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Fractal Paint User's Manual
Copyright (c) 1990-1991
International ComputerSmiths
3726 West Broadway
Vancouver, B.C., Canada, V6R 2C1
tel: (604) 224-5242
bbs: (604) 224-5247
Version 1.04
Jan. 26, 1991
1. Introduction to Fractal Paint
Fractal Paint is an interactive graphics design
program. Fractal Paint can draw lines, rectangles, ellipses
and text like any other drawing program. However, Fractal
Paint also lets you draw more complex images called
fractals. Before Fractal Paint, fractals were drawn out
laboriously on computer screens often taking overnight to
calculate. With Fractal Paint you can create fractal shapes
instantly.
- Fractal Paint is a tool for artists and scientists to
create complex landscapes quickly.
- Fractal Paint eliminates the tedium of computer graphics,
allowing different levels of self replication without
manually drawing in every line.
- Fractal Paint allows users to create their own unique
fractals.
- Fractal Paint can inspire designers of all mediums.
- Fractal Paint is an ideal program for producing business
cards, advertisements and other copy that benefits from
eye-catching graphics.
Fractal Paint runs under Microsoft Windows (Version 3.0
or higher) on any computer with a mouse that will run MS-
Windows. Fractal Paint objects can be exported into
Microsoft Paint as well as many other Windows-based programs
through the Windows Clipboard.
To run Fractal Paint, Microsoft Windows must be
installed on your hard drive. To install Microsoft Windows
refer to the Microsoft Windows manual. If you do not have
Microsoft Windows, then contact a local Computer Software
Dealer and purchase it. Make sure you purchase version 3.0
or higher. If you own a lesser version of Windows, it is
well worth your while to upgrade.
:1.1 Installation of Fractal Paint
To install Fractal Paint copy the files from the Program
Floppy Disk to a directory on your computer's hard drive.
For instance, to install Fractal Paint on the C: Drive
in its own directory C:\FP: and to create the subdirectory
type:
C: - select C: drive.
cd \ - start at the root directory.
Fractal Paint User's Manual/2
mkdir FP - create the FP subdirectory.
Fractal Paint User's Manual/3
Now you must copy the program files to this directory so
type (this assumes you have just typed what is above and
that the program floppy is in drive A:):
cd FP - enter the FP subdirectory
copy a:*.* - copy all the files over.
Now the easiest way to run Fractal Paint is to install
its icon in a program group in the Program Manager and
double click on that icon. First start Microsoft Windows,
and when in the Program Manager select the Windows
Applications program group as the current window. Then
choose File - New and select program item, then for the
program path choose C:\fp\fp.exe and choose the icon. Refer
to your MS-Windows manual for more information on the
Program Manager.
:1.2 Introduction to Fractals
What is a Fractal?
"A fractal is a curve whose Hausdorff-Besicovitch dimension
is larger than its Euclidian dimension." Dr. Benoit B.
Mandelbrot
Fractals are mathematical objects with the property of
being self-similar. Fractals are everywhere, they are the
geometric patterns found in nature: in tree branches, in
contours of a coast-line, in peaks of mountains, in veins on
leaves, in cumulus clouds.
Formerly called "monsters" and "dragons" by traditional
geometricians, fractals are now an accepted part of
geometry. These are objects that have a similar structure
when observed at any magnification. For instance, when you
look at a coast-line it looks similar no matter how closely
you look at (i.e., from 20,000 feet you see big bays and
peninsulas and from close up you see little bays and
peninsulas).
Fractal Paint User's Manual/4
2. The Menus
:2.1 The File Menu
+-----+
|File |
+-----+-----+
|New |
|Open... |
|Save |
|Save As... |
+-----------+
|Print... |
+-----------+
|Exit |
+-----------+
The file menu is used to clear the current drawing, load
a new drawing, save the current drawing, print the drawing,
or exit the program.
New. . .
Selecting New clears the current drawing and all
associated fractal or L-system definitions.
Open. . .
Selecting Open, brings up a dialog box with a list of
files to choose from, and space to enter a different file
spec or file name. You can use this dialog box to move
around directories as well. To choose a file select it and
then press return or click on OK, or alternately double
click on the file you wish to select.
By default this dialog box lists files with the ".FPL"
(for Fractal Programming Language) extension. If you want a
different extension enter "*.ext" where ext is the extension
you wish in the file name field and press return or click on
OK. To traverse directories select [..] to go up a
directory. Directories are listed in bold; to enter a
directory, select it. If you decide you don't want to
choose a file click on Cancel or press the escape key.
