Because the shapes and forms of many coral reefs resemble karst (erosion landforms created by dissolution of limestone), it is widely believed that those reefs have grown on karst foundations, and that Holocene growth perpetuates the underlying topography. However, this concept has become difficult to reconcile with the growing amount of seismic and coring evidence demonstrating that several karst-like reef features are entirely constructional. Here I use cellular automata simulations to show that coral reefs resemble karst limestones not because they are built on karst foundations, but because reef growth and limestone erosion are fundamentally the same process, running in opposite directions. Coral reef landscapes are in fact inverse karst—the basic spectrum of reef growth forms mirrors the basic spectrum of limestone erosion forms. In both growth and erosion, the development of form is a self-organised phenomenon emerging from the cumulative action of small-scale processes. The essential morphological control in both cases is slope stability, which depends on the composition of each system: coral type in reefs and lithology (rock type) in limestones. Solid, well cemented reefs and limestones, which can maintain steep slopes without collapsing, produce nodular reefs and pinnacle karst respectively, whereas unconsolidated, friable reefs and limestones, which frequently collapse, produce cellular reefs and cone karst.The growth forms produced in the model should theoretically apply to all modular skeleton-building organisms growing in a fluid medium, and may therefore provide useful templates in the search for extraterrestrial life. While none of the model forms can be considered unequivocally diagnostic of life, because all could conceivably arise through inanimate crystallisation, the model’s seemingly accurate rendition of biogenic carbonate morphology on earth suggests that it may provide a useful foundation for evaluating and exploring the range of macroscale self-organised biogenic structures that could arise on other planets.