In plants and parenchymatous brown algae the body arises through the activity of an apical meristem (a niche of cells or a single cell). The meristem produces lateral organs in specific patterns, referred to as phyllotaxis. In plants, two different control mechanisms have been proposed: one is position-dependent and relies on morphogen accumulation at future organ sites; the other is a lineage-based system which links phyllotaxis to the apical cell division pattern. Here we examine the apical patterning of the brown alga, Sargassum muticum, which exhibits spiral phyllotaxis (137.5° angle) and an unlinked apical cell division pattern. The Sargassum apex presents characteristics of a self-organising system, similar to plant meristems. In contrast to complex plant meristems, we were unable to correlate the plant morphogen auxin with bud positioning in Sargassum, nor could we predict cell wall softening at new bud sites. Our data suggests that in Sargassum muticum there is no connection between phyllotaxis and the apical cell division pattern indicating a position-dependent patterning mechanism may be in place. The underlying mechanisms behind the phyllotactic patterning appear to be distinct from those seen in plants.