Polar growth is a fundamental mode of cell morphogenesis observed in nearly all major groups of organisms. Among polarly growing cells, the angiosperm pollen tubes have emerged as powerful experimental systems in large part because of their oscillatory growth, which provides a window into the network of interactions regulating morphogenesis. Empirical studies of oscillatory pollen tubes have sought to uncover the temporal sequence of cellular and molecular events that constitutes an oscillatory cycle. Here we show that in lily pollen tubes the distance or wavelength (λ = 6.3 ± 1.7 μm) over which an oscillatory cycle unfolds is more robust than the period of oscillation (τ = 39.1 ± 17.6 s) (n = 159 cells). Moreover, the oscillatory cycle is divided into slow and fast phases, with each phase unfolding over precisely one half of the wavelength. Using these observations, we show that a simple spatial bi-oscillator predicts the most common modes of oscillation observed in pollen tubes. These results call into question the traditional view of pollen tube morphogenesis as a temporal succession of cellular events. Space, not time, may be the most natural metric to inteprete the morphogenetic dynamics of these cells.