This entity is actually mainly sediment, trapped by layers of the actual fanisid organisms.
These Fasinids photosynthesise, producing the necessary sugars to reproduce. They absorb many chemicals from the seawater, and interestingly are able to transport these minerals from the lower to higher levels through connective tubes, formed of cells with their organelles extracted.
The body is actually quite soft, and layers can be scraped away by those creatures feeding upon it.
These fanisids reproduce by spores. When the stromatolite reaches a critical mass, spores are emitted from the top of the mass and usually travel along the shore, forming a new stromatolite.