Those Weird Lines Spotted on Google Earth...

You may have noticed an article about some mysterious white lines being discovered in the Chinese desert using Google Earth.  So what are they, really?

Here is an entertaining sequence of news articles, each with a different conclusion...read the articles in this order (chronological):  First article, second article, third article.

Actually, we don't know for sure if what we are seeing is a "fractal screen" as posited, or whether there is an even better explanation yet to come.  This is really just my lead-in to a fascinating subject in mathematics and art:  fractals.  Okay, now that you've taken the bait, come right this way, please....

According to Wikipedia, fractals are often described as a "rough or geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole", a property called self-similarity.  Fractals often illustrate how a very simple algorithmic and/or statistical constraint can nevertheless result in a seemingly infinite degree of complexity and beauty...sort of analogous to how a collection of ants with tiny, simple brains can create a seemingly complex ant hill, or how tiny polyps can colonize and create a beautiful coral reef.

Fractals are mathematical constructs, and at the same time, they are beautiful.  Here is a web site with some collections of fractal art.  Fractals occasionally have an eerie resemblance to nature.  Beyond fractal art, actual technical uses of fractals now include fractal antennas, meta-materials, scientific analysis, etc.

The Mandelbrot set is a particularly interesting fractal set (see its mathematical description) and is the result of an infinite set of points that fulfill a simple mathematical criteria being plotted in the complex plane.  It has the unique characteristic of being the absolute maximum space filling curve possible in two or more dimensions, and its fantastically complex and varied patterns suggest an unknown, yet-to-be-clarified importance in many natural processes in nature.