I made a bit of a video:
I wrote a Python script which generated Tile API URLs centered on Regina at various scales. Piped that through to curl to fill a directory with images, then used ffmpeg to assemble them. Once I had the kinks worked out it only took about 10 minutes to render.
(I used the live site rather than my development machine. If you attempt something similar, be gentle and don't request more than one image at a time!)