Whorld is free, open-source software for creating moving geometric images. According to the website: "It uses math to create a seamless animation of mesmerizing psychedelic images." It is available as a standalone program (Win only, I'm afraid) or a Freeframe plug-in. It was apparently developed mainly for VJ use, and can sync to MIDI clock. Though it is kind of a one-trick pony, in that it only uses one method to generate images, that one method can produce a wide variety of output. There are a number of parameters that can be changed and each parameter has an associated oscillator that can modulate it, a setup that should be familiar to anyone who has used a synthesizer for music/audio. MIDI controllers can also be assigned to the parameters. Settings can be saved to patches, and these patches can be played manually, or set up to auto-play. You can also crossfade seamlessly between two patches. Output can be captured and saved to an .avi file, or individual frames can be exported as bitmaps.
This video is made with a pretty simple patch, I'm still figuring this one out myself. Also, note that I compressed this video quite a bit to keep the size manageable for uploading, the output .avi looks much better. The audio is an excerpt from the Skin Contact track "Glass", available here: https://skincontact.bandcamp.com/album/20-years-of-contact-vol-2
Link to the Whorld web page:
▶️ DTube
▶️ IPFS