I am looking for some links/algorithms to program some enemy attack waves (80s style shootem up).. For example,  enemies coming down in zig-zag patterns,  or entering the screen on the left, doing a circular loop and leaving the screen on the right (1942, or Galaxians style)..

Suprisingly, considering the amount of shootemups out there,  I can't find a single thing on google.  Am considering using Bezier Curves, or Sine Waves unless anyone can provide me with a better tip/method..      (ps.  For 4K, so looking for a few simple algorithms only).
Thnx  Edit:  Happy New Year Everyone!!

If you do go for sine waves then remind yourself about (or read up on) simple harmonic motion. No calls to Math.sin required...