Multibrot Sets

Susan Tarabulsi

October 26, 2020

George Mason University Math 401: Mathematics Through 3D Printing

A Multibrot set is a set of values in the complex plane whose absolute value remains below some finite value throughout iterations. In other words, the Multibrot set contains the mapping of z to z^d +c where d≥2 with z_0 = 0. In general, the number of main bulbs (caused by the first iteration) is d-1. The Mandelbrot set is a special case of a Multibrot set in which d=2. This print is the Multibrot set f(z) = z + c. Notice that there are seven main bulbs.

The code below was written in Mathematica. The number of iterations to produce the 3D plot is 30. It is then scaled to produce a printable object.

This object will be printed on a Makerbot printer. The estimated time to print will be three hours. There are no rafts or support necessary for successfully printing this object.

References: https://en.wikipedia.org/wiki/Multibrot_set https://en.wikipedia.org/wiki/Mandelbrot_set