Mathematical and Image Analysis of Stromatolite Morphogenesis

Abstract

Stromatolites are internally laminated organosedimentary structures that result from the environmental interactions of Benthic Microbial Communities. They have been traditionally described and classified either by quasi-Linnean taxonomic systems or by morphometric schemes. Neither of these approaches has proved entirely satisfactory. The application of the mathematics of evolving surfaces provides a promising alternative for the modelling and classification of stromatolites in terms of their morphogenesis. The suggestion of Grotzinger and Rothman that stromatolite-growth in general could be attributed to a combination of four processes that constitute the variables of the Kardar-Parisi-Zhang (KPZ) equation has been analyzed and found to be an oversimplification. While some stromatolites can be characterized in this way, because of local growth effects, the majority of stromatolite forms exhibit nonlocal growth characteristic of Laplacian growth. Work is being undertaken to model such growth.