If each step was 1 frame, and the video played at 240 frames per second, the video would last about 17.5 years

Since the video screen would be larger than 1 Bpxl wide, I would accept a FHD scaled-out video.

Sure! Here you go. Open paint. Set the canvas to FHD resolution. Draw a one pixel thick, gray (#777777) line from one side to the other. You now have a perfect render, with antialiasing.