The ‘turtle geometry’ of Logo can give rise to several types of non-Euclidean geometry,
each of which can be made available on the usual 2D computer screen. (Abelson
and diSessa 1980). In Logo, a turtle’s ‘state’ is defined intrinsically (by reference
to its own movement of forward–backward and its heading of turn left or right by
so many degrees) and locally (since measures of steps and amount of turn are
referred only to the turtle, not external coordinates). As a result, curvature in turtle
geometry is turn per step, and is intrinsic to the turtle’s behavior.