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Fractal/!Fractal/Help/!MainHelp/Readme
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File contents
________________________________________________________________________
/ \
| !Fractal v0.24: General Fractal Plotter |
| March 1992 |
| by Mike Curnow |
\________________________________________________________________________/
Introduction
============
!Fractal is designed to be a universal fractal generator. !Fractal has two
purposes. Firstly to provide you with a comprehensive application to examine
fractal functions and images. Secondly it is designed as a platform for
fractal programmers to add their own routines. This enables these routines
to get immediate Wimp access and support of the 3d functions etc.
A brief guide to usage.
----------------------
Double click on the filer icon to load, which will display the initial
fractal (a Mandelbrot). Select a 256 colour mode from the !Palette
application to see the image correctly. Alternatively you can click with
Adjust over the icon bar to open a full screen window (though still in
desktop mode). Clicking with Select re-opens the main window if closed.
Most of the main functions of !Fractal can be performed from the Tools pane
on the left. The main menu provides access to all of these functions and
more.
To Zoom in click with Select over the 1st tool icon, or use Adjust to zoom
out. A zoom box will appear - use the left mouse button to shrink the zoom
box, and the right button to enlarge it. Press the middle button to start
the redraw operation. The machine will be locked until the redraw is
complete or until you press Adjust, at which point multi-tasking mode will
be entered. Note that some functions never end until you select Image->Stop.
Also note that when in full screen mode the desktop is still active - its
just that the other windows are hidden. To close the full screen window
select Display->Hide.
The screen can be saved by using the Image->Save option. Saved drawings may
be reloaded by simply dragging the saved sprite onto the !Fractal icon,
allowing zooming to re-commence.
Full Operation Information
==========================
!Fractal requires a considerable amount of storage : 200k for code,
2*sprite image size (depends on mode), 1 or 2 banks of screen memory, and
60k for the shared C library, so be prepared. Some functions are disabled if
there is insufficient memory. To save space, some functions load their data
on first selection, so be prepared for further disk activity.
The fractal plot is displayed either in a full screen window, which may be
hidden at any time by selecting Hide from the menu, or in a standard
re-sizeable window. The colours will look strange if you are not in a 256
colour mode - no attempt is made to match the desktop colours so as to
retain as much image detail as possible.
When an image is re-drawn !Fractal attempts to enter the image mode to
allow the image generation to be seen. To avoid out of memory problems it
may be best to pre-select this mode from the Palette task or from the
'Options->Full screen mode' when in full screen mode. If the image size
is different from the screen size, then no attempt is made to show the
re-draw as it proceeds.
Automatic Last Display Save
---------------------------
Most operations which modify the current image will save it in memory. The
prior image may be recalled by selecting Display->Previous from the menu.
Thus you can zoom in to inspect an area, then quickly back out to the
previous display. To maintain further images use the load and save
facilities.
Tools
=====
The tools pane provides quick access to functions. For full details see the
corresponding function in the Menu section. The various tools are, in
descending order:
Zoom: click with Select to zoom in, Adjust to zoom out. Repeat the click to
cancel the zoom.
Mandelbrot: click on this to redraw an image after you have changed
parameters or function. The icon is displayed in reverse when plotting is
active. To stop a plot click on the icon again (after clicking Adjust to
return to desktop mode).
Wheel: enters colour cycling mode. Press menu to exit, or use the Select and
Adjust buttons to pause or change direction respectively.
Numbers: opens the data entry panel for the current function.
Palettes: 10 different display palettes can be chosen. These do not change
the image itself, merely the way it is shown on-screen. Press Adjust to
invert the selected palette - press Adjust again to re-invert.
Palette Shift (striped colours): Use Select to increment the colour by 1
(small stripes) or 8 (large stripes), and Adjust to decrement by 1 or 8. To
reset the shift, click on a display palette.
Rotation: shows the current rotation viewing angle with two icons to adjust
the viewpoint. This icon is used directly by the 3d drawing functions (such
as Lorenz) and image manipulators (such as 3d_View). You can also use this
tool at any time to rotate the current image on display - simply
double-click on the Rotation icon itself. Some clipping of the image is
inevitable and repeated rotation will result in the loss of image quality.
Rotation Arrows: Clicking with Select steps by 15 degrees, whilst Adjust
steps in 5 degrees. Keeping the button pressed will continuously move the
viewpoint. The left-hand adjust icon rotates clockwise, the right-hand icon
moves anti-clockwise. The new angle takes effect when you redraw the image.
Elevation: shows the current elevation viewing angle, as used by the 3d
functions. Use Select and Adjust as with the Rotate icons, stepping by 15 or
5 degrees respectively. The new angle takes effect when you redraw the
image. Some functions limit the elevation range.
Menus
=====
The icon bar menu shows the program Info window, access to the Help files
and the Quit option. The main menu is available from any !Fractal window.
The Main Menu
----------------
The menu options are available from the desktop or full screen window.
Pressing Adjust instead of Select will keep the menu open. Many selections
reset the image - to perform a redraw select Re-draw.
fractal: The currently selected fractal name appears as a menu selection.
Some fractal functions offer their own menu selection. Refer to the help
application !Functions for details.
----------------------------------------------
FUNCTION: Selects the Fractal function to be used. Reloading a saved sprite
automatically sets the function to that which created the sprite. When
switching back to a function, the function variables will be the same as
previously, allowing you to switch between functions without losing your
position.
----------------------------------------------
IMAGE: Controls the factors used to create the image such as the variables.
The image is held internally as a sprite which can be saved in AFG2 format.
ZOOM IN and ZOOM OUT:
Activates the zoom box and re-plotting process where supported by the
fractal function. Moving the mouse moves the box, even beyond the edge of
the image. The mouse buttons have the following effect:
Left: Zoom box in
Middle: Start zoom
Right: Zoom box out
When zooming out the box represents the current image size. The information
window at the top of the screen shows the bottom left x & y values and the
width and height, as used by the Fractal function.
On pressing Menu the new display will be drawn in dedicated mode (which is
the fastest) until you press Adjust, at which time desktop mode is
re-entered. The plotting will continue in the background and the screen will
not be automatically updated.
To see the state of the display when in background mode click on one of the
display palettes. When you are in desktop mode a time counter shows the
progress on the icon bar.
Background plotting allows you to carry on using other desktop applications,
though you will notice some reduction in speed (Nb. entering commands such
as *BASIC will halt all desktop operations!). Background plotting will take
much longer.
REDRAW: causes the image to be re-generated using the current data
variables. Same as clicking on the Mandelbrot tool icon.
STOP: Halts a redraw. You can only restart from the beginning using REDRAW.
Clicking on the Mandelbrot icon when it is displayed in reverse has the same
effect.
DATA: Leads to a data entry panel allowing you to directly enter the
function variables - these are dependant on the function being used. Use
!Fractal's standard editing keys to move around the panel (see later).
Select Ok to enter the variables and have them verified. Press Redraw to
enter the data and start plotting. Use Initial to return to the default
values for the function or Inital Zoom just to reset the zoom size.
SAVE: Leads to a standard dialogue panel to allow the current image and data
variables to be saved as an AFG2 sprite. Sprites can be re-loaded by
dragging onto the !Fractal icon.
