Wondering About Fractals.

What is a fractal?  There are two basic designs that I am aware of.  One is created by nature and the other is created by mathematics (man).  I like fractals and think that they are really pretty.  My wife used to make cards and sometimes she would draw multi-colored fractals on them.

One way to produce a fractal is to come up with a mathematical formula and feed it into a computer and, if you know what you are doing, you can come up with something that looks like this:

Or this:

Or this:

 But nature is really very good at coming up with fractal designs, like this:

 And this next one is even better, don't you think?

But the one that nature comes up with that everyone can relate to is the way water freezes into designs, whether a snow flake or the surface of a puddle or the outside of a window.  You know, something like this:

I sure hope that we will not see that cold object in that last picture down here in warm and sunny Texas. . . but who knows, I have seen snow and ice here before.  Granted, it is rare but every so many years, there seems to be an extra cold spell blow in here from the arctic circle.  You do know that the only thing between the north pole and here in Texas are few strands of barbed wire. . . Yes, I know it is in the 70's here and the humidity is high.  Maybe that last picture will help cool you off a bit.  Now, have a great day, you hear?