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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 …