Save. . .
Selecting Save will save your file with no further
prompting if you already have a file name associated with
the drawing (through Open or Save As). If there is not
already a file name (indicated in the title bar of the
program), then the Save As dialog box will be presented.
Fractal Paint User's Manual/5
Save As. . .
Selecting Save As will bring up a dialog box that allows
you to type in the desired file name. Type in the entire
file name including any path information, using the standard
DOS syntax for files and paths. If you do not provide an
extension then a default of ".FPL" will be used. Click OK
or press return to carry out the save, or click Cancel or
press escape to return to the drawing without saving.
Print. . .
Selecting Print will print the drawing to the printer.
Printing can take a long time, so while the drawing is being
composed for printing a dialog box is presented allowing you
to cancel the printing process. If you have the spooler
installed then the spooler will be given a temporary file to
print.
Exit. . .
Selecting Exit, terminates the program and returns you
to the MS-DOS Executive.
If you select Open, New or Exit and the drawing has been
altered without being saved then a dialog box asking you
whether you want to save the changes or not before exiting
the program will be displayed. To Save the drawing click OK
or press return. To exit without saving click on No to
return to the drawing without saving or exiting click on
Cancel.
:2.2 The Edit Menu
+-----+
|Edit |
+-----+------------------+
|Undo Alt+BkSp |
+------------------------+
|Cut Shift+Del |
|Copy Ctrl+Ins |
|Paste Shift+Ins |
|Clear Del |
+------------------------+
|Select next F2 |
|Select last F3 |
+------------------------+
Undo. . .
Selecting Undo undoes the last editing operation
performed (if it can). The Undo selection will be grayed in
the menu if there is nothing to undo.
Fractal Paint User's Manual/6
Cut. . .
Cut will copy a selected object to the clipboard and
delete the object from the drawing. If no object is
selected then Cut will be grayed in the menu. A object that
has been cut can be pasted back into Fractal Paint or pasted
into another Windows application.
Copy. . .
Copy will copy a selected object to the clipboard
without deleting it. If no object has been selected then
Copy will be grayed in the menu. A copied object can be
pasted into Fractal Paint or another Windows application
(such as Windows Paint).
Paste. . .
Paste will add the object in the clipboard to the
drawing. If there is nothing in the clipboard then paste
will be grayed in the menu. The data in the clipboard
should be a FPL (Fractal Programming Language) program
segment, such as something cut or copied from Fractal Paint
however, you can edit your own FPL code in Notepad and copy
it into Fractal Paint in this manner.
Clear. . .
Clear deletes the selected object without first copying
it to the clipboard (Clear in no way affects the clipboard).
If no object is selected then Clear will be grayed in the
menu.
:2.3 The View Menu
+-----+
|View |
+-----+--------+
|Fit in window |
|Actual size |
|2 X |
|3 X |
|4 X |
+--------------+
|Page... |
+--------------+
The View menu is used to change the magnification of the
drawing on the screen and adjust the page size and margins.
Fit in Window. . .
Fractal Paint User's Manual/7
Fit in Window will cause the entire drawing to be fitted
exactly into the drawing window.
Fractal Paint User's Manual/8
Actual Size. . .
Actual size will cause a display pixel to equal a
logical pixel for a maximal blowup.
2 X, 3 X and 4 X. . .
2 X, 3 X and 4 X will magnify the drawing two, three or
four times original size in the drawing window. When the
drawing is magnified, scroll bars are added to the drawing
window, so that you can scroll around the drawing.
Page. . .
Page brings up a dialog box to adjust the page size and
margins.
:2.4 The Program Menu
+--------+
|Program |
+--------++
|Edit... |
|Print... |
|Run |
+---------+
The program dropdown menu is used to edit, print or run
the FPL program that represents the drawing.
Edit. . .
Edit brings up an edit window containing the FPL
program. You can move or size the edit window like any
other window. When you are done with the edit window you
can close it from its system box. Use the scroll bars to
move around the program, type new text, or delete old text
with backspace (remember Del will clear the currently
selected object).
Print. . .
Print will print out the FPL program in text format on
the attached printer. If the Windows print spooler is
installed, then a temporary file will be spooled.
Run. . .
Run runs the FPL program. Use this selection to redraw
the screen. If you edit the program in the edit menu, then
you must use this to show the changes you made in the
drawing window.
Fractal Paint User's Manual/9
:2.5 The Draw Menu
+------+
|Draw |
+------+-----------------------------+
|Define base shape... |
|Define L-systems... |
+------------------------------------+
|Edit text and text type... Ctrl+T |
|Line style... Ctrl+L |
|Patterns... Ctrl+P |
+------------------------------------+
This dropdown menu allows you to define and edit fractal
definitions as well as alter or edit text, fill patterns or
line styles.
Define Base Shape. . .
The Define Base Shape item allows you to define the base
shape of your fractal:
The Base Shape is what starts the fractal. It is shown
in the tool box for you to select when you draw the fractal.
The Base Shape is what you get if you draw the fractal at
level 1 (set by the Options menu fractal dialog box). At
level 2 each line segment of the Base Shape is replaced with
a copy of the Base Shape. At level 3, each line segment of
the level 2 drawing is replaced by the Base Shape. This is
the fractal process.
To define a fractal Base Shape with this dialog box, you
draw the base shape by moving a little turtle around (a
pointing icon). You move this turtle forward and backwards
with the Forward: + and - buttons. You turn the turtle
using the Turn + and - buttons. The turn increment can be
altered from the Options menu in the fractal dialog box.
Normally you draw with the pen down, however you can put the
pen up to draw discontinuous fractals like a mainland with
islands. As you draw the Base Shape it will appear in the
drawing area on the right-hand side of the dialog box.
When you click on OK (or press return) the new fractal
Base Shape will appear in the tool box allowing you to draw
this fractal at any level in the drawing area. A computer
generated name for this fractal also appears in the tool
menu. Clicking on Cancel or pressing the escape key will
exit the dialog box discarding any drawing you may have
done.
Define L-systems. . .
Fractal Paint User's Manual/10
L-systems are a generalization of the Base Shape
definitions. They define a fractal by a number of symbolic
equations (called production rules) and an axiom to draw
them. This dialog box allows you to edit existing L-systems
and create new ones. You can also evolve L-systems by
creating a number of child systems obtained from the parent
system by random perturbation.
To edit an existing L-system select it in the list box
of current L-systems and click on the Load button to load
its production rules, axiom, name and angle into the dialog
box. To save an L-system make sure the Name field is what
you want (a new name for a new L-system, an old name to
replace an old L-system) and click on the OK button or press
Enter. To disregard any changes and exit with a click on
the Cancel button or press escape.
L-systems, or string rewriting systems, are algorithms
that produce character strings which are interpreted as
curves and pictures. L-systems provide an elegant way to
generate the classic fractal curves such as the von Koch
snowflake, von Koch islands, Hilbert and Peano space-filling
curves and branching patterns such as trees and bushes.
Fractal Paint Turtle
In the course of the algorithm, a long string of
characters is generated. Fractal Paint has a more direct
and efficient way of rendering these curves; however, this
is more instructive. The characters are letters of the
alphabet or special characters such as '+', '-', '[', ']',
'/', etc. Such a string corresponds to a picture. The
correspondence is established via a turtle which interprets
the characters sequentially as basic commands such as "move
forward", "turn left", "turn right", etc.
The main ingredient of the method is the algorithm for
string generation. A first string of only a few characters
must be given. It is called the axiom. Then each character
in the axiom is replaced by a string taken from a table of
production rules. This substitution procedure is repeated a
prescribed number of times according to the fractal level to
produce the end result.
In order to specify a complex curve or tree, only a few
production rules will suffice. The axiom along with the
production rules may be regarded as the genes which control
the "growth" of the object. This information is very small
as compared to the complexity of the resulting picture. The
challenge is to find the axiom and production rules
necessary to produce a given object or an object with given
properties. This is a topic of current research, but
methods do exist, such as evolution.
Fractal Paint User's Manual/11
As an introductory example, let's consider the von Koch
snowflake curve. Consider a turtle that obeys the following
commands: 'F' draw a line forward, '+' turn right by 60° and
'-' turn left by 60°. We start out with a straight line
denoted by "F". This is the axiom of the von Koch snowflake
curve.
In stage 1, the line is replaced by a line forward, a
left turn, a line, two right turns (for a total of 120°), a
line, a left turn and another line. In the turtle's
language this can be written as the string "F-F++F-F".
