Purple screen on IPhone 13 pro max

Could be almost anything, but the first thing I'm thinking is a software fault. However, while you can't necessarily see this yourself, a diagnostic can access data that will log all sorts of different faults. You might be able to do it remotely, although I'd recommend at an Apple Store if you can manage that.

Have found multiple instances of this happening on the internet, it happens to my 13 pro max 256GB on a regular basis, not good enough for a product that costs more than my rent. Apple support suggested resetting after backing up and then leaving the phone not backed up for a few days. Didn't work for me but when I downloaded everything back from the Icloud and force-restarted it, it didn't crash again for a week or more, may be just coincidence though.