Complex Numbers Are Your Imaginary Friends!

 Have you ever lazed in the sun on a balmy spring day, pondering the mathematical concept of i² = –1?  If so, this  article is for you! 

For more than 2,500 years, mathematicians have been obsessed with solving for x.  The story of their struggle to find the “roots” — the solutions — of increasingly complicated equations is one of the great epics in the history of human thought.
And yet, through it all, there’s been an irritant, a nagging little thing that won’t go away: the solutions often involve square roots of negative numbers.  Such solutions were long derided as “sophistic” or “fictitious” because they seemed nonsensical on their face.

To put in simply:

Ah, but then John Hubbard from Cornell added computers to the equation!  What do we have?  Why, fractals, of course!

In conclusion,

Hubbard’s work was an early foray into what’s now called “complex dynamics,” a vibrant blend of chaos theory, complex analysis and fractal geometry.  In a way it brought geometry back to its roots.  In 600 B.C. a manual written in Sanskrit for temple builders in India gave detailed geometric instructions for computing square roots, needed in the design of ritual altars.   More than 2,500 years later, mathematicians were still searching for roots, but now the instructions were written in binary code.

I love this stuff, don't you?