When organisms move forward or backward through their environment, they produce particular patterns of optic flow on their retina, i.e., the images of objects move in characteristic ways away from or towards a focus of expansion or contraction (Gibson, 1950, 1954). For straight motion without eye or head movements, the flow pattern is radial with a speed gradient and complete symmetry (Gibson, 1950). It is then straightforward to compute the heading direction, calculate the time to collision with objects or, indeed, take action to avoid collisions (van den Berg, 2000; Warren, 1998; Warren et al., 1988, 1991). The situation becomes more difficult when eye movements (e.g., pursuit movements) are made simultaneously, which is the rule and not the exception. Fixating an object that moves from left to right would create a lateral flow on the retina, giving a rightward motion to the images of all other objects. We call this a parallel flow to express the fact that all motion vectors would be parallel. This motion would be added to the appropriate radial motion for each image point, resulting in a complex flow pattern. This complex flow still contains the original radial flow that is needed for the extraction of heading direction. But the complex pattern would have to be decomposed to yield this information.