle concerns how brains exploit a spatial gradient of cells that respond at an ordered sequence of different rates. Such a rate gradient is found along the dorsoventral axis of the entorhinal cortex, whose lateral branch controls the development of time cells, and whose medial branch controls the development of grid cells. Populations of time cells can be used to learn how to adaptively time behaviors for which a time interval of hundreds of milliseconds, or several seconds, must be bridged, as occurs during trace conditioning. Populations of grid cells can be used to learn hippocampal place cells that represent the large spaces in which animals navigate. A fourth principle concerns how and why all neocortical circuits are organized into layers, and how functionally distinct columns develop in these circuits to enable map development. A final principle concerns the role of Adaptive Resonance Theory top-down matching and attentional circuits in the dynamic stabilization of early development and adult learning. Cortical maps are modeled in visual, auditory, temporal, parietal, prefrontal, entorhinal, and hippocampal cortices.

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