When losses are taken into account, the attractor which was a point in the two dimensional phase space and a line in the linear three dimensional space becomes a circle, which appears on the screen as an ellipse due to perspective, in this bent three dimensional phase space. If this seems like an awkward way to describe a pendulum it is, but the concepts apply elsewhere.
Notice that as time passes, the point where the orbit penetrates the sectioning (p,v) plane moves, stitching a pattern. In the present example this pattern is approximately a straight line walking right in along the p axis, approaching the time axis as a limit. In the case of the pendulum this is not particularly surprising or illuminating. It does demonstrate the approach of the orbit to the attractor and in time would demonstrate that the attractor itself had a cross section consisting of a single point.