The mammalian cortex is organized in a columnar fashion: neurons lying below each other from the pia to the white matter usually share many functional properties. Across the cortical surface, cells with similar response properties are also clustered together, forming elongated bands or patches. Some response properties, such as orientation preference in the visual cortex, change gradually across the cortical surface forming 'orientation maps'. To determine the precise layout of iso-orientation domains, knowledge of responses not only to one but to many stimulus orientations is essential. Therefore, the exact depiction of orientation maps has been hampered by technical difficulties and remained controversial for almost thirty years. Here we use in vivo optical imaging based on intrinsic signals to gather information on the responses of a piece of cortex to gratings in many different orientations. This complete set of responses then provides detailed information on the structure of the orientation map in a large patch of cortex from area 18 of the cat. We find that cortical regions that respond best to one orientation form highly ordered patches rather than elongated bands. These iso-orientation patches are organized around 'orientation centres', producing pinwheel-like patterns in which the orientation preference of cells is changing continuously across the cortex. We have also analysed our data for fast changes in orientation preference and find that these 'fractures' are limited to the orientation centres. The pinwheels and orientation centres are such a prominent organizational feature that it should be important to understand their development as well as their function in the processing of visual information.