Many cephalopods escape detection using camouflage1. This behaviour relies on a visual assessment of the surroundings, on an interpretation of visual-texture statistics2–4and on matching these statistics using millions of skin chromatophores that are controlled by motoneurons located in the brain5–7. Analysis of cuttlefish images proposed that camouflage patterns are low dimensional and categorizable into three pattern classes, built from a small repertoire of components8–11. Behavioural experiments also indicated that, although camouflage requires vision, its execution does not require feedback5,12,13, suggesting that motion within skin-pattern space is stereotyped and lacks the possibility of correction. Here, using quantitative methods14, we studied camouflage in the cuttlefishSepia officinalisas behavioural motion towards background matching in skin-pattern space. An analysis of hundreds of thousands of images over natural and artificial backgrounds revealed that the space of skin patterns is high-dimensional and that pattern matching is not stereotyped—each search meanders through skin-pattern space, decelerating and accelerating repeatedly before stabilizing. Chromatophores could be grouped into pattern components on the basis of their covariation during camouflaging. These components varied in shapes and sizes, and overlay one another. However, their identities varied even across transitions between identical skin-pattern pairs, indicating flexibility of implementation and absence of stereotypy. Components could also be differentiated by their sensitivity to spatial frequency. Finally, we compared camouflage to blanching, a skin-lightening reaction to threatening stimuli. Pattern motion during blanching was direct and fast, consistent with open-loop motion in low-dimensional pattern space, in contrast to that observed during camouflage.