Abstract Carpobrotus affine acinaciformis is one of the most harmful invasive plants in the Mediterranean basin. In this study, we built a numerical growth model containing simple, and essentially linear, growth rules that provided us a tool capable to analyse the complex non-linear behaviour observed in the dynamic growth of Carpobrotus spp. This model includes a set of ecologically relevant parameters such as: (1) the stolon elongation rate, setting the upper limit of the horizontal spreading of the clone, (2) the branching rate, closely related to the capacity of the plant to occupy the space forming a dense and complex network, (3) the branching angle, which is determinant in the efficiency of the space occupation during the growth process, (4) the node mortality, and (5) the node branching age. We found that young patches of Carpobrotus (<20 years old) are characterised by a biomass production and quantity and density of nodes that grow exponentially with an exponent that depends on the branching probability and the stolon elongation rate. The expansion in the diameter is initially produced from a very ramified morphology, characterised by a fractal dimension D f = 1.2 (100 nodes; <5 years old; velocidad ≈ 0.3 m/year) that later turns into a more compact plant with less occupied space in its interior (20,000 nodes; >50 years old; speed keeps oscillating around 0.27 m/year further on) with a dimension equal to the euclidean one ( D f = d = 2). Regarding the implications for the management of Carpobrotus, it is remarkable that with few relevant parameters we have been able to reproduce the patch dynamics of this plant, which may indeed be quite useful to improve the yield prediction of Carpobrotus growth in coastal Mediterranean zones. Our modelling approach can further be extended to interdisciplinary problems in which dendritic patterns and branched structures are developed.