The analysis of colour pattern geometry is not as well advanced as the analysis of colour, although this reflects a lack of an analytical framework. The present study proposes an approach based on a consideration of which colours are adjacent to each other. Both vertebrate and invertebrate eyes do not take static images of the world but move across the field of view. As a consequence, the eye takes transects across the field of view responding to the colours and luminances within patches and to the colour and/or luminance transitions between patches. The framework and methods suggested here are based upon transects across colour patterns and make it possible to estimate colour pattern parameters that capture not only the relative areas of each patch class, but also the relative frequencies of colour/luminance transitions or adjacency. This allows tests of new hypotheses about colour patterns at the same time as including colour, pattern, and texture. Eleven groups of predictions are made with respect to the often conflicting needs of communication with conspecifics, avoiding predation, and finding food. New phenomena may be discovered as a result of these methods and predictions. For example, certain colour transitions may be used for species recognition even though the same colours are used by all species. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ••, ••–••.