Clouds are not spheres, mountains are not cones, coastlines are not circles and bark is not smooth, nor does lightening travel in a straight line."

                      Benoit Mandelbrot

"This is a detail IN the Mandelbrot Set Fractal.
Detail is found by zooming in on the overall M Set image, finding edges&buds with interesting features.

Fractals are complex geometric shapes that exhibit patterns typified by self similarity or a tendency for the details of the shape to appear silimar to the shape itself.   Often the shapes resemble patterns occurring naturally in the physical world such as spiraling leaves, seemingly random coastlines,erosion and liquid waves.

Fractals are generated thru surprisingly simple underlying mathematical expressions producing subtle and spiraling patterns.

 The basic interative expression for the M. set is Z= Z squared + C operating in the complex (real, imaginary) number set."

Now that's a quote I found under that cool image.. now here's  the blurb from the Fractal Foundation Ed. pack as to How the Mandelbrot Set WORKS:

     " We start by plugging a value for the variable "C" into the simple equation below
                                                    Z new  = Z old (squared) +C
   Each complex number is actually a POINT IN A 2 DIMENSIONAL PLANE.
The equation gives an answer:  Znew.  We plug this back into the equation, as  'Z old' and calculate again. We are interested in what happens for different starting values of 'C'
   Generally, when you square a number, it gets bigger, and then if you square the answer, it gets bigger still. Eventually, it goes to infinity. This is the fate of most starting values of 'C'. However, some values of 'C' do not get bigger, but instead get smaller, or alternate between a set of fixed values. These are the points in the Mandelbrot Set which we COLOR BLACK   .  Outside the Set, all the values of  'C' cause the equation to go to infinity, and the colors are proportional to the speed at which they expand."

          Okay! That's the education for tonight! Coming up next? Who know.... that cloud image is from the front porch.. I'll see if I can find exactly WHY clouds are fractal rather than just claiming them so.... and thus again with water (oooh MORE cool images I have there.... )...... nite now.. and cheers.