There was a proposal in the 1980s for Peano Scanning. We thought about it for use in flight sim where the necessary wide band linear amplifier drive of the scans was commonplace. The basic 'curve' is here:
https://en.wikipedia.org/wiki/Peano_curve
It's a never ending pattern and whilst very difficult to do on a CRT (even with wideband linear amplifier drive), it could be done today on a fixed matrix - but why would you want to do it?
It was always good for a half hour's discussion!
Best regards,
Paul M