MODE & SIZE: Images can be generated in any 256 colour mode, including
multi-sync and custom overscan modes. This allows different resolutions to
be chosen as desired. Alternatively you can set the image size (in pixels)
via the SIZE entry - the size is limited only by memory. Small sizes help
speed up plotting. When using custom sizes you will not see the image being
replotted on screen, nor can you see all of the image in one go if it is
larger than full screen. A zoom feature may be provided at a later date to
handle this.
---------------------------------------------
EFFECTS: This menu entry allows manipulation of the generated image and
controls the 3d aspect.
3d DETAILS: Leads to a panel giving control over the 3d plotting. See the
section on 3d plotting for full details.
PALETTE: Leads to a selection of palette types. This performs a permanent
change of the image to the new palette. Note that this process may not be
reversible, though !Fractal will attempt to perform the translation as best
as possible if the initial palette is not the default. The display palette
should be reset to Default to see the colours correctly. This option is
provided primarily for saving images, or for inverting the palette for the
3d drawing routines. NB. The palette is reset to Default when the image is
re-drawn. External palettes may also be used - see the Palettes section.
To invert an image palette press Adjust over Default (assuming the Default
palette is not already in inverse order). In fact using Adjust converts the
image using the inverse of the selected palette (ie. the colours are in the
opposite order).
PAL. SHIFT: Leads to a submenu of palette changes. This allows the palette
colours to be permanently shifted up or down as required.
CYCLE 255 & 256: Allows the image colours to be stepped through. 255 does
not cycle black to avoid flicker but is slightly slower. To speed up the
rate try using a lower resolution display mode. When in cycle mode the mouse
keys act as follows:
Select: Halt cycling. Press Adjust to restart.
Menu : Exit cycling and restore the image colours.
Adjust: Reverse the direction of cycling.
Two screen banks will be used if there is sufficient memory to avoid
flicker. Note that in Modes 21, 24, 28 etc this is not possible due to the
480k VIDC limit. In other modes, if you get flicker, try to free up memory
using the task manager.
Colour cycling will work in non-default display palettes as long as the
image is normal screen size and the image mode can be entered. This can
produce some amazing effects - try the Fault function with different
palettes for example. This palette cycling feature is slower than using
straight image colour cycling. If palette cycling cannot be performed,
normal image cycling will be used which will produce strange results since
the cycling does not step through the palette, but merely increments the
displayed colours.
-----------------------------------------------
DISPLAY: Controls the image display, with these options:
PREVIOUS: If a previously plotted image exists, then you can select this to
quickly re-display it. To save older images, use the Save dialogue. If there
is insufficient memory available, this function is disabled.
PALETTE: Leads to a selection of palette types. This allows the current
image to be viewed with a different palette, but without actually modifying
the image itself, thus retaining the image detail. This method of palette
control is to be preferred over the permanent change provided by
Effects->Palette. This option only works when in a 256 colour mode.
With Default the colours are in the physical colour order (as seen in
!Paint). With RGB the colours step through the 4 Tints, Red, Green & Blue in
that order. With Logical the colours are in the same order as used with
COLOUR & TINT, ie. step through RGB in the 4 tints. Pressing Adjust rather
than Select uses the colours in the reverse order (ie. inverted). See the
Palettes section for details on the External palette.
PAL. SHIFT: Leads to a submenu of palette changes. This allows the palette
colours to be temporarily shifted up or down as required. Re-select the
display palette to cancel. This option only works when in a 256 colour mode.
Palette shifting is useful with the Landscape palette to get a balance
between sea and land.
HIDE: Closes the full screen window when open. This can be done even while
plotting is going on.
FULL SCREEN: Click on this to see the image in full screen mode.
Alternatively click with Adjust over the icon bar icon.
----------------------------------------------
OPTIONS: Leads to a panel listing the options currently in effect. Click on
the button to turn an option on/off. Press OK to enter your settings or Save
to make them permanent.
X/Y Guessing: Some functions such as Mandelbrots plot a pixel by pixel. With
X/Y Guessing a rough image is drawn and then the detail is filled in,
guessing if possible the colour in between. Not only does this allow you to
quickly see the image, but it is also up to 4 times quicker. The downside is
a slight loss in accuracy, so an option is provided to turn this mode off,
in which case each pixel will be drawn in sequence.
Tools Window: Allows the tools window to be turned on and off.
Previous Image Save: turns off the internal image storing feature which
helps to reduce memory requirements.
Full Screen Mode: The full screen display mode can be selected from any 256
colour mode. The default is the same as the image mode. When the display
mode is different from the image mode, the image mode will be entered when
plotting commences. This unfortunately produces some flicker but it allows
Mode 13 sprites (with square pixels and twice as quick to plot!) to be used
with a Mode 15 display. Click on Other to use the mode number you enter.
Screen Blank: High resolution screen modes (eg. Mode 21) slow down the
processor. With screen blank on, the screen is switched to Mode 13 when the
image is being generated. This will significantly reduce plotting time, with
the disadvantage that you will not see the image build up.
Full Precision Maths: Some functions such as Mandelbrots use integer
arithmetic or 32 bit floating point where possible to increase speed. This
reduces accuracy and can produce strange effects. Set this option on to
force use of full floating point, but be prepared for a great reduction in
speed. If you have a floating point hardware card, then turn this on to use
to exploit it.
Save: click on this icon to save the options as set for the next run of
!Fractal.
----------------------------------------------
3d Plotting
===========
There are three kinds of 3d plotting in !Fractal - 3d images, 3d mapping and
3d transformations.
3d Images
---------
This refers to functions which create 3d shapes - Lorenz, Pickover, Rossler
- these just all happen to be strange attractors at the moment. You will
find that you need to change the rotation and elevation to get an
appreciation of these shapes. To help in this process, you can change the
viewpoint whilst the plot is underway. Simply press the cursor keys to
change the viewpoint in increments of 5� in each direction. The plot stops
and the most recent part of the image is redrawn to indicate the new
viewpoint. Press the Spacebar to restart the plot.
The number of points redrawn is set by the 3d-buffer size - increase it for
more points, but this will slow down the redraw. Try 500 points with an
ARM-2, 1500 with an ARM-3. If possible !Fractal will redraw the image in
shadow memory to avoid flicker. For the Lorenz and Rossler functions
increase the Step Rate variable to around 2.0e-2 to show enough of the
image.
Note that when altering the viewpoint, the image is rotated about the origin
of the image, not the screen. This is most notable when changing the
elevation on the Lorenz attractor.
3d Mapping
----------
With pixel plotting functions the pixel colour can be used as the height
(Julia, Mandelbrot, Newton, Popcorn-Julia, Unity). The results are similar
to creating an image and then transforming it with 3d_View. The advantage of
the direct plot is that a full screen image is created, and you can zoom
into the image. The disadvantage is that it disables the pixel guessing
mechanism, resulting in a noticeable loss of speed.
When zooming the zoom box represents the approximate image area at zero
height - you will find you will need to zoom in lower, anticipating where the
base of the image is. Do not alter the viewpoint and zoom at the same time -
do these seperately, otherwise results will not be as expected. Note that
zooming does not change the height.
The height mapping parameters control how the pixel colour is mapped onto a
height. To increase the overall height increase the height scalar. Use the
min & max height parameters to clip the image to get a 'slice' - this is
most useful for smoothing spiky peaks. It can be useful to set the max
height value to the same as the iteration value of the function. Note that
heights above 255 are wrapped around to zero.