Subsequently, each line symbolized by the character 'F',
again has to be replaced by the string "F-F++F-F". Thus, in
stage 2 we have the string "F-F++F-F-F-F++F-F++F-F++F-F-F-
F++F-F" and so forth.
In summary, we have that when proceeding from one stage
to the next we must replace a character 'F' by the string
"F-F++F-F", while the characters '+' and '-' are preserved.
Thus, the L-system consists of the axiom "F", the production
rules: "F -> F-F++F-F", "+ -> +", "- -> -" and angle 60.
Generally if a production rule is not listed it is assumed
to be the identity mapping such as "+ -> +".
The turtle commands that Fractal Paint uses are:
'F': move forward in the present direction and draw a
line.
'G': move forward in the present direction without
drawing a line.
'+': turn left by the given angle.
'-': turn right by the given angle.
'|': turn back (turn by 180°).
'[': save the state of the turtle on the stack.
']': restore the state of the turtle from the top of the
stack.
'/': divide the drawing line length by 2.
'!': reverse the meaning of + and -.
'@nnn': multiply line length by nnn where nnn is a
decimal number such as 2.323, 'I' and 'Q' can
precede the number, 'I' meaning take its inverse and
'Q' meaning take its square root.
'Cnnn': set color to nnn where nnn is a 24 bit windows
RGB color. (i.e. the low order byte is how much red,
the next byte is how much green and the next byte is
how much blue.
'>nnn': increase the color by nnn.
'<nnn': decrease the color by nnn.
Any other symbols are ignored by the turtle in the final
rendering, but are still important for constructing the
drawing path.
Fractal Paint User's Manual/12
Note for the color's used 0 is black, FFFFFFH is white,
FFH is red, FF00H is green FF0000H is blue. You can use the
Windows Calculator accessory to convert hex values to
decimal to use in your fractal definition. (The L-systems
interpreter does not under stand hex values.)
Evolve
When you click on the Evolve button, then a dialog box
pops up which draws the current L-system, at a fractal level
set by the Evolve Level field, and seven child L-systems.
The child systems are derived from the parent (original) L-
system by randomly altering its axiom, production rules or
angle.
From this dialog box you can choose one of the child L-
systems to replace the parent, or choose the parent to stay
the same. By choosing the L-system that looks most like
the way you want it and iterating this process, you can use
evolution or controlled selection to construct an L-system
that has the properties that you desire. You can also use
this feature to generate variations on a theme, such as
drawing a forest of similar but not identical trees.
Edit Text & Text Style. . .
Selecting edit text and text style brings up the text
dialog box. With this dialog box you can Edit Text in the
drawing window as well as the Text Style. You can also set
the Text Style for future text and enter new text for the
drawing window. If some text is selected when you invoke
this dialog box, then that text will be displayed in the
Enter text field and can be edited there. Also the Text
Style characteristics will be displayed and can also be
edited.
Text height is the height of the text in points, the
text width is the width of each character in points, if
width is 0 then the character width will be whatever is
appropriate for this character height. In Character Format,
weight is a number between 0 and 1000 and refers to how bold
the character should be, 900 is bold and 0 is normal.
The Font Name list box lists all available printer fonts
and screen fonts. For the printer fonts to be correct, the
correct printer must be installed by Windows (see the
Windows manual on how to do this).
The Background field determines if each character will
erase a little square around it, or if the background will
be visible through the character.
Color sets the Text Color and Background Color sets the
color of the little rectangle drawn around the character in
Fractal Paint User's Manual/13
White Out background mode. Note that not all combinations
of Color and Background Color produce visible text. If you
have a color monitor then the color will be displayed, if
you have a monochrome display then you are limited to black
or white, and the same goes for the printer depending on its
color capability.
A sample of how the text will look on the screen is
presented on the bottom of the dialog box. Windows can not
accurately display printer fonts on the screen, but will do
the best it can.
Line Style. . .
The line style selection brings up the line style dialog
box. This dialog box allows you to change the line width,
color and style for the selected object and for future drawn
objects. You select the color by using the scroll bars to
select the composition out of red, blue and green. A sample
of the line is provided to help you choose. Click OK or
press Return to make the change, or click Cancel or press
escape to quit without making any changes.
Patterns. . .
The Patterns item brings up the patterns dialog box
This dialog box allows you to change the pattern of a
selected rectangle, rounded rectangle or ellipse as well as
set it for all future rectangles, rounded rectangles and
ellipses. Click OK or press Return to make the change, or
click Cancel or press Escape to return without making any
changes.
Fractal Paint User's Manual/14
:2.6 The Tools Menu
+-------+
| Tools |
+-------+-----------+
| Selection |
| Text |
| Line |
| Rectangle |
| Rounded Rectangle |
| Ellipse |
| F1 |
| F2 |
| LSYS1 |
| LSYS2 |
+-------------------+
This menu provides an alternative to using the Tools
box. If you maximize the drawing window, then the toolbox
becomes inaccessible and this provides an alternative method
of selecting tools. A check mark appears next to the
selected tool.
:2.7 The Options Menu
+--------+
|Options |
+--------+----+
|Show toolbox |
|Rulers |
+-------------+
|Fractal... |
+-------------+
This dropdown menu lets you set some miscellaneous
options.
Show toolbox. . .
Show toolbox will recreate the toolbox window if you
previously closed it from its system menu. If the toolbox
is displayed then this menu item is grayed.
Rulers. . .
Rulers will display rulers along the top and left side
of the drawing window. This is to aid in positioning
objects on the page. To remove the rulers then select this
item again.
Fractal. . .
Fractal Paint User's Manual/15
When you select the Fractal item from the Options drop
down menu, you can select a number of options that affect
drawing in other parts of the program.
The first set of buttons let you select the fractal
level that will be used when drawing any future fractals.
The turn increment box lets you enter the turn increment
that will be used when you press the '+' or '-' turn buttons
in the Define Base Shape dialog box.
The next check box select whether Fractal Paint will
automatically redraw the screen whenever required. You
might want to turn off this automatic redrawing if you have
a drawing that requires a long time to redraw and you are
doing a lot of switching between windows.
:2.8 Help
To get Help click on the Help menu item or press the F1
key. Help is a separate program to Fractal Paint that comes
with Microsoft Windows. It can be moved and sized like any
other Windows application. To move through the Help text
use the scroll bars in Help's text area. For more
information on the Help program refer to the MS-Windows
manual.
3. Fractal Programming Language
The image in the drawing window is represented
internally to Fractal Paint as a program in FPL (Fractal
Programming Language). You can write your own FPL programs
or edit existing FPL programs using the Edit window
(obtained from the Program dropdown menu), or by using
another text editor (and transferring the program to Fractal
Paint through the Clipboard or as ASCII text file usually
with an ".FPL" extension).
FPL is a very simple assembly-like language with one
statement per line and each statement consisting of a
command (like MOVETO) and a number of arguments separated by
white space (spaces and tabs).
When you edit drawings using the Tool Box and the
various dialog boxes, you are in fact editing an FPL
program, however Fractal Paint is handling all the details
for you.
If you write or edit FPL programs you should try to make
them look like programs that are generated using the toolbox
commands. Each object should have a label and coordinates
Fractal Paint User's Manual/16
should be zero extended to five digits. If you don't do
this then some of the toolbox command such as move and some
of the dialog boxes may have difficulty editing your
program.
Fractal Paint uses a logical coordinate system, where
(0,0) is at the lower left, the X axis extends right to
(10000, 0), and the Y axis extends up to (0, 10000). This
coordinate system is then mapped onto whatever page size you
have specified with the Page Size dialog box.
Following is a list of all the FPL commands and a quick
description of their arguments:
FRACDEF NAME CUTFAC NUMPTS T1 P1 T2 P2 ... TNUMPTS
PNUMPTS
- Define fractal NAME, with cut factor CUTFAC, number of
defining points NUMPTS, Tn turn after point n, Pn pen
pos while drawing to point n.
LSYSDEF NAME TURN_INC AXIOM NUM_PROD_RULES
INP_PROD_RULE1 OUT_PRODRULE1 ... INP_PROD_RULEn
OUT_PROD_RULEn
- Defines a L0-system fractal with the given production
rules and axiom.
FRAC NAME SIZE LEVEL
- Draw fractal NAME, SIZE units across, of level LEVEL.
LSYS NAME LEVEL SEG_LENGTH
- Draw L0-system NAME, at level LEVEL with line segments
SEG_LENGTH long.
LINE DIST
- Draw a line DIST units in the current direction.
LINETO X Y
- Draw a line from the current position to (X,Y).
RECT X Y
- Draw a rectangle with one corner at (X,Y) and the other at
the current position.
RNDR X Y XE YE
- Draw a rounded rectangle with one corner at (X,Y) and the
other at the current position. The width and length of
the ellipses used to round the corners are XE and YE.
ELLI X Y
- Draw an ellipse enclose in the rectangle with one corner
at the current position and the opposite corner at (X,Y)
Fractal Paint User's Manual/17
MOVE DIST
- Move forward DIST units in the current direction (without
drawing).
MOVETO X Y
- Move the current position to coordinates (X,Y) (without
drawing).
TURN ANG
- Turn ANG degrees.
TURNTO ANG
- Turn to ANG degrees direction.
TEXT "String of text"
- Write the text contained between the quotes starting at
the current position.
TSTYLE HEIGHT WIDTH WEIGHT ITALIC
UNDERLINE STRIKEOUT CHARSET PITCHANDFAMILY BKMODE
RED BLUE GREEN BKRED BKBLUE BKGREEN "FACENAME"
- Set text style, gives all parameters that Windows can
accept when rendering text.
LSTYLE WIDTH STYLE RED BLUE GREEN
- Sets the line style.
PATTERN STYLE COLOR HATCH BACK_MODE
- Sets the pattern to use for filling regions.
CLEAR
- Pauses and then clears the screen.
4. A Tutorial
The following is a step by step guide through
constructing a number of fractals, and through drawing a
number of objects.
4.1 Basic Drawing
To draw a line; click the mouse on the line tool in
the Toolbox Window. Position the mouse in the drawing
window over where you want the line to start. Press the
left mouse button down and hold it down. Drag the mouse
around, notice that a line follows the mouse around
connected to the starting point. When the line is where you
want it, release the mouse button. To draw most other
objects you follow the same procedure, you select the object
you wish to draw, from the Toolbox Window (or Tools menu)
and then press the mouse button down over the start point
and release the mouse button over the end point. The
Fractal Paint User's Manual/18
exception to this rule is drawing text; which is
explained further down.
To alter the way the line looks choose Line style from
the Draw Menu. Try altering some of the controls in this
box and then drawing lines to see what effect they have.
Notice that there is a sample line to show what you are
selecting in the Line style dialog box.
To alter the way rectangles and circles look you can
alter the line that forms their boundary using the Line
style dialog box. Plus you can choose Patterns from the
Draw menu and alter the way their interiors are drawn. Try
playing with these controls and drawing some rectangles to
get the feel for how it works.
To draw text, choose the text tool in the Toolbox Window
(a big T). The click the mouse in the Drawing window where
you want the text to start. A vertical bar will start
flashing at this point. This is a cursor that indicates
where typed text will be placed in the drawing. Now type
some text. The text will probably be very small, this is
because the default view in the drawing window is of an
entire page. You can make the text bigger by selecting Edit
text and text style in the Draw Menu. You can make the text
bigger by making the height bigger, perhaps 40. You could
also "blow up" your view of the drawing using the View menu.
Try experimenting with this. Try altering different text
styles as well, such as different fonts, colors, italics,
etc.
To delete draw objects, choose the selection tool from
the Toolbox Window (an arrow in the upper left). Then click
on the object you wish to delete. A dashed rectangle should
appear around the selected object. Then choose Clear from
the Edit menu (or press Del). If you wanted the object
copied to the Windows clipboard so that you can paste it
back into Fractal Paint or into another Windows application
choose Cut instead. (Copy copies it to the clipboard
without deleting the object.)
To move an object, choose the move tool from the Toolbox
Window (a four headed arrow second from the top on the
left). Then push down the left mouse button over the
desired object, a dashed rectangle should appear around the
object, then while holding down the mouse button, move the
mouse until the dashed rectangle is where you want to move
the object. Then release the mouse button and the object
will be moved for you.
If you have a number of objects stacked on top of each
other and you wish to select one that is under another one,
use the Select next and Select previous menu items from the
Fractal Paint User's Manual/19
edit menu to bring the desired object to the top of the
stack so that you can select it.
4.2 Defining and Drawing Fractals
There are two basic ways to define Fractals with Fractal
Paint. The first we'll try is the simplest. We use the
Define Base Shape Dialog Box. These Fractals are made from
a base shape, the first level of these fractals is simply
the base shape itself. The next level is reached by
replacing each line in the current level with the base
shape. To illustrate, first set the turn increment in
Options - Fractal from the main menu to 60 (degrees), and
start with a new drawing (File - New). Then go into the
Define Base Shape Dialog Box from the Draw menu. Press the
+ button after Forward. The turtle should move to the right
leaving a trail. Press Turn +, and the turtle should turn
60 degrees left, now press forward + to move the turtle, now
press turn - twice and press forward + again. Now press
turn + and finally press forward + again. Now press OK.
