Display Screen or Portion Thereof with Animated Graphical User Interface Having a Three-dimensional Appearance

FIG. 1 is a front view of a display screen or portion thereof with animated graphical user interface having a three-dimensional appearance showing the claimed design; FIG. 2 is a second image thereof; FIG. 3 is a third image thereof; and, FIG. 4 is a fourth image thereof. The outermost dashed broken lines in the figures show a display screen or portion thereof, and form no part of the claimed design. The other dashed broken lines in the figures show portions of the animated graphical user interface having a three-dimensional appearance that form no part of the claimed design. The dot-dash broken lines in the figures show environment that forms no part of the claimed design. The appearance of the animated image sequentially transitions between the images shown in FIG. 1 . The process or period in which one image transitions to another forms no part of the claimed design. The gray shading in FIG. 2 represents the appearance of light.