I used to use SuperGenPass[1] to do exactly this, but what you'll soon find is that every website has slightly different password rules, so you'll have to start memorizing unique settings for each site (i.e. website X can't have certain chars, website Y can't be longer than 12 chars, etc...). Then you run into the issue of multiple things you need to remember, such as secret answers for various questions, birthdays that you may lie about, etc...
Much easier to just use a vault to store all this.
Much easier to just use a vault to store all this.
[1] https://chriszarate.github.io/supergenpass/mobile/