Why not use a segmented control instead?
Segmented controls with text labels are unambiguous, and allow the user to see the state and the name of the state (and all available states) in the same view.
download bmml source – Wireframes created with Balsamiq Mockups
if space is at a premium, you could bring these down to just icons, although beware that icons without a text label can be problematic.
iOS guidelines use the example of a segmented control for maps:
Segmented controls are often used to display different views. In Maps, for example, a segmented control lets you switch between Map, Transit, and Satellite views.
Either way, hiding functions under a button means that you are forcing the user to remember all the possible display modes. This can even be problematic in a dropdown, where all the items are labeled, but only one can be seen at a time.