The biological origin of stromatolites is proven for recent rocks, less than 350 million years old. It is caused by micro-organisms, such as cyanobacteria, which precipitate bicarbonate into calcium carbonate. This calcium carbonate (or limestone) is deposited in successive layers on the surface of the cauliflower which ensures its upward growth.
This biological origin is discussed for older stromatolites. However, work published in February 2008 by a Franco-American team (Institut de physique du globe, Institut national des sciences de l'univers, Stanford Synchrotron Radiation Laboratory) on Australian stromatolites demonstrated the biological origin of specimens dated 2.724 billion years.
What you must remember:
The study of the rare stromatolites still forming today (in Australia for example) has shown that their formation is linked to the activity of Cyanobacteria and bacteria living on their surface. The photosynthetic activity of the former, by consuming CO2, leads to the precipitation of calcium carbonate from the calcium bicarbonate in solution in the water. The reaction below is moved to the right.
This calcium carbonate (or limestone) is deposited in successive layers on the surface of the cauliflower which ensures its upward growth.
Each "cauliflower" or "mushroom" is formed by the accumulation of thin layers of calcium carbonate deposited during the photosynthetic activity of living Cyanobacteria located at the top of the mushroom.
Stromatolites are layered biochemical accretionary structures formed in shallow water by the trapping, binding and cementation of sedimentary grains in biofilms (specifically microbial mats), especially cyanobacteria. They exhibit a variety of forms and structures, or morphologies, including conical, stratiform, domal, columnar, and branching types. @Bachir Achour