Pattern formation in stromatolites: insights from mathematical modelling

To this day, computer models for stromatolite formation have made substantial use of the Kardar-Parisi-Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper.