+======================== AVAILABLE COMMANDS ==============================+
| H  - Help!                          ? - Available commands               |
| SH - Show current settings          G - Generate picture                 |
| D  - Redisplay picture              Q - Quit                             |
|                                                                          |
| SR n / SI n / ER n / EI n - Starting and ending coordinates              |
| MX n / MY n - X/Y display size      MC n - Max examination count         |
| XR n / XI n - Shift coordinates     F  n - Dragon function               |
| ZR n / ZI n / ZB n - Zoom around the center point                        |
|                                                                          |
| CM n - Graphics mode                CS n - Color set #                   |
| CI n - Color increment              CD n - Color divisor                 |
| CO n - Color offset                 CR n r g b - Change individual color |
| CT n - Color for points in set      P  n - Start from Preset             |
|                                                                          |
| SA filename - Save set data         SQ filename - Save squeezed          |
| SC filename - Save color info       SP filename - Save preset            |
| LO filename - Load set data         <  filename - Redirect input         |
+==========================================================================+
>
                        Mandelbrot 3.00 Help System
                        ===========================

   Hello there!  I will be your guide through the magical land of self-
squared dragons.  This help system is organized in a hierarchial tree.
After each screen, you will see a list of additional topics.  You may
abbreviate a topic name to the least number of unambiguous characters.
When you select a topic, that screen will be displayed, perhaps with a list
of its additional topics.  Simply press <RETURN> by itself to exit help.

   Here we go!

/
Licensing
Author Information
Donations
Bug Reporting
General Information
Getting Started
Commands
.
>0
                           Mandelbrot 3.00
                           ===============

        Copyright (c) 1986, Robert S. French and Robert J. Mical
                         All Rights Reserved

   This program has been placed in the public domain.  It may be copied
and distributed as desired as long as this notice is retained.  No fee
may be charged for copies of this program, its use, or its source.
Programmers are welcome to use any routines from this program in their
own software as long as due credit is given at the source code level.
No warranties, either express or implied, accompany this software.  The
user is completely responsible for any and all damage incurred during the
use of this program.

   Please direct questions to the addresses in the "Author Information"
section.
/
.
>1
                               Authors
                               =======

Name:    Robert S. French              Name:    Robert J. Mical
Address: 2740 Frankfort Avenue         Address: Commodore-Amiga, Inc.
         Louisville, KY  40206                  983 University Avenue
Phone:   (502) 897-5096                         Los Gatos, CA  95030
ARPA:    French#Robert%d@LLL-MFE
         RFrench@MIT-MULTICS
UUCP:    ... ihnp4!ptsfa!well!french

Robert French is the author of several Amiga public domain programs,
including MULTIDIM, and TREE.

Robert Mical is the author of the Amiga user interface, Intuition, as well
as Graphicraft.
/
.
>2
                              Donations
                              =========

   By the very nature of public domain software, its authors rarely realize
any monetary reward for their work.  All software development is performed
during valuable free-time.  As such, donations are actively solicited, but
are in no way required.  Please send any donations to Robert S. French
(address in the Author Information section).  A donation will register you
as an official owner of this program, and will entitle you to notices of
program updates, bug fixes, and other public domain product announcements.
Thank you for your support of the Amiga and the public domain concept.
/
.
>3
                             Bug Reports
                             ===========

   Bugs should be reported to Robert French at one of the addresses listed
in the "Author Information" section.  The following information would be
greatly appreciated:

* Type of error that occurred (Guru # if applicable)
* Place where error occurred
* Environment (machine size, hardware connected, other programs running
               concurrently)
* Program environment (color settings, area of analysis, etc.)
  This information may be obtained using "SH" or "SP".
* Operating System version
* Compiler brand and version

   All bug reports will be investigated and responded to.
/
.
>4
                            General Information
                            ===================

   This program displays in graphical form a region of the complex plane.
Each point is carried through a number of iterations with the transformation
Z = Z^2-u, where Z is initially 0 and u is a point on the plane.  The
iterations continue until either |Z| (the distance of Z from the origin) is
greater than 2, or a certain maximum number of iterations has been exceeded.
The number of iterations determines the color at any given point.  If the
maximum number of iterations is exceeded without |Z| becoming greater than
2, the point is considered to be "in the set."  The edge of this set,
called by many the "Mandelbrot set" after its inventor, Benoit Mandelbrot,
is a "fractal."
/
Mandelbrot
Mathematics
Fractals
Bibliography
.
>40
                            Benoit B. Mandelbrot
                            ====================

   Benoit B. Mandelbrot is an IBM Fellow at the Thomas J. Watson Research
Center in Yorktown Heights, New York.  He has been hailed as "the father
of fractals" and was recently elected a Fellow of the American Academy of
Arts and Sciences.  His research has concentrated on extreme and unpredic-
table irregularity in natural phenomena in the physical, social, and
biological sciences.

(  Mandelbrot, Benoit B.  The Fractal Geometry of Nature.  W.H. Freeman
      and Company, 1983.  )
/
.
>41
                         Mathematical Interpretation
                         ===========================

   Technically speaking, the name for this set is a "Self-Squared Dragon."
The properties of self-squared functions were first investigated by Fatou
in the early 1900's.
   This particular function can be stated as the set of all points in the
complex plane such that the iterates of
                              2
         z  = 0  under  z -> z -u   (z and u complex)
          0
fail to converge to infinity.  It has been proven that if, at any time,
the point z strays outside of the circle of radius 2 centered at the
origin, the iterates of the function must inevitably converge to infinity.
Thus, since computers are not adept at counting to infinity, a good
boundary condition can be defined.
/
.
>42
                              Fractals
                              ========

   The term "fractal" refers to a variety of shapes, surfaces, hyper-
surfaces, etc., that have a specific "fractal dimension."  Fractal
dimensions differ from topological dimensions in that topological dimensions
are always integer, while fractal dimensions can take on any positive real
value.  They were in invented by Benoit Mandelbrot (q.v.) to describe
irregular things in nature, such as mountains, clouds, line noise, static,
and coastlines.  They are particularly suited to computers because of either
their inherently random nature or their self-similar regularity (depending
on what kind of fractals you are discussing).
/
.
>43
                            Bibliography
                            ============

       (This is only a cursory overview of the available articles)

Dewdney, A.K.  Computer Recreations.  Scientific American, August 1985.
   pp. 16-20.

Mandelbrot, Benoit B.  The Fractal Geometry of Nature.  W.H. Freeman and
   Company, 1983.

McDermott, Jeanne.  Geometrical forms known as fractals find sense in
   chaos.  Smithsonian,  December, 1983.  pp. 110-117.

Sorensen, Peter R.  Fractals.  Byte, September, 1984.  pp. 157-72.
/
.
>5
                           Getting Started
                           ===============

   You only need to know a few commands in order to start producing very
nice looking pictures.  The easiest method is to use the built-in presets.
To do this, type "P n" at the "Command: " prompt.  For example:

   Command: P 2          ;Set preset 2

   This will set you up with preset number 2.  You will see the preset
being loaded.  To view the preset, enter the "G" command.  "G" stands
for "Go" and is used whenever you wish to see a new picture.  Most of the
presets are designed for the maximum size of the screen.  Thus, the pictures
may take upwards of 25 minutes to draw.  If you wish to see the picture on
a smaller scale, you use the MX and MY commands.
/
Next
.
>50
   The MX command sets the size of your picture in the X (horizontal)
direction, and the MY command sets the size of your picture in the Y
(vertical) direction.  For example:

   Command: MX 50        ;Set X size to 50
   Command: MY 30        ;Set Y size to 30

   This will draw the next picture with a size of 50x30.  It will be drawn
MUCH faster than a full-screen picture (perhaps in 10 seconds).  The
picture you see is determined by the region of the complex plane you select
to view (see Background Information for more info).  Thus you must have
the ability to select the starting and ending points for the real and
imaginary axis.  The SR, ER, SI, and EI commands serve this purpose.
/
Next
.
>500
   The SR command sets the Starting point on the Real axis; the ER command
sets the Ending point on the Real axis.  The ER and EI commands perform
similar functions for the imaginary axis.  For example, to view the
region with -1 + 1.5i as the top left corner and 1 - .5i as the bottom
right corner, you would enter:

   Command: SR -1        ;Set Starting Real
   Command: ER 1         ;Set Ending Real
   Command: SI -.5       ;Set Starting Imaginary
   Command: EI 1.5       ;Set Ending Imaginary

   Many more commands are available to do such things as change the colors,
save pictures, and create presets.  Type "?" at the "Command:" prompt
to see a list of the available commands.  Pull-down menus are also available
while a picture is being displayed.  Read the "Commands" section of <H>elp
for more information.
/
.
>6
                          Command Summary
                          ===============

   A quick-list of available commands may be obtained by using the "?"
command at the main prompt.  Below are the various categories of commands.
Within each are specific commands, their usage, and examples.
/
Setting Boundaries
Color and Graphics
Saving and Loading
Shifting and Zooming
Generating the Picture
Miscellaneous
.
>60
                         Setting Boundaries
                         ==================

   The following commands are used to change the minimum and maximum
real and imaginary coordinates, and the X and Y resolution of the displayed
screen.
/
SR - Starting Real
ER - Ending Real
SI - Starting Imaginary
EI - Ending Imaginary
MX - Maximum X
MY - Maximum Y
.
>600
                       SR - Starting Real value
                       ========================

   The SR command is used to set the starting (leftmost) real value for
the Mandelbrot function.  It accepts a positive or negative real number
as an argument.  Example:

   Command: SR -0.5
/
.
>601
                        ER - Ending Real value
                        ======================

   The ER command is used to set the ending (rightmost) real value for
the Mandelbrot function.  It accepts a positive or negative real number
as an argument.  Example:

   Command: ER 2.5
/
.
>602
                      SI - Starting Imaginary value
                      =============================

   The SI command is used to set the starting (bottommost) imaginary value
for the Mandelbrot function.  It accepts a positive or negative real number
as an argument.  Example:

   Command: SI -1.25
/
.
>603
                       EI - Ending Imaginary value
                       ===========================

   The EI command is used to set the ending (topmost) imaginary value for
the Mandelbrot function.  It accepts a positive or negative real number as
an argument.  Example:

   Command: EI 1.25
/
.
>604
                          MX - Maximum X size
                          ===================

   The MX command is used to set the number of horizontal pixels used to
generate the picture.  The value must be between 30 and the horizontal
resolution of the current graphics mode (see the CM command).  Example:

   Command: MX 100
/
.
>605
                           MY - Maximum Y size
                           ===================

   The MY command is used to set the number of vertical pixels used to
generate the picture.  The value must be between 30 and the vertical
resolution of the current graphics mode (see the CM command).  Example:

   Command: MY 100
/
.
>61
                        Color and Graphics Commands
                        ===========================

   The following commands are used to change the color palette and graphics
resolution of the displayed screen.
/
CM - Graphics Mode
CS - Color Set
CR - Color Register
CO - Color Offset
CI - Color Increment
CD - Color Divisor
CT - Color in Set
.
>610
                          CM - Graphics Mode
                          ==================

   The CM command is used to set the graphics mode.  Its argument is a
single number between 0 and 7 inclusive, derived as follows:
   * Start with 0
   * If you do not want Hold and Modify (4096 color) mode, add 1
   * If you want an interlaced display (400 vertical resolution), add 2
   * If you want a hi-res display (640 horizontal resolution), add 4
   Since Hold and Modify is not available in hi-res, color modes 4 and 6
are illegal.  Example:

   Command: CM 5          ;Set 640x200 16-color display
/
.
>611
                            CS - Color Set
                            ==============

   The CS command is used to select the default color set.  Its argument is
a single number between 0 and 2 inclusive, as follows:
   * 0 - Colors 0-4095 are the sequence of RGB values determined by the
         color number (high 4 bits are red, next are green, low 4 bits are
         blue)
   * 1 - Colors 0-4095 are the repeating sequence of black, 15 blues, 15
         greens, 15 reds, 15 cyans, 15 magentas, 15 yellows, and 15
         whites
   * 2 - Colors 0-15 or 0-31 are user-defined by the CR command or the
         Modify Colors pull-down menu
   Example:

   Command: CS 1
/
.
>612
                           CR - Color Register
                           ===================

   The CR command is used to set the 16 or 32 color registers used while
in color set 2 (see the CS command).  The format is:

   CR color red green blue

   Color is the color number (0-15 or 0-31), red is the red content (0-15),
green is the green content (0-15) and blue is the blue content (0-15).
Example:

   Command: CR 3 15 8 0
/
.
>613
                            CO - Color Offset
                            =================

   The CO command is used to set the color offset for the first color
used (iteration count 1).  It can be between 0 and 4095 inclusive, but the
maximum count (MC) times the color increment (CI) plus the color offset
(CO) must not exceed 4095.  Example:

   Command: CO 91
/
.
>614
                           CI - Color Increment
                           ====================

   The CI command is used to set the color increment between each
iteration count.  For example, if CI is 5, then an iteration count of 2
would reference color register 10.  It can be between 0 and 4095 inclusive,
but the maximum count (MC) times the color increment (CI) plus the
color offset (CO) must not exceed 4095.  Example:

   Command: CI 3
/
.
>615
                            CD - Color Divisor
                            ==================

   The CD command is used to set the divisor for the color registers.  For
example, if CD is 2 then color register 5 would be equal to color 10.
Example:

   Command: CD 1
/
.
>616
                            CT - Color in Set
                            =================

   The CT command is used to set the color given to points that are in
the Mandelbrot Set.  Example:

   Command: CT 0
/
.
>62
                            Saving and Loading
                            ==================

   The following commands are used to save and load data sets, colors, and
presets.
/
SA - Save Data
SQ - Save Compressed
LO - Load Data
SP - Save Preset
SC - Save Colors
P - Load Preset
Redirection
.
>620
                             SA - Save Data
                             ==============

   The SA command is used to save the current set data (iteration counts).
It takes a single filename as an argument, and saves the contents of SR,
ER, SI, EI, MX, and MY.  It may be directly reloaded by the LO command.
Example:

   Command: SA MandData1
/
.
>621
                           SQ - Save Compressed
                           ====================

   The SQ command is used to save the current set data (iteration counts)
in a run-code compressed format.  It takes a single filename as an
argument, and saves the contents of SR, ER, SI, EI, MX, and MY.  It may
be directly reloaded by the LO command, but due to the virtual memory
handling the loading will take significantly longer than a file saved with
SA.  Example:

   Command: SQ MandData1
/
.
>622
                             LO - Load Data
                             ==============

   The LO command is used to load set data previously saved with SA or SQ.
The contents of SR, ER, SI, EI, MX, and MY are restored.  Example:

   Command: LO MandData1
/
.
>623
                             SP - Save Preset
                             ================

   The SP command is used to save all user-definable information, including
color settings, into the indicated file.  Example:

   Command: SP Preset5
/
.
>624
                             SC - Save Colors
                             ================

   The SC command is used to save the contents of CI, CO, CS, CM, CD, CT,
and all CR's.  Example:

   Command: SC Color1
/
.
>625
                             P - Load Preset
                             ===============

   The P command is used to load a preset saved with the SP command.  It
essentially takes the numeric argument and appends it to the end of the
string "Preset", and then performs an input redirection with that filename.
Thus preset 5 must be stored in the file "Preset5".  Example:

   Command: P 5
/
.
>626
                              Redirection
                              ===========

   The < command is used to specify a file for input redirection.  This
means that all subsequent commands will come from this file until the
end of file is reached.  Redirections may perform other redirections,
but they do NOT nest.  Comments in an input file may be indicated by a
leading semicolon.  Example:

   Command: < File1
/
.
>63
                         Shifting and Zooming
                         ====================

   The following commands are used to shift the picture by a certain aomunt
or to zoom in on a center point:
/
XR - Xlate Real
XI - Xlate Imaginary
XB - Xlate Both
ZR - Zoom Real
ZI - Zoom Imaginary
ZB - Zoom Both
.
>630
                         XR - Translate Real
                         ===================

   The XR command is used to move the real axis by a certain amount.  Both
the starting and ending real values are displaced by this amount.  Example:

   Command: XR .0125
/
.
>631
                       XI - Translate Imaginary
                       ========================

   The XI command is used to move the imaginary axis by a certain amount.
Both the starting and ending imaginary values are displaced by this amount.
Example:

   Command: XI -.0125
/
.
>632
                         XB - Translate Both
                         ===================

   The XB command is used to move both the real and imaginary axis by a
certain amount.  All four coordinates are displaced by this amount.
Example:

   Command: XB .09
/
.
>633
                            ZR - Zoom Real
                            ==============

   The ZR command is used to zoom the real axis about the center of the
starting and ending points.  Example:

   Command: ZR .5
/
.
>634
                          ZI - Zoom Imaginary
                          ===================

   The ZI command is used to zoom the imaginary axis about the center of
the starting and ending points.  Example:

   Command: ZI 2
/
.
>635
                             ZB - Zoom Both
                             ==============

   The ZB command is used to zoom both the real and imaginary axes about
the center of the display.  Example:

   Command: ZB .5
/
.
>64
                          Generating the Picture
                          ======================

   The following two commands are used to generate and display the
picture:
/
G - Generate
D - Display
.
>640
                              G - Generate
                              ============

   The G command is used to actually draw the picture which has been
defined by the various system parameters.  It processes each pixel and
determines the proper iteration count.  This may take a VERY long time
(over 4 hours) depending on the complexity of the chosen area and the
screen resolution.  Example:

   Command: G
/
.
>641
                               D - Display
                               ===========

   The D command is used to redisplay (in 2 dimensions) a picture which
has already been computer with the G command or loaded with the LO command.
This is useful if you wish to change the color settings which are not
accessible from the pull-down menus and do not wish to regenerate the
iteration counts.  Example:

   Command: D
/
.
>65
                             Miscellaneous
                             =============

   The following commands perform various system functions:
/
? - Display Commands
H - Get Help
SH - Show Settings
Q - Quit Program
.
>650
                          ? - Display Commands
                          ====================

   The ? command will display a concise list of the available commands.
Example:

   Command: ?
/
.
>651
                              H - Get Help
                              ============

   The H command is used to get more detailed help on various aspects of
running the program.  The help file is arranged in a "tree", and each
help screen may have additional topics on which help is available.
Example:

   Command: H
/
.
>652
                            SH - Show Settings
                            ==================

   The SH command is used to show the current settings of various
system parameters.  Example:

    Command: SH
/
.
>653
                             Q - Quit Program
                             ================

   The Q command is used to exit the Mandelbrot program.  It releases
all system resources and deletes the temporary file, if it exists.  Example:

   Command: Q
/
.
