Visual cortex's hierarchical, multi-level organization is captured in many biologically inspired computational vision models, the general idea being that progressively larger scale, more complex spatiotemporal features are represented in progressively higher areas. However, most earlier models use localist representations (codes) in each representational field, which we equate with the cortical macrocolumn (mac), at each level. In localism, each represented feature/event (item) is coded by a single unit. Our model, Sparsey, is also hierarchical but crucially, uses sparse distributed coding (SDC) in every mac in all levels. In SDC, each represented item is coded by a small subset of the mac's units. SDCs of different items can overlap and the size of overlap between items can represent their similarity. The difference between localism and SDC is crucial because SDC allows the two essential operations of associative memory, storing a new item and retrieving the best-matching stored item, to be done in fixed time for the life of the model. Since the model's core algorithm, which does both storage and retrieval (inference), makes a single pass over all macs on each time step, the overall model's storage/retrieval operation is also fixed-time, a criterion we consider essential for scalability to huge datasets. A 2010 paper described a nonhierarchical version of this model in the context of purely spatial pattern processing. Here, we elaborate a fully hierarchical model (arbitrary numbers of levels and macs per level), describing novel model principles like progressive critical periods, dynamic modulation of principal cells' activation functions based on a mac-level familiarity measure, representation of multiple simultaneously active hypotheses, a novel method of time warp invariant recognition, and we report results showing learning/recognition of spatiotemporal patterns.