Intro - Fractals and the Mandelbrot Set
---------------------------------------

    The Mandelbrot set is probably the most well-known example of an
iterated function: one where the next state depends on the current
state.  The equation of the Mandelbrot set is:

    Z = Z^2 + C

with Z and C being complex numbers.  To go from an equation to a
picture, treat the x,y coordinates of the display as representing
real,imag pairs from the complex plane.  Initialize Z to 0,0 and
C to the current display point, scaled by the magnification level,
and iterate the equation until either the magnutide of Z diverges
(if |Z| ever exceeds 4, it will continue to grow forever) or you're
satisfied that it won't.  If it diverged, plot the point with a
color representing the iteration count, otherwise it's in the set
so plot it black.

    That's all pretty simple.  The amazing thing about it is the
complexity that can arise from such simple rules.

    The Mandelbrot set is only one of a family of such systems.
Any iterated system (where the current state of the equation
depends on the previous state) can be treated similarly, and many
yield similarly complex and beautiful plots.


MeanderBot - the program
------------------------

    Installation is simple:  just unzip the included files into
your windows directory (\windows), then go to Control Panel, select
Display, choose Screen Saver, and then select MeanderBot from the
list.

    Configuring the options is pretty simple, too, because there aren't
a whole lot of them.

    o   Fractal Type - currently disabled, until I implement Julia sets.

    o   Max Iterations - must be between 1 and 1000; 50 or 100 are good
        numbers.  This determines how soon a point is declared to be in
        the Mandelbrot set.  Smaller numbers make quicker pictures, but
        may cause blurriness.  The number is automatically adjusted
        upwards based on the zoom level, to help prevent loss of resolution.

    o   Zoom Factor - Each succeeding display is a magnifaction of the
        previous one.  This factor determines how fast you zoom in.  It
        must be between 1 and 1000.  Values of 2, 5, or 10 are good.  Larger
        values zoom in faster.  Too large and it might lose track of the
        edge of the set; if that happens it will reset to full scale and
        start over.

    o   Registration Code - Once you've paid and received the code, enter
        it here to prevent the nag screen from showing.


Registering the software
------------------------

    Writing this was a labor of love, but even so I need to eat.  Future
versions and new features depend on my earning a few dollars from this
project.  Therefore, if you like it and would like to see it continue
and improve, please register.

    Send $7 (US) to:

    Kevin Kelley
    30703 Rd. 28
    La Junta, CO  81050

    Be sure to include your email or snail address so I can send your
registration code.


Distributing the Software
-------------------------

	This package may be freely distributed, as long as it is unchanged.
No parts may be added, modified, or removed, and no fee may be charged 
except to cover distribution costs.  Buying a cdrom that contains this
package does not represent purchase of this software.  To purchase it,
you must follow the instructions in 'Registering the software' above.


Contacting the author
---------------------

    Send email with comments and suggestions to:

    kelley@iguana.ruralnet.net