A reaction-diffusion type mathematical model for the growth of corals in a tank has been proposed based on the model suggested by Mistr and Bercovici, emphasizing the effect of nutrient concentration and domain size on growth patterns. The Turing type pattern formation of the proposed model has been considered and the pattern formation parameter spaces (Turing spaces) of the model were determined. The model is solved numerically when the parameters lie in Turing space and the results are represented graphically. These numerical solutions resemble branching structures of some branching corals. It has been observed that the behaviour of the branching structures vary with parameter values as well as the considered domain size (dimensions of the tank).

A reaction-diffusion type mathematical model for the growth of corals in a tank, describing the spatial time evolution of the biomass of dissolved nutrients (food of polyps) and dissolved solid materials (calcium carbonate) of the tank, is considered. Some properties of the spatial patterns when the model parameters lie in the Turing space are investigated based on dispersion relation and unstable wave numbers of the linearised system. Branching structure formation process in the model is explained analytically. The model is solved conditions and it is shown that the numerical results agree with the analytically derived properties of the solutions.Dispersion relation, reaction-diffusion equations, spatial temporal pattern formation, Turing instability.