Abstract A mathematical model for the clonal growth of the alga Bostrychia radicans was constructed based on architectural growth rules and Lindenmayer systems. The sequence of theoretical growth and invasive strategy of space is shown in several graphical schemes which represent different steps of the model. We postulate that Bostrychia radicans has a `phalanx' strategy of colonization (Lovett Doust, L. 1981. J. Ecol. 69, 743–755.) based on the biological interpretation of the model and field observations.