dhenry:
there really is no way to replace the recommended three terminal potentiometer with a single two terminal resistor.
A pot is the simplest way to go. But it is extreme to say that there is other alternative. For example, you can pwm through a rc network to create a voltage there, and be able to adjust contrast in software.
You are offering help to a beginner or trying to show you know more than others? I'm confused here. As a teacher, I don't always tell my students the "complete" story on day one. There are reasons not to tell "complete" stories. I will wait at least another 30 days for the OP to get the RC stuff, which I'm sure floresta knows how to do. Right now, potentiometer is perfect. I am a teacher and liquid crystal physicist, do you see me blabbing about knowing all more about LCD stuff than others? Most HD44780 display spec sheets I read didn't say they recommend RC and PWM anyway, they say 2k to 20k pot.