Continual mutations to the hemagglutinin (HA) gene of influenza A virus generate novel antigenic strains that cause annual epidemics. Using a database of 560 viral RNA sequences, we study the structure and tempo of HA evolution over the past two decades. We detect a critical length scale, in amino acid space, at which HA sequences aggregate into clusters, or swarms. We investigate the spatio-temporal distribution of viral swarms and compare it to the time series of the influenza vaccines recommended by the World Health Organization. We introduce a method for predicting future dominant HA amino acid sequences and discuss its potential relevance to vaccine choice. We also investigate the relationship between cluster structure and the primary antibody-combining regions of the HA protein.