Continuous curves {Riemann-Weierstrass curve} can have no direction at all points. Start with straight line segment with slope +1 and straight line segment with slope -1, meeting in middle, like this: ^. Then, on line segments, repeat construction, to make shape like M, with four line segments, placing base endpoints half as far apart as before. If repeated, both endpoints approach same point, and slopes approach infinity.
Mathematical Sciences>Geometry>Plane>Curve>Kinds
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Date Modified: 2022.0224