I'd like to suggest that a line or two be added about Purple squares being privately owned and that entering them without the owner's permission can get one into trouble.Red squares denote public buildings that anyone can enter. There are several public buildings in Tutorial City and your next task is to find one and enter it.
It's certainly important information. This is especially true for human characters since there's no barrier to warn them it's a private abode. It's also something that new players aren't going to know instinctively.
