We have used simple learning rules to study how firing maps containing triangular grids-as found in in vivo experiments-can be developed by Hebbian means in realistic robotic simulations. We started from typical non-local postrhinal neuronal responses. We found that anti-Hebbian weight pruning can develop triangular grids under certain conditions. Experimental evidences and the present study suggest that within this model, whitening is a bottom-up process, whereas weight pruning and possibly the non-linear extension of whitening to bottom-up information maximization are guided by top-down influences that reorganize entorhinal responses. We connect our model to the computational model of the entorhinal-hippocampal region of Lorincz and Buzsaki. In the joined model, the hippocampus is the origin of response reorganization. The joined model may provide insights for memory reorganization guided by hippocampal supervision.