Brendan Rafferty of SFA (not Super Furry Animals!) tells all: "It was originally (in 1987) black-and- white and was only changed to red to stand out behind the band name in white lettering. The symbol itself was my own variation on a traditional chaos symbol (Nb. designed by Jim Cawthorn in 1962): eight arrows pointing out in all directions. The inner circle, half filled in, was meant to be dark on one side, light on the other. It was a personal design I had tattooed on myself over 20 years ago. It was not meant to be the band's logo. For a while, our band had two singers, including myself. Some shows he sang, some I sang, and other times we both sang. The other singer also had his own personalized abstract tattoo. So, as an inside joke for our friends, whenever we printed flyers to promote our shows, we would draw in his tattoo next to the name of the band if he was singing, my tattoo if I was singing, and both our tattoos if we were both singing. After a while, I was singing most of the shows and my tattoo was always next to our band name. By the time the other singer left the band, we were gaining local popularity and local punks who didn't know us personally (who were writing our name on their jackets) were also drawing my tattoo. The symbol was next to the band name on so many flyers people assumed it was the band's logo. Other people making flyers for our shows also put the symbol next to our band name assuming it was our logo. We never intended to use it as our logo. In fact, we never intended to have a logo at all, but we figured "Why not?" and kept it."
The Song of the Moment is "Only the Lonely" by The Motels, who never had a logo as far as I could find.