You find Mutropolis after the passageway from the village. Talk to Clayton so that he lets you visit Mutropolis.
This is the low-spoiler guide for "Getting into Mutropolis" puzzle in Mutropolis. Unlike in normal walkthrough, you get gradual hints on how to solve the puzzle. Click the big button below to see your first hint. If the hint contains a spoiler, you will be warned about it before clicking.