**Zusammenhang zwischen Fraktaler Dimension und Konvergenzgeschwindigkeit der Spektralreihe bei rationalen Fraktalen**

(this roughly translates to "*The connection between fractal dimension and convergence speed of the spectral series for rational fractals*")

This is the topic of my diploma thesis. Interestingly the topic has been given to me by a professor in the CS department, although it doesnt sound like this – but there is stuff like finite automatons and regular languages in it `:-)`

It is a mathemathics thesis though...

At the end of the last week the stuff I already wrote for the thesis suddenly shrank. I had cited some things from a book. It was a highly complicated way to be able to compute P^n quickly when P is a matrix (n matrix multiplications are expensive, especially when they appear in a limes for n->infinity...). It involved stuff like characteristic polynomials, partial fraction expansion, comparing coefficients, wild index shuffling and had some quite annoying prerequisites.

Last Friday I visited my supervising mathematics professor and he had a look into that stuff. He wanted to understand what actually happens there. After five minutes he found it: The theoretical base for this is the Jordan decomposition of matrices. And poof: If you write this down by means of the linear algebra suddenly the whole stuff suddenly becomes shorter, easier to understand and – that is the best thing about it – more general. `:-)`

However, the GIMPs new path tool suffers heavily because of this thesis...