The Dimension of Weierstrass' Function

Tom Withers

Frank Adams 2,

Maths at its purest is the concept of ask a question, work out an answer - remember high school? The only problem is that these days the simpler the question, the more difficult the answer seems to be. Weierstrass' function is an incredibly "wobbly" graph, fractal dimension is a way of measuring how "wobbly" something is. Weierstrass function was defined in 1872, (Hausdorff's) fractal dimension was defined in 1918 and studying the two together was first done in 1937.
So what is the fractal dimension of Weierstrass' function? It's taken at least 78 years, but last summer a paper appeared which has solved this long standing problem and I'm going to explain it... with pictures and a few A-Level infinite sums.
As with all talks in this seminar, I'll assume you have no idea what I'm talking about and motivate everything. As usual, proofs and (proper) definitions are off limits on Friday afternoons.
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