Mandelbrot's Cousin -- The Mandelbar

Despite the intricate complexities of the Mandelbrot set, one can start to become less interested in it after awhile.  Fortunately for those who appreciate new territories, there are other fractal sets to explore.  The obvious first choice to explore is the Mandelbar Set (also called "Tricorn").  I say it's obvious because it's closely related to Mandelbrot, but for you to understand its relation, we have to talk a little math first.

Actually, let's let wikipedia tell us.  I choose wikipedia as a reference because it has the most words.  I mean, it has more examples in easy-to-understand language.  It even explains where the term "Mandelbar" comes from.  So without further ado, here are wikipedia's entries for complex conjugates and Mandelbar.

Since a picture is worth a thousand wikipedia articles, here are a few pictures of Mandelbar that I generated.

This is the basic Mandelbar.  You can see why fractal artists also call this the Tricorn.  The smooth parts near the center are not as interesting as the rough parts on the points.  

This miniature Mandelbar is located to the left of the figure above.  This example of self-similarity confirms that the Tricorn is indeed a fractal in the same ways the parent fractal, Mandelbrot is.  In fact, if you look closely, you will find Mandelbrot contained in the Mandelbar:

I really like the coloring of this one.

OK, so what if you're starting to get bored by Mandelbar too?  Let's try pumping them up a bit in our next blog.