I have three of your passwords and the domain each is associated with. The pattern is obvious, so now I have all your other passwords too.

Also, you don’t need to remember only the base password and the rule. You also need to have an exceptions process for when your “generated” password is incompatible with the esoteric requirements of a new site (length, character restrictions, etc.). And you need to remember this at login time, when you aren’t presented with the same information about those requirements as you were when you registered.