Mandelbrot Set Variant

Mandelbrot Set Variant
George Mason University 401: Mathematics Through 3D Printing

Mandelbrot and Julia sets are objects of study in complex analysis in which investigates the boundedness of complex numbers under certain iterations of complex-valued functions. Specifically, the Mandelbrot and Julia sets are of great interest even in pop culture due to certain properties such objects have. For example, the Mandelbrot set is self-similar at certain points of the set, giving the Mandelbrot set a fractal-like appearance which makes sense considering it is a fractal (although it has dimension 2.

The Mandelbrot set refers to the set of all complex numbers c such that starting at z_0=0 the iterated function z_n+1=z_n^2+c remains bounded after infinitely many iterations. In this case, I have instead created a Mandelbrot set but instead uses the function z_n+1=z_n^3+c and using the same initial condition of z_0=0. The print shown above represents at each layer the complex numbers c th