Mandelbrot set:  (see last section of the book)
      (occurs in nature!)
	A simple fractal based on the equation:
	    Z(n+1) = Zn*Zn+Z0  where Z is an arbitrary starting value:
	      e.g. starting at Z0 = -2, we reach 2,2,2,2,2,2.....

              Z0's that stay below 2 are considered IN THE SET...
	      Z0s  that go outside of 2 are consider OUT OF THE SET.
		(this is called the escape set)
		 (the faster a node leaves the set is its "temperature".)

      Consider  -1. Is it in the Mandelbrot set?
	   z0 = -1
	   z1=  1 - 1 = 0
	   z2  = -1    (we are in a dynamic equilibrium  between -1,0...) so -1
	   is in the Mandelbrot set.

      Consider 1
	 z0 = 1
	 z1 = 1+ 1 = 2
	 z2 = 4+1 = 5....   (so 1 is NOT in the Mandelbrot set).

    =======================
    But we can also have complex numbers in the Mandelbrot set.
      recall that (a+bi) squared = (asquared - bsquared + 2abi)

    Is i in the Mandelbrot set??
	   z0 = i
	    z1 = z0squared + z0
	       =  -1 + i
            z2 = z1squared + z0
	       =  0 + -2i  + i
	       = -i
            z3 = z2squared + z0
	       =   1   + i
            z4 =  z3squared + z0
	       =   (0 + 2i) + i = 3i   (which is too big)

              thus i is NOT in the Mandelbrot set...