We would like suggestions that take an AI from being on an internet-connected computer to controlling substantial physical resources, or having substantial manufacturing ability.

1) Make money online. 2) Use money to purchase resources. 3) Increase capabilities.

1 should be easy for a superintelligent being. People pay for information processing.

But what does "take over the world" mean? Take over all people? Be the last agent standing? Ensure his own continued rule for the foreseeable future?