Display screen or portion thereof with an animated graphical user interface of a programmed computer system

FIG. 1 is a front view of the first image of a display screen or portion thereof with an animated graphic user interface of a programmed computer system;

FIG. 2 is a front view of a second image thereof;

FIG. 3 is a front view of a third image thereof;

FIG. 4 is a front view of a fourth image thereof; and,

FIG. 5 is a front view of a fifth image thereof.

The appearance of the image transitions sequentially between the images shown in FIGS. 1-5 , respectively. The process or period in which an image transitions to another forms no part of the claimed design. The broken lines showing a display screen or portion thereof, lines and text form no part of the claimed design.