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Generalized Mandelbrot Sets, Aaron Schlenker
Generalized Mandelbrot Sets, Aaron Schlenker
Undergraduate Honors Thesis Collection
A complex point Z0 is defined to be a member of the famous Mandelbrot set fractal when the iterative process using the function Z2 stays bounded when applied to Z0. We investigate what happens if we change the iterative process so that Z2 is now composed with, for example, a Mobius transformation, indexed on a parameter a. The Mandelbrot set corresponds to a = O. What happens when we change a = 0 to other values, repeating the iterative process and then drawing the sets? Do these Generalized Mandelbrot sets have similar properties to …
A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson
A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson
Undergraduate Honors Thesis Collection
The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …