Xenia sp. (possibly Xenia elongata?)
Click for 5 second movie of pulsing Red Sea Xenia
Though the function of this pulsing is not completely known, most likely the pulsing improves gas exchange and food capture by moving more water past the polyps. This hypothesis is consistent with the observation that Xenia often pulse less or stop pulsing under conditions of high water flow, conditios under which the additional water flow provided by pulsing would be superfluous.
Xenia biology:
Xenia are extremely fast growing corals that require good water flow and strong lighting. Healthy colonies can double in size over the course of a month or so, so established stands of Xenia in aquaria typically require thinning on a regular basis.
Xenia get most of their energy from the products of photosynthesis by their zooxanthellae (symbiotic dinoflagellate algae that live in their tissues). They are not thought to feed on particulate foods, though they are known to absorb dissolved organic compounds from the water.
The soft bodies of these corals would seem at first glance to be extremely vulnerable to attack from predators, but soft corals such as Xenia produce an arsenal of toxic compounds (including diterpenes). These toxins not only deter most predators, but also can harm neighboring corals, thus helping Xenia colonies maintain a patch of reef for themselves. Due to these defensive componds, Xenia are very smelly when handled out of the water (e.g. when colonies are being pruned).
Xenia do have some predators though, including various nudbranchs (sea slugs) that specialize on eating soft corals. Some of these are even camouflaged by appendages resembling the Xenia polyps they eat and live among. Apparently these nudibranchs are unharmed by Xenia's toxins.
Analogies to terrestrial plants and their herbivores:
The Xenia - nudbranch situation is analogous to the interactions between terrestrial plants and the herbivorous insects that feed on them. Most plants produce toxins called secondary plant compounds that deter most herbivores (though some of these compounds, such as caffiene, or the aromatic oils in culinary herbs are enjoyed by humans!). Consequently, each species or family of plants has its own group of specialist insect herbivores that have evolved mechanisms for dealing with that plant's unique toxins, and these specialists normally don't eat any other plant species. Often, these specialized herbivores even cue in on their host plant's unique toxins, recognizing the plant by its toxins and refusing to eat any plant that lacks the toxins. In some cases, the toxin alone is enough to stimulate feeding. For example corn rootworm beetles (Diabrotica sp.), which as adults feed extensively on members of the cucurbit family (e.g., squash, cucumbers, etc) will eat paper that has been soaked in a solution of cucurbitacins. Cucurbitacins are compounds that are widespread in plants in the cucurbit family and that sometimes make cucumbers bitter.