Mandelbrot Set

Mandelbrot Set

The following post is by Henry Delgado as part of George Mason University Math 493, Mathematics Through 3D Printing.

The Mandelbrot Set named after Benoit Mandelbrot.  Mr. Mandelbrot began working for IBM in 1958, which provide him access to IBM computers.  At IBM he used computer graphics to create fractal images leading to the Mandelbrot set in 1979.

Figure 1 Iteration = 1024

The Mandelbrot is the set of complex numbers in which the function    produces a sequence of iterations when initiated at z=0.  The solution to each function 

(, , ... ) is reiterated and the sequence gets arbitrary larger.  The images in figure 2 were created in Mathematica 10.1 using complex number a+bi.  The number of iterations were increased from 0, 5, 20, and 120.

Figure 2 Mathematica 10.1

The distance of the Mandelbrot set is bounded and never larger than 2.  The image below demonstrates that everything in the Mandelbrot set has to be within the distance of 2.

Figure 3 http://mathworld.wolfram.com/MandelbrotSet.html

Figure 4 Makerbot 5x

I was able to generate a Mandelbrot set using a 3D Makerbot 5x printer found in figure 4.  This model took roughly 4 hours to generate.