Yellow Tang obsessive swim pattern

[bromion]

I have a small-ish yellow tang (3" or so), added a few weeks ago. It's been grazing voraciously on my tank's algae (doesn't eat anything else yet), and seems ok, but it swims an obsessive loop around the tank with uncanny precision. It's a 5' long 90g tank. The swimming is all against the back wall: to the right along the top (with a dip in the middle), then down, then to the left along the bottom, then up. Repeat indefinitely unless it gets startled or decides to stop to graze on some algae. The tang is definitely grazing on algae, but for long periods of time it swims this loop, and pretty fast, too.

Is this normal?

I have very few fish (2 ocellaris and 1 fairy wrasse) and they all ignore each other completely.

 

[Aquattro]

Can it see it's reflection in the back glass?

 

[bromion]

Nope. It's black acrylic and not shiny anymore.