Fractals and Wavelets

In the first chapters, which cover fractals, I study an unusual mathematical structure. Snowflakes, bridges, and trees all have some fractal pattern. I try to give meaning to a calculus problem on a fractal structure by attempting to find the vibration frequency spectrum for one particular fractal. Wavelets are an analytical tool that can be used to study fractals. In the middle chapters, I have applied wavelets to the fractal structure with which I began. Fourier analysis applies to the frequency spectrum of some objects. I tried to use wavelet analysis to express the solution I constructed in the previous section. In the final chapters, I study wavelets themselves and apply wavelet analysis to some of the Proton Decay Experiment photomultiplier patterns. The primary goals are to construct useful wavelets and to use wavelets to detect patterns obscured by noise.