Mandelbrot Cube – Introduction

 

The Mandelbrot Cube project is a fascinating exploration of fractal mathematics.  Fractals are functions such that whenever you look deeper into a section of the curve you see repetitions and self-similarities to what you first started with. Fractals are recursive and iterative and chaotic.  And, they are truly beautiful.

For the bronze figure in this work I am going to make a cast of Ryoko Inoue from Roommate, a Sega Saturn role playing game released in Japan in 1997.  The basic plot of Roommate is fairly simple. Ryoko is seventeen, her family has moved from Tokyo to New York, and she is staying behind to finish school. Her father, who is a friend of your father’s, has asked that she move in with you in your apartment so she can complete her studies. But Ryoko misses her family and is emotionally vulnerable.  In Roommate Ryoko you have three years to develop a relationship with her.

Ryoko Inoue garage kit

 

So, what does Ryoko have to do with fractals?  Well, in 1997 role playing games could often have self-similarities and repetitions.  This was an artifact of the limited capabilities of computers at that time.  And, both the girl Ryoko and the game Roommate can be considered similar to fractals in that they each portray the wonderful beauty and chaos of youth.

The proposed model for this work is shown below.  I have a cube where each of the six faces is etched with the shape of a Julia Set.  The cube represents structure and regularity and repetition. The Julia Sets show the beauty of the mathematics.

Ryoko is standing beside a road contemplating her path.  Signposts point to Mandelbrot mathematical directions.  Where might Ryoko’s future lead?

Mandelbrot Project Model

Mandelbrot Cube

Ryoko Inoue

 

To show the fractal mathematics I have chosen to use six basic function plots.  These are the Mandelbrot Set and the related Julia Sets at (-0.2,-0.7i), (-0.12,0.75i), (0.26,0.0i), (-1.0,0.0i), and (-0.73,0.07i).  Each of these sets is shown in color below.

 

I have developed a Java application to generate and display these fractal images based on earlier work by Evgeny Demidov[1]. My Java application shown below can be launched to show the Julia sets at various places on the complex plane. This application will automatically traverse the boundary of the Mandelbrot set. Click anywhere in the Julia set or the Mandelbrot set to stop the animation. When stopped, click on any point in the Mandelbrot set to see the related Julia set. An <alt>-click will zoom in to either the Mandelbrot set or the Julia set to see fractal repetition. A <ctrl>-click zooms out. The Mandelbrot and Julia set images can each be saved.

Fractal Image Explorer

You can securely run this application now if you have Java installed on your computer. For more information on fractals, see here.

 

The road used in the model will be constructed from a brass sheet.  It is styled to give the perspective of moving off into the distance.  The template is shown below.

Road Template

 

References

1. Evgeny Demidov http://www.people.nnov.ru/fractal/MSet/Contents.htm