I’m unlikely ever to get a tattoo, but if I did, I incline to the armband type; and I just got an idea for one: a ‘Mercator projection’ of Escher’s hyperbolic fish. Instead of a circle, the horizon would be two parallel lines, with one straight line of fish through the middle.
Later: See also.
The prominent white arcs in that print are not hyperbolic straight lines but equidistant curves. One such arc could become a straight line along the Mercator band, but off-center.