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fractal.txt
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1992-02-26
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------------------------------------------------------------------
FRACTAL.EXE
------------------------------------------------------------------
FRACTAL.EXE can generate three different types of fractals:
Mandelbrot, Julia, and Lyapunov. FRACTAL.EXE is not meant as
general fractal exploration devices. It was written as a means
of generating landscape for use with VistaPro. You can control
several of the parameters of the fractals. After saving them
they can be further manipulated by VistaPro.
All three types of fractals are mathematical objects. They have
infinite complexity (although the calculating precision of
computers limits the amount of complexity that can be rendered)
and can make for interesting and unusual landscapes. These
fractal landscapes use a different method of generation than
VistaPro does. VistaPro's fractal landscapes are intended to
mimic real landscapes but FRACTAL.EXE's are just "pictures" of
the three mathematical objects.
FRACTAL.EXE uses the same type of graphical user interface as
VistaPro. It also uses the same file requestor. You can refer
to the VistaPro manual for general instructions on how menus,
buttons, and gadgets work. FRACTAL.EXE requires a VGA graphics
card and a Microsoft compatible mouse.
This document makes no attempt to explain what these fractals
are or the mathematics behind them. You should be able to find
many books at your local bookstore which describe fractals and
iterated functions.
------------------------------------------------------------------
PROJECT MENU
------------------------------------------------------------------
Project --> Spawn DOS
---------------------
This menu item allows you to start a DOS command line while
keeping FRACTAL.EXE in memory. When you return to FRACTAL.EXE
all your settings will be intact. This function allows you to
perform any DOS functions without quitting FRACTAL.EXE. For
instance, you could format a new diskette for saving your
landscapes. To exit from the DOS and return to FRACTAL.EXE you
should type EXIT at the DOS prompt.
Project --> Save DEM
--------------------
This item saves the current landscape as a VistaPro DEM file.
You will be allowed to select the directory and filename of the
file using the file requestor.
Project --> Quit
----------------
Select this item when you are done exploring and wish to quit the
program.
------------------------------------------------------------------
FRACTAL MENU
------------------------------------------------------------------
Fractal --> Lyapunov
--------------------
This item selects the Lyapunov type landscape. It also resets
many the settings on the control panel to the defaults for this
type of landscape.
Fractal --> Mandelbrot
----------------------
This item selects the Mandelbrot type landscape. It also resets
many of the settings on the control panel to the defaults for this
type of landscape.
Fractal --> Julia
-----------------
This item selects the Julia type landscape. It also resets many
of the settings on the control panel to the defaults for this type
of landscape.
------------------------------------------------------------------
HEIGHT MENU
------------------------------------------------------------------
Height --> Linear
-----------------
This menu item selects linear heights in the landscape.
Calculated values are used exactly as is in the landscape. For
example, a mandelbrot escape time of 10 becomes 10 meters, 20
becomes 20 meters etc.
Height --> Sqrt
---------------
This menu item selects square root heights in the landscape. The
sqare root of calculated values are used in the landscape. For
example, a mandelbrot escape time of 9 becomes 3 meters, 16
becomes 4 meters etc. Use this altitude type if you want to
compress a wide range of altitudes into a smaller range.
Height --> Log
--------------
This menu item selects logrithmic heights in the landscape. The
log (base 10) of calculated values are used in the landscape. For
example, a mandelbrot escape time of 10 becomes 1 meter, 100
becomes 2 meters etc. Use this altitude type if you want to
compress a very wide range of altitudes into a smaller range.
------------------------------------------------------------------
CONTROL PANEL
------------------------------------------------------------------
Lyapunov Control String
-----------------------
This is the control string which determines which of the two
lyapunov equations is executed for each iteration. Only the
least sinificant bit of each character is acually used so the
letter "a" is the same as the letter "c" is the same as the
letter "e" etc.... and "b" = "d" = "f" etc.... All you really
need to know is that changing this character string will change
the landscape -- different control strings will lead to different
landscapes. We allow you to use all letters of the alphabet so
you can generate landscapes based on your name or any text that
you want. This string is only used in the generation of lyapunov
landscapes.
Start X
-------
The topographic map area is a window onto the two dimesional
mathmatical plane. Start X is the coordinate of the horizontal
coordinate of the left edge of the topographic window. You can
reposition the window by typing a new value into this gadget.
Gererally, all the intersting parts of all three fractal types
fall within the range of -2 to +2 on both the X and Y axis.
Start Y
-------
The topographic map area is a window onto the two dimesional
mathmatical plane. Start Y is the coordinate of the vertical
coordinate of the bottom edge of the topographic window. You can
reposition the window by typing a new value into this gadget.
Gererally, all the intersting parts of all three fractal types
fall within the range of -2 to +2 on both the X and Y axis.
Size
----
This value controls the range (on the X and Y axis) that the
topographic window covers. For example, a value of 2.0 means
that the window will cover a range of 2.0 accross the X and Y
axis of the topographic map. If the Start X value is 1.0 then
the window will cover the range from 1.0 to 3.0 on the horizontal
axis.
Julia X
-------
This represents the coordinate on the Mandelbrot set for which
the gernerated Julia set is based. This is the "real" part of
the coordinate. As with the Start X value, most of the
interesting values will range from -2 to +2. This value is only
used in generating Julia landscapes.
Julia Y
-------
This represents the coordinate on the Mandelbrot set for which
the gernerated Julia set is based. This is the "imaginary" part
of the coordinate. As with the Start Y value, most of the
interesting values will range from -2 to +2. This value is only
used in generating Julia landscapes.
Seed
----
This is starting value used to generate Lyapunov landscapes. It
should be set between 0 and 1. It's value becomes less and less
critical as the interation count is raised.
Iteratns
--------
This controls the maximum number of iterations allowed before
"timing out" on calculations of all three objects. The larger
you make this value the longer calculations will take -- but
larger values will also bring out additional detail.
VScale
------
This controls the vertical scale of the landscape. Large values
will result in landscapes with tall features, smaller values will
result in flatter landscapes. This setting is used for all three
fractal types. "Good" values range from 1000 to 5000 but you are
free to enter small or larger values.
Zoom Var
--------
This is the variable zoom function. It allows you to zoom into
or out of a section of the fractal object. After selecting the
button you must mark a box on the topomap to zoom in to. Use the
mouse (position and click the left mouse button) to select both
corners of the area of interest. If you mark an area smaller
than the topographic map you will zoom in to that area. If you
mark an area larger than the topographic area you will zoom out
to that area. Zooming in or out changes the Start X, Start Y,
and Size variables. Generation of the new area will start
automatically.
Zoom +2x
--------
This button allows you to zoom in two fold onto the fractal
object. After selecting the button you must select the area to
zoom into by moving the visible box over the area of interest and
pressing the left mouse button. Zooming in or out changes the
Start X, Start Y, and Size variables. Generation of the new area
will start automatically.
Zoom -2x
--------
This button allows you to zoom out two fold onto the fractal
object. You have no further choise of area, the window is simply
expanded two fold around the current center of the topographic
window. Zooming in or out changes the Start X, Start Y, and Size
variables. Generation of the new area will start automatically.
Generate
--------
This initiates the generation of a new fractal landscape using
the current settings. Generation is not automatic when you
change some of the settings since it is assumed that you might
also want to change some of the other settings. In these cases
you will need to use the Generate button to start calculating a
new landscape.
Escape
------
You can press the escape key to terminate the generation of the
current landscape. When the program is done with the current
horizontal line it will stop calculating and you will be able
to change other settings or quit.