Zebrafish fins grow by sequentially adding new segments of bone to the distal end of each fin ray. In wild type zebrafish, segment addition is regulated such that an isometric relationship is maintained between fin length and body length over the lifespan of the growing fish. Using a novel, surrogate marker for fin growth in conjunction with cell proliferation assays, we demonstrate here that segment addition is not continuous, but rather proceeds by saltation. Saltation is a fundamental growth mechanism shared by disparate vertebrates, including humans. We further demonstrate that segment addition proceeds in conjunction with cyclic bursts of cell proliferation in the distal fin ray mesenchyme. In contrast, cells in the distal fin epidermis proliferate at a constant rate throughout the fin ray growth cycle. Finally, we show that two separate fin overgrowth mutants, long fin and rapunzel, bypass the stasis phase of the fin ray growth cycle to develop asymmetrical and symmetrical fin overgrowth, respectively.