Coral reefs are one of the most fascinating ecosystems in the world. Even without considering interactions with the whole reef wildlife, corals biology is plenty of complex phenomena such as the symbiosis with microalgae and emergent properties such as synchronized sexual events under very specific conditions. Many coral species self-organize into well defined structures such as: massive, branching and table coral colonies. Colonies living in the same region constitute a reef. Various coral species synthesize aragonite (a phase of calcium carbonate) during their clonal growth to build themselves a hard exoskeleton. When an entire colony dies, another new coral polyp can settle over the hard structure left behind by the dead colony and start a new colony on top of these remains. This process is repeated over centuries leading to the formation of large aragonite structures which display some recognizable patterns that can be spotted around the world. These include closed atolls and parallel stripes, together with large groups of closed atolls and little halos inside these big atolls (an example of self-similarity in this system).
In this work, we address the study of pattern formation in coral reefs by proposing a set of differential equations that govern the spatiotemporal evolution of some variables describing the system, taking into account corals ecology and the key role of hydrodynamics in reef shaping.
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