Flounders and cuttlefish have an impressive ability to change colouration, for camouflage and, in the case of cuttlefish, for communication. We pursue the hypothesis that these diverse patterns are created by combining a small number of distinct pattern modules. Independent component analysis (ICA) is a powerful tool for identifying independent sources of variation in linear mixtures of signals. Two versions of ICA are used, one assuming that sources have independence over time, and the other over space. These reveal the modularity of the skin colouration system, and suggest how the pattern modules are combined in specific behavioural contexts. ICA may therefore be a useful tool for studying animal camouflage and communication.