Mandelbulb and Christmas Tree Ornament

thingiverse

An update: it has been printed! Check photos. The Mandelbulb is a 3D version of the renowned Mandelbrot set that employs 'triplex' numbers instead of typical complex ones (triplex numbers represent Cartesian 3D coordinates). Similar to how taking a complex number to a power involves multiplying the angle by the power and using the magnitude to the power, taking a triplex number to a power requires multiplying the angles and ɸ by the power while maintaining the magnitude's power. The Mandelbulb operates similarly to the Mandelbrot set, with the only difference being that it uses triplex numbers. In the Mandelbulb, numbers are taken to the power of 8. To create the Mandelbulb, a Java program was written, which produced a .csv file on stdout. The .csv file was then imported into Mathematica using the ListSurfacePlot3D[] function to plot it. Finally, the plot was exported as an STL file. Note: In Mathematica's ListSurfacePlot3D function, MaxPlotPoints must be set to a value greater than 50. Stay tuned for Juliabulbs! For more information, visit http://www.skytopia.com/project/fractal/2mandelbulb.html. To showcase your nerdy side, download the STL file or the .zip and print it with support and infill. Share photos of your printed Mandelbulb Christmas tree ornament!