Simple Cartography

Another problem I looked at was the Simple Cartography problem. My favourite part of the problem outline is that the number was specified as non-negative, because of course we all know how negative lines drawn on a sheet of paper appear.
Many solutions to this problem have the minimum number of colours as two, but I think this is incorrect after the number of lines is greater than two. Those who assume two is the minimum talk about how their papers or spaces would be symmetrical, but for a non-symmetrical space, more than two would be needed. Or that's what I thought. In MS Paint, I tried making difficult lines to show that more than two colours would be needed, but eventually after I ended up with this picture, I found myself to be wrong. Well, this is why testing is important :)