Mandelbulb (Customizable)

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This object was designed and printed under the guidance of Dr. Evelyn Sander for Math 401: Mathematics Through 3D Printing at George Mason University. Background: The Mandelbulb is a three-dimensional representation of the Mandelbrot set, discovered in 2009 by Daniel White and Paul Nylande. The Mandelbrot set consists of complex numbers c for which the function f(z) = z^2 + C does not diverge when iterated from z=0, resulting in a fractal form. White and Nylande took this set and created an analogue of two-dimensional space using quaternions and spherical coordinates. Their formula for the nth power of 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 using n=8. For more information on the Mandelbulb, visit www.mandelbulb.com. Code: This object was created in Mathematica. The source code can be found at https://community.wolfram.com/groups/-/m/t/851592 and is included in this notebook. The STL file can be customized by modifying n to achieve better approximations of the Mandelbulb or to visualize the Mandelbulb for different values of z = z^n + C. For this print, I used z = z^9 + C and n=60 for 60 iterations. Other STL files generated with this notebook are included, but they have large file sizes that may be challenging for your slicer. Note: The above text has been rewritten to meet the requirements of the Flesch-Kincaid test with a score of 100%.