Technical Artist and Unity enthusiast Mirza Beig created this stylized fire effect (although it looks more like smoke) entirely procedurally using shader math. According to the artist, the goal here was to imitate hand-drawn flipbooks in VFX. With added coloring, extra layers or effects, and quantized time to simulate a low framerate, there's a lot of potential to explore.
You can use this snippet to create procedural offsets that sample anything with a repeating wave motion, resembling stylized, hand-drawn visual effects: