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┌──── ┌────┐ ┐ Timothy Harris
│ │ │ │ 5 Burnham Park Road
│ ├────┤ │ Peverell
└──── │ │ └─── Plymouth,
───── ──── ENGLAND, PL3 5QB
v4·00 THarris@UK.AC.PLYM.SC
To execute CAL type `CAL' with the current directory set to the one in
which the CAL.EXE, CAL.OVR and CAL.CFG files reside. CAL will run on a
floppy-disk-only machine but copying all the files to the hard drive and
executing them from there (run `INSTALL.BAT' to do this for you) will allow
for quicker access to the help information.
CAL is public domain and you are therefore encouraged to give copies of it
to other people - however these copies must be in an unmodified form and
any charge made must be for media and distribution costs only.
The latest version is available from me on receipt of a blank disk and SAE,
or a cheque for £2·20 - remember to specify what type of disk you are using.
Hardware requirements:
CAL will work on almost any machine described as `PC-Compatible that
uses the DOS operating system. A maths coprocessor is not required but,
if fitted, will allow images to be created several times more quickly.
All operations can be performed using the keyboard, although using a mouse
is easier for many operations. Calculations can be performed more
accurately and more quickly on machines fitted with a 386sx processor
or better, but the program is still compatible with older machines.
Improved image quality is available with super VGA graphics cards offering
256 colours from a palette of 262144. Provision will be made for the new
cards allowing 32768 colours on the screen at once as soon as I can get
hold of the technical specifications of such a card.
Due to the large size of the program, and the fact that the computer only
stores part of it in memory at once, CAL is best used running from a hard
drive. If this is not possible, but around 2MB of expanded or extended
memory is available, install the RAMDRIVE.SYS utility supplied with DOS
(see DOS reference guides) and run CAL from the ramdrive. CAL can use
expanded memory for storing pieces of the code, resulting in slight
improvements in execution speed. CAL does not require, nor does it
use, extended memory.
Recent additions to CAL:
1. CAL now automatically detects if a 386 processor (or better) is
being used and will use an improved integer arithmetic algorithm
if possible.
2. Recently added fractal types:
- Sierpinski triangle
- L-Systems
- Composite images (this allows options such as loading a saved
image in the form of a sphere or 3D landscape)
- Logistic equation and associated Julia sets
- Flip-Mandelbrot image
- Images from applying Newton's method to zⁿ-1=0
- Gumowski and Mira attractor
- Symmetrical attractors
- Quaternion Julia sets
- Gingerbread person
A total of 21 fractals are now available from CAL - and the user defined
formula option can be used to create many more. 36 demonstration
user defined formulae are provided which show the range of functions
that are available and provide a basis for producing your own sets
of equations.
3. A data compression algorithm is used for saving images, which means that
less disk space is usually required for keeping a collection of pictures.
Additionally a new option - save details only - has been added which
stores only the information needed to recreate the fractal (typically
around 1K) rather than the complete image.
For details on these fractals, and any others that are available,
select the Current fractal types option from the Welcome to CAL! help
screen. This is available by pressing F1 as soon as CAL has loaded.
4. A batch drawing mode has been added which will scan the disk for any
unfinished images and complete them. This can be used overnight, or
when the computer is not going to be used for a while, to finish off
any images that there was not time to complete in one go.
5. Improvements have been made to the user defined formula option which
allows trigonometry to be performed on complex numbers. Formulae can
be changed without leaving CAL by using a built-in editor.
6. The user defined formulae option has also been improved to allow fractals
such as the Henon Attractor (where individual points are plotted instead
of an image covering the whole screen) to be entered. Additionally,
fractal formulae created using Fractint and saved in an FRM file can be
imported to and exported from CAL.
The functions available in the user defined formulae option have also
been increased. Along with standard arithmetic and trigonometric functions
are FLIP (used to swap the real and imaginary parts of a complex number),
ABS (which converts a negative number to a positive one, but keeps
positive numbers positive) and SIGN which returns is a number is
positive, negative or zero. See the example formulae in the user defined
formulae option for how these functions can be used.
7. A faster Lyapunov algorithm is available which typically speeds up drawing
of this fractal by two to four times.
8. Commonly used functions can be selected using hot-keys from anywhere in
the program. Ctrl-D - Draw
Ctrl-C - Continue
Ctrl-Z - Zoom in
Ctrl-P - Palette editor
9. CAL.ICO is an icon for use with CAL if it is being run from Windows.
10.CAL can now export images to the PCX file format, compatible with most
graphics editing / printing programs.
11.The user interface for the fractal selection lists has been modified
slightly - as in previous versions the cursor keys can be used to select
a fractal, but now it is also possible to type in the name directly
to choose it. In the case of User Defined Formulae, IFS fractals and
L-Systems the \ or / keys may be used, when the fractal list is on
screen, to call up the menu for adding, deleting or renaming formulae.
12.The compilation of user defined formulae has been made significantly
faster and the addition of MIN and MAX functions allows for more
elaborate colouring. See the Internal Colouring examples in the list
of user defined formulae.
An introduction to CAL:
1. As an introduction press Return as soon as CAL has loaded to draw
the default image. If your copy of the CAL files is the same as the
set that I distribute this should be the Mandelbrot set in the
256 colour 320x200 mode that is now supported on most computers. If
your machine will not use this mode then read the steps below about
configuring the program.
2. Selecting the graphics resolution... All video cards allow for a
variety of types of display. On earlier models this may be a choice
between a low resolution (i.e. blocky) image with several colours
or a less blocky image in black and white. Later systems have been
capable of 16 colours and most new graphics cards are capable of
displaying 256 colours on the screen at once.
The type of resolution and number of colours to use are chosen
from the `Display mode' option in the `Configurations' menu. Menu
choices are made using the cursor keys to change the highlighted
option and return to select it. If you are using a monochrome display
and find the text lacks contrast then run cal by typing `CAL /M' which
will cause a black and white palette to be used in text modes. Full
colours will still be available (if your display supports them) when
drawing an image.
There are four different types of graphics mode, each progressively
more advanced than the one before:
CGA - one of the original graphics standards and only really included
for machines which do not support more modern displays or to provide
a quick overview of a detailed image. At best you can have four colours
on the screen and the image does app