Singularities in Weierstrass Functions

Dave Naughton

Frank Adams 2,

In this seminar I intend to talk about a class of continuous functions and the conditions under which said functions can be nowhere differentiable and exhibit fractal behaviour. In particular I will look at the original function of Weierstrass, and rather than regularity or dimension theoretic (global) properties, look locally at properties of points on the graph. I will concentrate on singularities, specifically Knot points and how it can be shown that such graphs possess large sets of these Knot points. All will be explained, no previous knowledge required.

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