RPi (cheap), plus
Video Player Program, plus
Display, of your choice, plus
Video editor software (Free/OS. Maybe run it on a bigger computer, faster/ more powerful, to create the video)
Take a picture of, or clip, or import, the beginning desired display picture. Take a separate copy, of the image, and add any features, that you like... A new radar image, an Indiana Jones style moving flight line, etc. Crop the before and after pictures, in Paint (etc.), to create the round screen, that you want. Save the first and second picture, separately. Place the two pictures, on the video editor timeline. Use the video editor's sweep transition feature to morph between the two images. Spread the sweep out, over time. Radar sweeps are, often, a transition sweep type. Create the "movie." Run it, on the RPi.
Here's my tutorial: