Using the "paper form" has only the drawback of being available for everyone in your environment.
If you want to keep the paper form and also have the ability to securely generate new passwords:
Buy a cheap, widely, available book (maybe two or three of the same), start at a random page and use the first letters/sentences in this book as your new password. To make it even more secure, I would suggest you add a "standard" to every password you have created ... like "SuperSecurePa##".
So for example: You have bought a book and like to add a new password ... you might start at page one, where the sentence would be:
"Once upon a time, there were two developers ..."
=> this will become your password:
"Ouat,twtdSuperSecurePa##"
Even more secure password (due to the size):
"Onceuponatime,thereweretwodevelopersSuperSecurePa##"
You can level this up by:
- Your chosen appendix has even more "secure" chars, like #*+?="§%&/() (you know what I mean)
- You prepend and append your new password with your "common" pass (here "SuperSecurePa##") ... or maybe prepend with a different common pass??