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This paper describes a biologically inspired approach to vision-only simultaneous localization and mapping (SLAM) on ground-based platforms. The core SLAM system, dubbed RatSLAM, is based on computational models of the rodent hippocampus, and is coupled with a lightweight vision system that provides odometry and appearance information. RatSLAM builds a map in an online manner, driving loop closure and relocalization through sequences of familiar visual scenes. Visual ambiguity is managed by maintaining multiple competing vehicle pose estimates, while cumulative errors in odometry are corrected after loop closure by a map correction algorithm. We demonstrate the mapping performance of the system on a 66 km car journey through a complex suburban road network. Using only a web camera operating at 10 Hz, RatSLAM generates a coherent map of the entire environment at real-time speed, correctly closing more than 51 loops of up to 5 km in length.