Weierstrass function
From Academic Kids
In mathematics, the Weierstrass function was the first example found of a kind of function with the property that it is continuous everywhere but differentiable nowhere. Almost all continuous functions are nowhere differentiable, and this property is both stable and generic. Weierstrass functions are defined by
<math>f(x)=\sum_{n=0}^\infty a^n\cos(b^n\pi x),<math>
where <math>0 The following graphs display the function <math>f(x)=\sum_{n=0}^\infty (1/2)^n\cos(20^n\pi x),<math>
(Note: These graphs do not correctly display the function, they display only a subsampled version of this function.)
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WeierstrassFunction_000.gif
Image:WeierstrassFunction_000.gif
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WeierstrassFunction_001.gif
Image:WeierstrassFunction_001.gif
See also