The centre of rotation and elevation is the centre of the image. Decreasing
the elevation will therefore bring more of the foreground and distance into
view. Note that the integer plot functions (such as Mandelbrots) can't fully
cope with vey low viewpoints, and may produce no image at all. Try zooming
in to overcome this, or switch to floating point maths.
3d Transformations
------------------
These are functions which take an image and perform a 3d transformation
(3d_Plane, 3d_View, Render, Riemann). All but the Riemann transform the
image by using the pixel colour as the height, using the same mapping
process as described above and controlled by the same height mapping
parameters. The Riemann function projects the image onto a Riemann sphere.
For full details see the help file !Functions.
3d Details Panel
----------------
You must click on OK to enter your new settings.
3d X/Y Plot: Activates the 3d pixel plotting for functions that plot each
pixel on an X/Y map (eg. Mandelbrots).
Height Mapping: controls the process of mapping pixel colours into heights.
Log: uses a logarithmic map which favours lower colours. It gives the best
results for 3d mapping.
Inverse Log: uses an inverse logarithmic map, favouring the higher colours.
It is of most use when using a 3d transform with an image that has had its
palette inverted via Effects->Invert. This produces an upside down image.
Linear: maps the pixel colour number directly into the height.
Scalar: increasing this value by 1 doubles the height mapping. It is useful
where the pixel values are all low to exagerate the height. Also as the
elevation increases the height decreases - increase the scalar to compensate
if required.
Rotation: specifies the viewpoint angle in degrees anti-clockwise, ie. the
clockwise angle of rotation of the image. The value can be -360 to 360�.
Elevation: specifies the viewpoint angle in degrees from -90� to 90�. Many
of the functions limit this angle to positive angles only.
3d Buffer: the number of points stored for re-plotting when using the 3d
image functions. Larger values provide a better impression of the image, but
take longer to re-draw.
----------------------------------------------
Palettes
--------
The palette in 256 colour modes cannot be changed by the !Palette utility.
However !Fractal allows the 256 colours to be arranged in any sequence or
for a subset of the colours to be used. This is useful to highlight detail
or produce more realistic displays in 3d mapping eg. the landscape palettes.
Palettes may be editted via the supplied !FracPal application and a
selection of ready made palettes are in the 2 directories supplied. Palettes
can be loaded by double clicking, dragging onto a !Fractal window, or
directly from the !FracPal save menu option.
The palettes "primary" and "primary_8" are useful for colour printing since
they use only the 8 primary colours - black, red, green, blue, cyan, magenta,
yellow and white.
----------------------------------------------
Data Editing Keys
-----------------
There are several data entry panels used within !Fractal. To move around
these panels use these keys (which follow RiscOS conventions) or the mouse:
Mouse click: moves the caret to the icon under the mouse.
Return, Tab or Down-cursor go to the next editable icon.
Shift Tab or Up-cursor go to the previous icon.
Shift-Cursor-up/down or Page-Up/Down move to the icons above and below.
Standard RiscOS keys are used to edit data. As a reminder these are:
Delete : deletes to the left of the caret
Copy : deletes to the right of the caret
Ctrl-U : delete all
Ctrl-Copy : delete to the right of the caret
----------------------------------------------------------------------------
Adding Your Own Routines
------------------------
!Fractal allows your own fractal routines written in ARM code to be
dynamically added at start time. For full details refer to the help
application !Interface.
Programming
-----------
!Fractal is written in C and ARM assembler for maximum speed. Contact me if
you would like to contribute your own Fractal function to !Fractal. You will
get full credits and become part of the best Archimedes fractal program ever
(well I am hoping so).
Bugs
----
I am aware that this release still contains many bugs. Sorry, but if you
treat it kindly things should be ok. One day I'll methodically go through
and add more extensive error checking and handling. The problem is that the
program is growing all the time and I am sure you want me to add new
features rather than pretty things up.
History
-------
0.10 03/07/91 : Initial versions sent out to attract developer interest.
0.11 08/07/91 : Cleaned up palette handling, added Mbrot<->Julia routines.
Added palette stepping and timing of non x/y functions.
0.12 24/07/91 : Cycle with only 1 screen bank for modes 21,24,28 etc.
Created Fraclib for assembler functions and documented
programming interfaces.
0.13 04/08/91 : Added IFS 2d plus extra internal !Fractal functions.
0.14 10/08/91 : Added full desktop operation.
0.15 05/09/91 : Lots of additions and experiments. Added tools, fast x/y
plotting, Render and Riemann functions. Extended Mandelbrot
and Julia functions, plus better Assembler support.
0.16 12/09/91 : Cleaned up some bugs; colouring options for Mandelbrot;
provided data variables for 3d plotting control.
0.17 29/09/91 : Added Options control; Henon and Newton functions; inverse
Mandelbrots
0.18 27/10/91 : Added Popcorn, Lorenz and L-systems. Major enhancements to
3d control and Riemann now works properly. Periodicity
checking added to Mandelbrots. Unknown sprite import. Also
improved error trapping.
0.19 15/11/91 : Added fast floating point support - Newton & Riemann changed
to use it. Added 3d tools icons, 2 more palettes, 2 more
Mandelbrots. Added Midpoint function. General tidy up ready
for release.
0.20 25/11/91 : Sent to Archimedes World for public release. Included speeded
up version of Popcorn using FPE_Lib.
0.21 14/12/91 : Added Pickover, Rossler & Unity functions. Lorenz to 3d.
Added 3d image generation and realtime 3d control. Sent to
Acorn User.
0.22 26/02/92 : Added palette editing and interactive help. 3d style push buttons.
Sent to Micro User.
0.23 08/03/92 : Added Quaternion.
0.24 24/03/92 : Added Fault and Bifurcate. Colour cycling now works on all
palettes.
To obtain the latest version send a blank formatted disk + SAE to Mike
Curnow. Contributions (money or fractal programs) to help run the Archimedes
Fractal Group are welcome - you'll get sent Newsletters on fractals in
return.
The Future
----------
To come (amongst other essential features), in not any specific order :
Loads more fractal functions (volunteers please).
Automatically update the Save sprite name on a numerical basis.
Compressed sprite files?
Batch operation - ie. create a text file function data, feed it into
!Fractal, go to sleep, then come back to find loads of nice sprites on your
disk (this will definitely require sprite compression).
Many more image manipulation facilities.
Contributors (people who have supplied code or algorithms)
============
Many thanks to Joyce Haslam for the Mandelbrot and Julia equations, Popcorn
and one of the Henon's.
Credits
=======
This program would not exist without the benefit of previous work by many
people. In particular Fractal Report and Fractint have been a major source
of inspiration. More detailed sources are given in the !Functions help file.
Thanks to A.Fedonczuk for the original 32 bit integer routines.
Stuart Payne of Acorn for the original Render algorithm.
To Fractal Report for many of the ideas including the X/Y Guessing
algorithm, Riemann plot, IFS affine maths. For a free copy of Fractal Report
write to RTL Ltd, West Towan House, Porthtowan, Truro, Cornwall, TR4 8AX.
To the authors of Fractint for initial inspiration and many bits that don't
get credit otherwise. Stone soup forever!
John Greening for some of the L-system codes and inspiration.
Copywright Notice
=================
The copywright of this material belongs to Mike Curnow except for the !Help
application which belongs to J R�ling. This software is not "Public Domain".
However permission is granted for non-commercial use of this software and
associated material as long as NO CHARGES ARE LEVIED except to cover costs.
Copies of this software may be freely distributed amongst individuals on a
no-charge basis. Public Domain and commercial organisations are kindly asked
to contact the author prior to circulation and use of this program.
Archimedes Fractal Group (AFG)
==============================
This software is part of the Archimedes Fractal Group collection. If you
have obtained this software outside of the AFG and would like to find out
more about fractal programming on the Archimedes, contact me (the AFG
administrator) at the address below. Send a SAE and a disk to get a copy of
the latest newsletter and programs disk.
Mike Curnow,
30 Bowen Drive,
West Dulwich,
London
SE21 8PN
SAE with all correspondance please.
<<<< MAY CHAOS BE WITH YOU! >>>>
00000000 20 20 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f | ______________| 00000010 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f |________________| * 00000040 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 0a 20 2f 20 20 20 |__________. / | 00000050 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000090 20 20 20 20 20 5c 0a 7c 20 20 20 20 20 20 20 20 | \.| | 000000a0 20 20 20 20 20 20 20 20 21 46 72 61 63 74 61 6c | !Fractal| 000000b0 20 76 30 2e 32 34 3a 20 47 65 6e 65 72 61 6c 20 | v0.24: General | 000000c0 46 72 61 63 74 61 6c 20 50 6c 6f 74 74 65 72 20 |Fractal Plotter | 000000d0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000000e0 20 20 7c 0a 7c 20 20 20 20 20 20 20 20 20 20 20 | |.| | 000000f0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000100 20 20 20 20 4d 61 72 63 68 20 31 39 39 32 20 20 | March 1992 | 00000110 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000120 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 7c | || 00000130 0a 7c 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |.| | 00000140 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 62 | b| 00000150 79 20 4d 69 6b 65 20 43 75 72 6e 6f 77 20 20 20 |y Mike Curnow | 00000160 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000170 20 20 20 20 20 20 20 20 20 20 20 20 7c 0a 20 5c | |. \| 00000180 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f 5f |________________| * 000001c0 5f 5f 5f 5f 5f 5f 5f 5f 2f 20 0a 0a 49 6e 74 72 |________/ ..Intr| 000001d0 6f 64 75 63 74 69 6f 6e 0a 3d 3d 3d 3d 3d 3d 3d |oduction.=======| 000001e0 3d 3d 3d 3d 3d 0a 21 46 72 61 63 74 61 6c 20 69 |=====.!Fractal i| 000001f0 73 20 64 65 73 69 67 6e 65 64 20 74 6f 20 62 65 |s designed to be| 00000200 20 61 20 75 6e 69 76 65 72 73 61 6c 20 66 72 61 | a universal fra| 00000210 63 74 61 6c 20 67 65 6e 65 72 61 74 6f 72 2e 20 |ctal generator. | 00000220 21 46 72 61 63 74 61 6c 20 68 61 73 20 74 77 6f |!Fractal has two| 00000230 0a 70 75 72 70 6f 73 65 73 2e 20 46 69 72 73 74 |.purposes. First| 00000240 6c 79 20 74 6f 20 70 72 6f 76 69 64 65 20 79 6f |ly to provide yo| 00000250 75 20 77 69 74 68 20 61 20 63 6f 6d 70 72 65 68 |u with a compreh| 00000260 65 6e 73 69 76 65 20 61 70 70 6c 69 63 61 74 69 |ensive applicati| 00000270 6f 6e 20 74 6f 20 65 78 61 6d 69 6e 65 0a 66 72 |on to examine.fr| 00000280 61 63 74 61 6c 20 66 75 6e 63 74 69 6f 6e 73 20 |actal functions | 00000290 61 6e 64 20 69 6d 61 67 65 73 2e 20 53 65 63 6f |and images. Seco| 000002a0 6e 64 6c 79 20 69 74 20 69 73 20 64 65 73 69 67 |ndly it is desig| 000002b0 6e 65 64 20 61 73 20 61 20 70 6c 61 74 66 6f 72 |ned as a platfor| 000002c0 6d 20 66 6f 72 0a 66 72 61 63 74 61 6c 20 70 72 |m for.fractal pr| 000002d0 6f 67 72 61 6d 6d 65 72 73 20 74 6f 20 61 64 64 |ogrammers to add| 000002e0 20 74 68 65 69 72 20 6f 77 6e 20 72 6f 75 74 69 | their own routi| 000002f0 6e 65 73 2e 20 54 68 69 73 20 65 6e 61 62 6c 65 |nes. This enable| 00000300 73 20 74 68 65 73 65 20 72 6f 75 74 69 6e 65 73 |s these routines| 00000310 0a 74 6f 20 67 65 74 20 69 6d 6d 65 64 69 61 74 |.to get immediat| 00000320 65 20 57 69 6d 70 20 61 63 63 65 73 73 20 61 6e |e Wimp access an| 00000330 64 20 73 75 70 70 6f 72 74 20 6f 66 20 74 68 65 |d support of the| 00000340 20 33 64 20 66 75 6e 63 74 69 6f 6e 73 20 65 74 | 3d functions et| 00000350 63 2e 0a 0a 41 20 62 72 69 65 66 20 67 75 69 64 |c...A brief guid| 00000360 65 20 74 6f 20 75 73 61 67 65 2e 0a 2d 2d 2d 2d |e to usage..----| 00000370 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| 00000380 2d 2d 0a 44 6f 75 62 6c 65 20 63 6c 69 63 6b 20 |--.Double click | 00000390 6f 6e 20 74 68 65 20 66 69 6c 65 72 20 69 63 6f |on the filer ico| 000003a0 6e 20 74 6f 20 6c 6f 61 64 2c 20 77 68 69 63 68 |n to load, which| 000003b0 20 77 69 6c 6c 20 64 69 73 70 6c 61 79 20 74 68 | will display th| 000003c0 65 20 69 6e 69 74 69 61 6c 0a 66 72 61 63 74 61 |e initial.fracta| 000003d0 6c 20 28 61 20 4d 61 6e 64 65 6c 62 72 6f 74 29 |l (a Mandelbrot)| 000003e0 2e 20 53 65 6c 65 63 74 20 61 20 32 35 36 20 63 |. Select a 256 c| 000003f0 6f 6c 6f 75 72 20 6d 6f 64 65 20 66 72 6f 6d 20 |olour mode from | 00000400 74 68 65 20 21 50 61 6c 65 74 74 65 0a 61 70 70 |the !Palette.app| 00000410 6c 69 63 61 74 69 6f 6e 20 74 6f 20 73 65 65 20 |lication to see | 00000420 74 68 65 20 69 6d 61 67 65 20 63 6f 72 72 65 63 |the image correc| 00000430 74 6c 79 2e 20 41 6c 74 65 72 6e 61 74 69 76 65 |tly. Alternative| 00000440 6c 79 20 79 6f 75 20 63 61 6e 20 63 6c 69 63 6b |ly you can click| 00000450 20 77 69 74 68 0a 41 64 6a 75 73 74 20 6f 76 65 | with.Adjust ove| 00000460 72 20 74 68 65 20 69 63 6f 6e 20 62 61 72 20 74 |r the icon bar t| 00000470 6f 20 6f 70 65 6e 20 61 20 66 75 6c 6c 20 73 63 |o open a full sc| 00000480 72 65 65 6e 20 77 69 6e 64 6f 77 20 28 74 68 6f |reen window (tho| 00000490 75 67 68 20 73 74 69 6c 6c 20 69 6e 0a 64 65 73 |ugh still in.des| 000004a0 6b 74 6f 70 20 6d 6f 64 65 29 2e 20 43 6c 69 63 |ktop mode). Clic| 000004b0 6b 69 6e 67 20 77 69 74 68 20 53 65 6c 65 63 74 |king with Select| 000004c0 20 72 65 2d 6f 70 65 6e 73 20 74 68 65 20 6d 61 | re-opens the ma| 000004d0 69 6e 20 77 69 6e 64 6f 77 20 69 66 20 63 6c 6f |in window if clo| 000004e0 73 65 64 2e 0a 0a 4d 6f 73 74 20 6f 66 20 74 68 |sed...Most of th| 000004f0 65 20 6d 61 69 6e 20 66 75 6e 63 74 69 6f 6e 73 |e main functions| 00000500 20 6f 66 20 21 46 72 61 63 74 61 6c 20 63 61 6e | of !Fractal can| 00000510 20 62 65 20 70 65 72 66 6f 72 6d 65 64 20 66 72 | be performed fr| 00000520 6f 6d 20 74 68 65 20 54 6f 6f 6c 73 20 70 61 6e |om the Tools pan| 00000530 65 0a 6f 6e 20 74 68 65 20 6c 65 66 74 2e 20 54 |e.on the left. T| 00000540 68 65 20 6d 61 69 6e 20 6d 65 6e 75 20 70 72 6f |he main menu pro| 00000550 76 69 64 65 73 20 61 63 63 65 73 73 20 74 6f 20 |vides access to | 00000560 61 6c 6c 20 6f 66 20 74 68 65 73 65 20 66 75 6e |all of these fun| 00000570 63 74 69 6f 6e 73 20 61 6e 64 0a 6d 6f 72 65 2e |ctions and.more.| 00000580 0a 0a 54 6f 20 5a 6f 6f 6d 20 69 6e 20 63 6c 69 |..To Zoom in cli| 00000590 63 6b 20 77 69 74 68 20 53 65 6c 65 63 74 20 6f |ck with Select o| 000005a0 76 65 72 20 74 68 65 20 31 73 74 20 74 6f 6f 6c |ver the 1st tool| 000005b0 20 69 63 6f 6e 2c 20 6f 72 20 75 73 65 20 41 64 | icon, or use Ad| 000005c0 6a 75 73 74 20 74 6f 20 7a 6f 6f 6d 0a 6f 75 74 |just to zoom.out| 000005d0 2e 20 41 20 7a 6f 6f 6d 20 62 6f 78 20 77 69 6c |. A zoom box wil| 000005e0 6c 20 61 70 70 65 61 72 20 2d 20 75 73 65 20 74 |l appear - use t| 000005f0 68 65 20 6c 65 66 74 20 6d 6f 75 73 65 20 62 75 |he left mouse bu| 00000600 74 74 6f 6e 20 74 6f 20 73 68 72 69 6e 6b 20 74 |tton to shrink t| 00000610 68 65 20 7a 6f 6f 6d 0a 62 6f 78 2c 20 61 6e 64 |he zoom.box, and| 00000620 20 74 68 65 20 72 69 67 68 74 20 62 75 74 74 6f | the right butto| 00000630 6e 20 74 6f 20 65 6e 6c 61 72 67 65 20 69 74 2e |n to enlarge it.| 00000640 20 50 72 65 73 73 20 74 68 65 20 6d 69 64 64 6c | Press the middl| 00000650 65 20 62 75 74 74 6f 6e 20 74 6f 20 73 74 61 72 |e button to star| 00000660 74 0a 74 68 65 20 72 65 64 72 61 77 20 6f 70 65 |t.the redraw ope| 00000670 72 61 74 69 6f 6e 2e 20 54 68 65 20 6d 61 63 68 |ration. The mach| 00000680 69 6e 65 20 77 69 6c 6c 20 62 65 20 6c 6f 63 6b |ine will be lock| 00000690 65 64 20 75 6e 74 69 6c 20 74 68 65 20 72 65 64 |ed until the red| 000006a0 72 61 77 20 69 73 0a 63 6f 6d 70 6c 65 74 65 20 |raw is.complete | 000006b0 6f 72 20 75 6e 74 69 6c 20 79 6f 75 20 70 72 65 |or until you pre| 000006c0 73 73 20 41 64 6a 75 73 74 2c 20 61 74 20 77 68 |ss Adjust, at wh| 000006d0 69 63 68 20 70 6f 69 6e 74 20 6d 75 6c 74 69 2d |ich point multi-| 000006e0 74 61 73 6b 69 6e 67 20 6d 6f 64 65 20 77 69 6c |tasking mode wil| 000006f0 6c 0a 62 65 20 65 6e 74 65 72 65 64 2e 20 4e 6f |l.be entered. No| 00000700 74 65 20 74 68 61 74 20 73 6f 6d 65 20 66 75 6e |te that some fun| 00000710 63 74 69 6f 6e 73 20 6e 65 76 65 72 20 65 6e 64 |ctions never end| 00000720 20 75 6e 74 69 6c 20 79 6f 75 20 73 65 6c 65 63 | until you selec| 00000730 74 20 49 6d 61 67 65 2d 3e 53 74 6f 70 2e 0a 41 |t Image->Stop..A| 00000740 6c 73 6f 20 6e 6f 74 65 20 74 68 61 74 20 77 68 |lso note that wh| 00000750 65 6e 20 69 6e 20 66 75 6c 6c 20 73 63 72 65 65 |en in full scree| 00000760 6e 20 6d 6f 64 65 20 74 68 65 20 64 65 73 6b 74 |n mode the deskt| 00000770 6f 70 20 69 73 20 73 74 69 6c 6c 20 61 63 74 69 |op is still acti| 00000780 76 65 20 2d 20 69 74 73 0a 6a 75 73 74 20 74 68 |ve - its.just th| 00000790 61 74 20 74 68 65 20 6f 74 68 65 72 20 77 69 6e |at the other win| 000007a0 64 6f 77 73 20 61 72 65 20 68 69 64 64 65 6e 2e |dows are hidden.| 000007b0 20 54 6f 20 63 6c 6f 73 65 20 74 68 65 20 66 75 | To close the fu| 000007c0 6c 6c 20 73 63 72 65 65 6e 20 77 69 6e 64 6f 77 |ll screen window| 000007d0 0a 73 65 6c 65 63 74 20 44 69 73 70 6c 61 79 2d |.select Display-| 000007e0 3e 48 69 64 65 2e 0a 0a 54 68 65 20 73 63 72 65 |>Hide...The scre| 000007f0 65 6e 20 63 61 6e 20 62 65 20 73 61 76 65 64 20 |en can be saved | 00000800 62 79 20 75 73 69 6e 67 20 74 68 65 20 49 6d 61 |by using the Ima| 00000810 67 65 2d 3e 53 61 76 65 20 6f 70 74 69 6f 6e 2e |ge->Save option.| 00000820 20 53 61 76 65 64 20 64 72 61 77 69 6e 67 73 20 | Saved drawings | 00000830 6d 61 79 0a 62 65 20 72 65 6c 6f 61 64 65 64 20 |may.be reloaded | 00000840 62 79 20 73 69 6d 70 6c 79 20 64 72 61 67 67 69 |by simply draggi| 00000850 6e 67 20 74 68 65 20 73 61 76 65 64 20 73 70 72 |ng the saved spr| 00000860 69 74 65 20 6f 6e 74 6f 20 74 68 65 20 21 46 72 |ite onto the !Fr| 00000870 61 63 74 61 6c 20 69 63 6f 6e 2c 0a 61 6c 6c 6f |actal icon,.allo| 00000880 77 69 6e 67 20 7a 6f 6f 6d 69 6e 67 20 74 6f 20 |wing zooming to | 00000890 72 65 2d 63 6f 6d 6d 65 6e 63 65 2e 0a 0a 46 75 |re-commence...Fu| 000008a0 6c 6c 20 4f 70 65 72 61 74 69 6f 6e 20 49 6e 66 |ll Operation Inf| 000008b0 6f 72 6d 61 74 69 6f 6e 0a 3d 3d 3d 3d 3d 3d 3d |ormation.=======| 000008c0 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d |================| 000008d0 3d 3d 3d 0a 21 46 72 61 63 74 61 6c 20 72 65 71 |===.!Fractal req| 000008e0 75 69 72 65 73 20 61 20 63 6f 6e 73 69 64 65 72 |uires a consider| 000008f0 61 62 6c 65 20 61 6d 6f 75 6e 74 20 6f 66 20 73 |able amount of s| 00000900 74 6f 72 61 67 65 20 3a 20 32 30 30 6b 20 66 6f |torage : 200k fo| 00000910 72 20 63 6f 64 65 2c 0a 32 2a 73 70 72 69 74 65 |r code,.2*sprite| 00000920 20 69 6d 61 67 65 20 73 69 7a 65 20 28 64 65 70 | image size (dep| 00000930 65 6e 64 73 20 6f 6e 20 6d 6f 64 65 29 2c 20 31 |ends on mode), 1| 00000940 20 6f 72 20 32 20 62 61 6e 6b 73 20 6f 66 20 73 | or 2 banks of s| 00000950 63 72 65 65 6e 20 6d 65 6d 6f 72 79 2c 20 61 6e |creen memory, an| 00000960 64 0a 36 30 6b 20 66 6f 72 20 74 68 65 20 73 68 |d.60k for the sh| 00000970 61 72 65 64 20 43 20 6c 69 62 72 61 72 79 2c 20 |ared C library, | 00000980 73 6f 20 62 65 20 70 72 65 70 61 72 65 64 2e 20 |so be prepared. | 00000990 53 6f 6d 65 20 66 75 6e 63 74 69 6f 6e 73 20 61 |Some functions a| 000009a0 72 65 20 64 69 73 61 62 6c 65 64 20 69 66 0a 74 |re disabled if.t| 000009b0 68 65 72 65 20 69 73 20 69 6e 73 75 66 66 69 63 |here is insuffic| 000009c0 69 65 6e 74 20 6d 65 6d 6f 72 79 2e 20 54 6f 20 |ient memory. To | 000009d0 73 61 76 65 20 73 70 61 63 65 2c 20 73 6f 6d 65 |save space, some| 000009e0 20 66 75 6e 63 74 69 6f 6e 73 20 6c 6f 61 64 20 | functions load | 000009f0 74 68 65 69 72 20 64 61 74 61 0a 6f 6e 20 66 69 |their data.on fi| 00000a00 72 73 74 20 73 65 6c 65 63 74 69 6f 6e 2c 20 73 |rst selection, s| 00000a10 6f 20 62 65 20 70 72 65 70 61 72 65 64 20 66 6f |o be prepared fo| 00000a20 72 20 66 75 72 74 68 65 72 20 64 69 73 6b 20 61 |r further disk a| 00000a30 63 74 69 76 69 74 79 2e 0a 0a 54 68 65 20 66 72 |ctivity...The fr| 00000a40 61 63 74 61 6c 20 70 6c 6f 74 20 69 73 20 64 69 |actal plot is di| 00000a50 73 70 6c 61 79 65 64 20 65 69 74 68 65 72 20 69 |splayed either i| 00000a60 6e 20 61 20 66 75 6c 6c 20 73 63 72 65 65 6e 20 |n a full screen | 00000a70 77 69 6e 64 6f 77 2c 20 77 68 69 63 68 20 6d 61 |window, which ma| 00000a80 79 20 62 65 0a 68 69 64 64 65 6e 20 61 74 20 61 |y be.hidden at a| 00000a90 6e 79 20 74 69 6d 65 20 62 79 20 73 65 6c 65 63 |ny time by selec| 00000aa0 74 69 6e 67 20 48 69 64 65 20 66 72 6f 6d 20 74 |ting Hide from t| 00000ab0 68 65 20 6d 65 6e 75 2c 20 6f 72 20 69 6e 20 61 |he menu, or in a| 00000ac0 20 73 74 61 6e 64 61 72 64 0a 72 65 2d 73 69 7a | standard.re-siz| 00000ad0 65 61 62 6c 65 20 77 69 6e 64 6f 77 2e 20 54 68 |eable window. Th| 00000ae0 65 20 63 6f 6c 6f 75 72 73 20 77 69 6c 6c 20 6c |e colours will l| 00000af0 6f 6f 6b 20 73 74 72 61 6e 67 65 20 69 66 20 79 |ook strange if y| 00000b00 6f 75 20 61 72 65 20 6e 6f 74 20 69 6e 20 61 20 |ou are not in a | 00000b10 32 35 36 0a 63 6f 6c 6f 75 72 20 6d 6f 64 65 20 |256.colour mode | 00000b20 2d 20 6e 6f 20 61 74 74 65 6d 70 74 20 69 73 20 |- no attempt is | 00000b30 6d 61 64 65 20 74 6f 20 6d 61 74 63 68 20 74 68 |made to match th| 00000b40 65 20 64 65 73 6b 74 6f 70 20 63 6f 6c 6f 75 72 |e desktop colour| 00000b50 73 20 73 6f 20 61 73 20 74 6f 0a 72 65 74 61 69 |s so as to.retai| 00000b60 6e 20 61 73 20 6d 75 63 68 20 69 6d 61 67 65 20 |n as much image | 00000b70 64 65 74 61 69 6c 20 61 73 20 70 6f 73 73 69 62 |detail as possib| 00000b80 6c 65 2e 0a 0a 57 68 65 6e 20 61 6e 20 69 6d 61 |le...When an ima| 00000b90 67 65 20 69 73 20 72 65 2d 64 72 61 77 6e 20 21 |ge is re-drawn !| 00000ba0 46 72 61 63 74 61 6c 20 61 74 74 65 6d 70 74 73 |Fractal attempts| 00000bb0 20 74 6f 20 65 6e 74 65 72 20 74 68 65 20 69 6d | to enter the im| 00000bc0 61 67 65 20 6d 6f 64 65 20 74 6f 0a 61 6c 6c 6f |age mode to.allo| 00000bd0 77 20 74 68 65 20 69 6d 61 67 65 20 67 65 6e 65 |w the image gene| 00000be0 72 61 74 69 6f 6e 20 74 6f 20 62 65 20 73 65 65 |ration to be see| 00000bf0 6e 2e 20 54 6f 20 61 76 6f 69 64 20 6f 75 74 20 |n. To avoid out | 00000c00 6f 66 20 6d 65 6d 6f 72 79 20 70 72 6f 62 6c 65 |of memory proble| 00000c10 6d 73 20 69 74 0a 6d 61 79 20 62 65 20 62 65 73 |ms it.may be bes| 00000c20 74 20 74 6f 20 70 72 65 2d 73 65 6c 65 63 74 20 |t to pre-select | 00000c30 74 68 69 73 20 6d 6f 64 65 20 66 72 6f 6d 20 74 |this mode from t| 00000c40 68 65 20 50 61 6c 65 74 74 65 20 74 61 73 6b 20 |he Palette task | 00000c50 6f 72 20 66 72 6f 6d 20 74 68 65 0a 27 4f 70 74 |or from the.'Opt| 00000c60 69 6f 6e 73 2d 3e 46 75 6c 6c 20 73 63 72 65 65 |ions->Full scree| 00000c70 6e 20 6d 6f 64 65 27 20 77 68 65 6e 20 69 6e 20 |n mode' when in | 00000c80 66 75 6c 6c 20 73 63 72 65 65 6e 20 6d 6f 64 65 |full screen mode| 00000c90 2e 20 49 66 20 74 68 65 20 69 6d 61 67 65 20 73 |. If the image s| 00000ca0 69 7a 65 0a 69 73 20 64 69 66 66 65 72 65 6e 74 |ize.is different| 00000cb0 20 66 72 6f 6d 20 74 68 65 20 73 63 72 65 65 6e | from the screen| 00000cc0 20 73 69 7a 65 2c 20 74 68 65 6e 20 6e 6f 20 61 | size, then no a| 00000cd0 74 74 65 6d 70 74 20 69 73 20 6d 61 64 65 20 74 |ttempt is made t| 00000ce0 6f 20 73 68 6f 77 20 74 68 65 0a 72 65 2d 64 72 |o show the.re-dr| 00000cf0 61 77 20 61 73 20 69 74 20 70 72 6f 63 65 65 64 |aw as it proceed| 00000d00 73 2e 0a 0a 41 75 74 6f 6d 61 74 69 63 20 4c 61 |s...Automatic La| 00000d10 73 74 20 44 69 73 70 6c 61 79 20 53 61 76 65 0a |st Display Save.| 00000d20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| 00000d30 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 4d 6f 73 74 |-----------.Most| 00000d40 20 6f 70 65 72 61 74 69 6f 6e 73 20 77 68 69 63 | operations whic| 00000d50 68 20 6d 6f 64 69 66 79 20 74 68 65 20 63 75 72 |h modify the cur| 00000d60 72 65 6e 74 20 69 6d 61 67 65 20 77 69 6c 6c 20 |rent image will | 00000d70 73 61 76 65 20 69 74 20 69 6e 20 6d 65 6d 6f 72 |save it in memor| 00000d80 79 2e 20 54 68 65 0a 70 72 69 6f 72 20 69 6d 61 |y. The.prior ima| 00000d90 67 65 20 6d 61 79 20 62 65 20 72 65 63 61 6c 6c |ge may be recall| 00000da0 65 64 20 62 79 20 73 65 6c 65 63 74 69 6e 67 20 |ed by selecting | 00000db0 44 69 73 70 6c 61 79 2d 3e 50 72 65 76 69 6f 75 |Display->Previou| 00000dc0 73 20 66 72 6f 6d 20 74 68 65 20 6d 65 6e 75 2e |s from the menu.| 00000dd0 0a 54 68 75 73 20 79 6f 75 20 63 61 6e 20 7a 6f |.Thus you can zo| 00000de0 6f 6d 20 69 6e 20 74 6f 20 69 6e 73 70 65 63 74 |om in to inspect| 00000df0 20 61 6e 20 61 72 65 61 2c 20 74 68 65 6e 20 71 | an area, then q| 00000e00 75 69 63 6b 6c 79 20 62 61 63 6b 20 6f 75 74 20 |uickly back out | 00000e10 74 6f 20 74 68 65 0a 70 72 65 76 69 6f 75 73 20 |to the.previous | 00000e20 64 69 73 70 6c 61 79 2e 20 54 6f 20 6d 61 69 6e |display. To main| 00000e30 74 61 69 6e 20 66 75 72 74 68 65 72 20 69 6d 61 |tain further ima| 00000e40 67 65 73 20 75 73 65 20 74 68 65 20 6c 6f 61 64 |ges use the load| 00000e50 20 61 6e 64 20 73 61 76 65 0a 66 61 63 69 6c 69 | and save.facili| 00000e60 74 69 65 73 2e 0a 0a 54 6f 6f 6c 73 0a 3d 3d 3d |ties...Tools.===| 00000e70 3d 3d 0a 54 68 65 20 74 6f 6f 6c 73 20 70 61 6e |==.The tools pan| 00000e80 65 20 70 72 6f 76 69 64 65 73 20 71 75 69 63 6b |e provides quick| 00000e90 20 61 63 63 65 73 73 20 74 6f 20 66 75 6e 63 74 | access to funct| 00000ea0 69 6f 6e 73 2e 20 46 6f 72 20 66 75 6c 6c 20 64 |ions. For full d| 00000eb0 65 74 61 69 6c 73 20 73 65 65 20 74 68 65 0a 63 |etails see the.c| 00000ec0 6f 72 72 65 73 70 6f 6e 64 69 6e 67 20 66 75 6e |orresponding fun| 00000ed0 63 74 69 6f 6e 20 69 6e 20 74 68 65 20 4d 65 6e |ction in the Men| 00000ee0 75 20 73 65 63 74 69 6f 6e 2e 20 54 68 65 20 76 |u section. The v| 00000ef0 61 72 69 6f 75 73 20 74 6f 6f 6c 73 20 61 72 65 |arious tools are| 00000f00 2c 20 69 6e 0a 64 65 73 63 65 6e 64 69 6e 67 20 |, in.descending | 00000f10 6f 72 64 65 72 3a 0a 0a 5a 6f 6f 6d 3a 20 63 6c |order:..Zoom: cl| 00000f20 69 63 6b 20 77 69 74 68 20 53 65 6c 65 63 74 20 |ick with Select | 00000f30 74 6f 20 7a 6f 6f 6d 20 69 6e 2c 20 41 64 6a 75 |to zoom in, Adju| 00000f40 73 74 20 74 6f 20 7a 6f 6f 6d 20 6f 75 74 2e 20 |st to zoom out. | 00000f50 52 65 70 65 61 74 20 74 68 65 20 63 6c 69 63 6b |Repeat the click| 00000f60 20 74 6f 0a 63 61 6e 63 65 6c 20 74 68 65 20 7a | to.cancel the z| 00000f70 6f 6f 6d 2e 0a 0a 4d 61 6e 64 65 6c 62 72 6f 74 |oom...Mandelbrot| 00000f80 3a 20 63 6c 69 63 6b 20 6f 6e 20 74 68 69 73 20 |: click on this | 00000f90 74 6f 20 72 65 64 72 61 77 20 61 6e 20 69 6d 61 |to redraw an ima| 00000fa0 67 65 20 61 66 74 65 72 20 79 6f 75 20 68 61 76 |ge after you hav| 00000fb0 65 20 63 68 61 6e 67 65 64 0a 70 61 72 61 6d 65 |e changed.parame| 00000fc0 74 65 72 73 20 6f 72 20 66 75 6e 63 74 69 6f 6e |ters or function| 00000fd0 2e 20 54 68 65 20 69 63 6f 6e 20 69 73 20 64 69 |. 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This sof| 00006800 74 77 61 72 65 20 69 73 20 6e 6f 74 20 22 50 75 |tware is not "Pu| 00006810 62 6c 69 63 20 44 6f 6d 61 69 6e 22 2e 0a 48 6f |blic Domain"..Ho| 00006820 77 65 76 65 72 20 70 65 72 6d 69 73 73 69 6f 6e |wever permission| 00006830 20 69 73 20 67 72 61 6e 74 65 64 20 66 6f 72 20 | is granted for | 00006840 6e 6f 6e 2d 63 6f 6d 6d 65 72 63 69 61 6c 20 75 |non-commercial u| 00006850 73 65 20 6f 66 20 74 68 69 73 20 73 6f 66 74 77 |se of this softw| 00006860 61 72 65 20 61 6e 64 0a 61 73 73 6f 63 69 61 74 |are and.associat| 00006870 65 64 20 6d 61 74 65 72 69 61 6c 20 61 73 20 6c |ed material as l| 00006880 6f 6e 67 20 61 73 20 4e 4f 20 43 48 41 52 47 45 |ong as NO CHARGE| 00006890 53 20 41 52 45 20 4c 45 56 49 45 44 20 65 78 63 |S ARE LEVIED exc| 000068a0 65 70 74 20 74 6f 20 63 6f 76 65 72 20 63 6f 73 |ept to cover cos| 000068b0 74 73 2e 0a 43 6f 70 69 65 73 20 6f 66 20 74 68 |ts..Copies of th| 000068c0 69 73 20 73 6f 66 74 77 61 72 65 20 6d 61 79 20 |is software may | 000068d0 62 65 20 66 72 65 65 6c 79 20 64 69 73 74 72 69 |be freely distri| 000068e0 62 75 74 65 64 20 61 6d 6f 6e 67 73 74 20 69 6e |buted amongst in| 000068f0 64 69 76 69 64 75 61 6c 73 20 6f 6e 20 61 0a 6e |dividuals on a.n| 00006900 6f 2d 63 68 61 72 67 65 20 62 61 73 69 73 2e 20 |o-charge basis. | 00006910 50 75 62 6c 69 63 20 44 6f 6d 61 69 6e 20 61 6e |Public Domain an| 00006920 64 20 63 6f 6d 6d 65 72 63 69 61 6c 20 6f 72 67 |d commercial org| 00006930 61 6e 69 73 61 74 69 6f 6e 73 20 61 72 65 20 6b |anisations are k| 00006940 69 6e 64 6c 79 20 61 73 6b 65 64 0a 74 6f 20 63 |indly asked.to c| 00006950 6f 6e 74 61 63 74 20 74 68 65 20 61 75 74 68 6f |ontact the autho| 00006960 72 20 70 72 69 6f 72 20 74 6f 20 63 69 72 63 75 |r prior to circu| 00006970 6c 61 74 69 6f 6e 20 61 6e 64 20 75 73 65 20 6f |lation and use o| 00006980 66 20 74 68 69 73 20 70 72 6f 67 72 61 6d 2e 0a |f this program..| 00006990 0a 41 72 63 68 69 6d 65 64 65 73 20 46 72 61 63 |.Archimedes Frac| 000069a0 74 61 6c 20 47 72 6f 75 70 20 28 41 46 47 29 0a |tal Group (AFG).| 000069b0 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d |================| 000069c0 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 54 |==============.T| 000069d0 68 69 73 20 73 6f 66 74 77 61 72 65 20 69 73 20 |his software is | 000069e0 70 61 72 74 20 6f 66 20 74 68 65 20 41 72 63 68 |part of the Arch| 000069f0 69 6d 65 64 65 73 20 46 72 61 63 74 61 6c 20 47 |imedes Fractal G| 00006a00 72 6f 75 70 20 63 6f 6c 6c 65 63 74 69 6f 6e 2e |roup collection.| 00006a10 20 49 66 20 79 6f 75 0a 68 61 76 65 20 6f 62 74 | If you.have obt| 00006a20 61 69 6e 65 64 20 74 68 69 73 20 73 6f 66 74 77 |ained this softw| 00006a30 61 72 65 20 6f 75 74 73 69 64 65 20 6f 66 20 74 |are outside of t| 00006a40 68 65 20 41 46 47 20 61 6e 64 20 77 6f 75 6c 64 |he AFG and would| 00006a50 20 6c 69 6b 65 20 74 6f 20 66 69 6e 64 20 6f 75 | like to find ou| 00006a60 74 0a 6d 6f 72 65 20 61 62 6f 75 74 20 66 72 61 |t.more about fra| 00006a70 63 74 61 6c 20 70 72 6f 67 72 61 6d 6d 69 6e 67 |ctal programming| 00006a80 20 6f 6e 20 74 68 65 20 41 72 63 68 69 6d 65 64 | on the Archimed| 00006a90 65 73 2c 20 63 6f 6e 74 61 63 74 20 6d 65 20 28 |es, contact me (| 00006aa0 74 68 65 20 41 46 47 0a 61 64 6d 69 6e 69 73 74 |the AFG.administ| 00006ab0 72 61 74 6f 72 29 20 61 74 20 74 68 65 20 61 64 |rator) at the ad| 00006ac0 64 72 65 73 73 20 62 65 6c 6f 77 2e 20 53 65 6e |dress below. Sen| 00006ad0 64 20 61 20 53 41 45 20 61 6e 64 20 61 20 64 69 |d a SAE and a di| 00006ae0 73 6b 20 74 6f 20 67 65 74 20 61 20 63 6f 70 79 |sk to get a copy| 00006af0 20 6f 66 0a 74 68 65 20 6c 61 74 65 73 74 20 6e | of.the latest n| 00006b00 65 77 73 6c 65 74 74 65 72 20 61 6e 64 20 70 72 |ewsletter and pr| 00006b10 6f 67 72 61 6d 73 20 64 69 73 6b 2e 0a 0a 4d 69 |ograms disk...Mi| 00006b20 6b 65 20 43 75 72 6e 6f 77 2c 0a 33 30 20 42 6f |ke Curnow,.30 Bo| 00006b30 77 65 6e 20 44 72 69 76 65 2c 0a 57 65 73 74 20 |wen Drive,.West | 00006b40 44 75 6c 77 69 63 68 2c 0a 4c 6f 6e 64 6f 6e 0a |Dulwich,.London.| 00006b50 53 45 32 31 20 38 50 4e 0a 0a 53 41 45 20 77 69 |SE21 8PN..SAE wi| 00006b60 74 68 20 61 6c 6c 20 63 6f 72 72 65 73 70 6f 6e |th all correspon| 00006b70 64 61 6e 63 65 20 70 6c 65 61 73 65 2e 0a 20 20 |dance please.. | 00006b80 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00006b90 20 20 20 20 20 0a 20 20 20 20 20 20 20 20 20 20 | . | 00006ba0 20 20 20 20 20 20 20 20 20 3c 3c 3c 3c 20 4d 41 | <<<< MA| 00006bb0 59 20 43 48 41 4f 53 20 42 45 20 57 49 54 48 20 |Y CHAOS BE WITH | 00006bc0 59 4f 55 21 20 3e 3e 3e 3e 0a |YOU! >>>>.| 00006bca
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