Laser light shows use the equivalent of a scanning technology, so (in principle at least) laser based projectors wouldn't necessarily have fixed resolutions. Bear in mind, however, that all sources are now digital, so only fixed-resolution source material is available, with a fixed color palate. Even when film is used for recording, it promptly gets scanned and digitized for downstream processing. Unless you're using a CRT projector with separate RGB tubes, even the screen of a CRT monitor has a fixed resolution with each individual pixel containing three or four separate phosphor regions.
Marantz SR7009/7.1.4/FH+TM/DefTech PM1000/LCR+TM amped