Update: it printed! See pictures.
This is the "Mandelbulb"-- a 3D version of the famous Mandelbrot set. It utilizes 'triplex' numbers instead of the normal complex. (Triplex numbers are Cartesian 3D coordinates). Just like taking a complex number to a power means multiplying the angle ð›‰ by the power and taking the magnitude to the power, taking a triplex number to a power means multiplying the angles ð›‰ and É¸ by the power, and taking the magnitude to the power. Everything else about the Mandelbulb is the same as the Mandelbrot set, except for that with the Mandelbulb the numbers are taken to the power of 8.
To generate the mandelbulb, I wrote a java program that outputted a .csv file on stdout. From there, I imported it into Mathematica, and used the ListSurfacePlot3D function to plot it. From there I exported it to STL.
(A word of warning-- in Mathematica, MaxPlotPoints in the ListSurfacePlot3D function
needs to be set to >50.)
Juliabulbs are coming!
Download the stl file or the .zip and print with support and infill. I've only tried it with with MiracleGrue, and even with that it comes out somewhat foamy, so good luck!
Print out the christmas tree ornament and show off your nerdiness!