Mandelbulb (Customizable)

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This was designed and printed for Math 401: Mathematics Through 3D Printing at George Mason University under the instruction of Dr. Evelyn Sander. Background: This object is known as the Mandelbulb. It is a 3D visualization of the Mandelbrot set. It was discovered in 2009 by Daniel White and Paul Nylande. The Mandelbrot set is the set of complex numbers, c, for which the function f(z) = z^2 + C does not diverge when iterated from z=0. This results in a fractal form. White and Nylande took this set a created an analogue of the 2-dimensional space of complex numbers using quaternions and spherical coordinates. Their formula for the nth power of a vector v = <x,y,z> is v^n := r^n<sin(n\*theta)cos(n\*phi),sin(n\*theta)sin(n\*phi),cos(n\*theta)> with r = sqrt(x^2 + y^2 + z^2), theta = arctan(y/x), and phi = arccos(z/r). The Mandelbulb is the set of points, c, for which v -> v^n + c is bounded. It is typically visualized with n=8. For more information on the Mandelbulb, visit www.mandelbulb.com Code: This object was designed in Mathematica. The source of the code can be found here: https://community.wolfram.com/groups/-/m/t/851592, and is included in the notebook. The STL can be customized by modifying the values of n to obtain better approximations of the Mandelbulb and to obtain the Mandelbulb for different z = z^n + C. For the print shown, I used z = z^9 + C and n=60 for the number of iterations. I included other STL files that were generated with this notebook. Notice that the more refined STLs have a large file size so your slicer will probably have a hard time.