DeluxePaint III or higher for creating the animation. You need to pick up an AnimBrush - this is the only way to save a animation sequence that is not the size of the screen - ie Fullscreen animation would take too much bandwidth. Save the Animbrush as "thingy.animbrush". (here you can get of demo of DPaintV)
I then used MainActor1.55 to load "thingy.animbrush" and then save out each frame as an individual IFF file.
Then I used ImageFX to convert the IFF files to Gif87a format. I have made a rather shoddy Arrexx Script, so I can do a batch job with only one or two mouse clicks. The script will first convert from a AnimBrush to IFF's (dumping the contents in sys:AnimToBrush directory), then from IFF to Gif87a.
Finally, I used WhirlGif to convert the Gifs into the final composite.
To see some Gifs created with that procedure...
Trippy Visuals page.