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pathological curve

A curve often specifically devised to show the falseness of certain intuitive concepts. In particular, the image of continuity as a smooth curve in our mind's eye severely misrepresents the situation and is the result of a bias stemming from an overexposure to the much smaller class of differentiable functions. A chief lesson of pathological curves is that continuity is a weaker notion than differentiability. Many pathological curves are fractals, such as Cantor Dust, including space-filling curves, such as the Peano Curve. The earliest known example is the graph of Weierstrass' Nondifferentiable Function.

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