The Animal Coats are unique for each species in the sense that they differ in texture, colour, pattern etc. Major factors such as habitat, lifestyle, camouflaging etc. influence the formation of the animal coat. Melanin is the major pigment in the body of the organism responsible for the pigmentation on surface of the skin and other appendages. Melanin is produced by specialised cells in the basal layer of the epidermis called ‘Melanocytes’ whose distribution determines the pattern and overall colour concentration of the pigmentation. The distribution of Melanocytes is specific in each organism determined by chemical signals called ‘Morphogens.’ A number of authors have put forth theories regarding Melanogenesis and its subsequent distribution to form patterns. Turing and Murray have been considered the pioneer in the work of using differentiation to form a reaction diffusion model to explain the movement of melanocytes and the melanin pigment through a concentration gradient by Morphogens. According to them, body surface area and its uniformity throughout the organism plays an important role in dispersion of Melanocytes. Various patterns like strips, spots, colour variations and other criteria can be explained on the basis of such mathematical theorems and models. In this article, we have made an attempt to study a biological concept that is animal coat pattern formation, in a mathematical way. Ordinary differential equations and Partial differential equations are being used for determining the colours and patterns occurring in Animal coats.