Mandelbrot Set

Kenyu Koga
November 7, 2023

George Mason University Math 401: Mathematics Through 3D Printing

The Mandelbrot set is a two-dimensional set with a simple definition that displays great complexity. It is generated by iterating a simple function on the points of the complex plane. The set is obtained from the quadratic recurrence equation, z_(n+1)=z_n^2+C with z_0=C where C is the point in the complex plane.

The purpose of this assignment for the 3D printing class was to create the parts or all of a Mandelbrot or Julia set using Mathematica and export it into STL file. I designed a whole Mandelbrot set with a function of z = |-I Cos(z^3) + C| with z_0 = 0 + 0 I and iterate up to 100 times.

As for 3D printing, I used Creality Ender-3 Pro at George Mason University to print the Mandelbrot set. However in Mathematica, the measurements were very big so before printing I scaled down to make it smaller in UltiMaker Cura 5.4.0 to reduce the printing time.