The animation compares two different mental models for the same projection. In the moving map on the left, the center point changes with the globe. The visible hemisphere stays circular because it is always centered on the projection. In the fixed map on the right, the projection center stays at 30°N, 0°E while the globe view moves. The visible hemisphere then stretches and bends as it moves away from that fixed center.
This difference explains why azimuthal equidistant maps are easiest to read when the center point is part of the question. If the map is centered on your location, distance rings and straight radial bearings have direct meaning. If the feature of interest is far from the center, the map still follows the projection formula, but shapes and areas become progressively less intuitive.