The Fractal you just define should now appear in the
toolbox. Try drawing this Fractal first at level 1 and then
at level 2 and then at level 3 (set by the Fractal Level in
Options - Fractal). You should be able to see how this
Fractal is generated from the level 1 base shape you
created. Play with the Define Base Shape Dialog Box to see
what wonderful Fractals you can come up with. One good rule
of thumb is to always have the turtle end up in the
direction it started from (i.e. all the turns sum to zero),
also a turn increment of 90 degrees will often generate nice
looking Fractals easily.
5. A Guide to the Enclosed Samples;
The following table outlines what is in each of the
sample files contained on the distribution disk. Load the
file using File - Open from the main menu.
SAMPLSYS.FPL - Some sample L-System definitions. Try
drawing these at different fractal levels and different
sizes.
SAMPFRAC.FPL - Some sample Fractals made with the Define
Base Shape Dialog Box. Try drawing these at different
fractal levels and different sizes.
TREE1.FPL - A Fractal Tree.
TREE2.FPL - Another Fractal Tree.
Fractal Paint User's Manual/20
KOCH1.FPL - A Koch Island.
KOCH2.FPL - Some Koch Snowflakes.
LSYS1.FPL, LSYS2.FPL, LSYS3.FPL, LSYS4.FPL, LSYS5.FPL,
LSYS6.FPL: Some more predefined L-Systems to play with.
When you load them, they appear as tools in the toolbox.
You can then draw with them or play with them through
the Define L-Systems dialog box.
DEMO.FPL - A demo of many Fractals and many of Fractal
Paints capabilities. If you plan to load this, it might
be a good idea to turn off automatic redraw in Options -
Fractal from the menu and then draw the program using
Program - Run from the main menu. Notice that this demo
is entirely written in FPL itself.
6. Support for Fractal Paint;
Support for Fractal Paint is available for registered
users. Have your registration number handy for verification
when you call. We can be reached at ComputerSmiths, between
8:30 a.m. to 5:00 p.m. Pacific Time at 604-224-5242, or you
can download our 24 hour BBS line at 604-224-5247.
We would love to hear your comments and find out what
our users are doing with this new drawing program. Call or
write please.
Fractal Paint User's Manual/21
7. References
To learn more about fractals see the following
references:
Abelson, H., DiSessa, A.A. "Turtle Geometry: The Computer
as a Medium for Exploring Mathematics." Cambridge,
Massachusetts: The MIT Press, 1980.
Art Matrix, "Mandelbrot Sets and Julia Sets", A Video tape
of evolving Mandelbrot and Julia sets, available from:
Art Matrix, PO 880MJ Ithaca, NY, 14851-0880 USA.
Mandelbrot, B.B. "The Fractal Geometry of Nature." New
York: W.H. Freeman and Co., 1982.
Peitgen, H.-O., Saupe, D. (eds.). "The Science of Fractal
Images." New York: Springer-Verlag, 1988.
To learn more about C and Windows programming see the
following references:
Petzold, C. "Programming Windows." Redmond, Washington:
Microsoft Press, 1988.
Stevens, R.T. "Fractal Programming in C." Redwood City,
California: M & T Books, Inc., 1989.
Fractal Paint User's Manual/22
Appendix A: Updating WIN.INI;
You can add a line to "WIN.INI" so that when you double
click on a file with the extension ".FPL", Fractal Paint
will automatically be run by Windows and Fractal Paint will
automatically open this file when it starts up.
To do this you must edit the file "WIN.INI" which is in
the directory in which you installed Windows. First, save
the current copy of "WIN.INI", so that if something goes
wrong you can recover. To edit the file use some standard
text editor such as Notepad which comes with Windows. All
you have to do is add one line to the [extensions] section
of "WIN.INI". Look for a line containing only
"[extensions]" in "WIN.INI", it is then followed by a number
of lines that look like "cal=calendar.exe ^.cal". To these
lines add the line "fpl=c:\fp\fp.exe ^.fpl", assuming you
installed Fractal Paint on the C: drive in \fp, otherwise
substitute the drive and path of where you installed Fractal
Paint.
Then save "WIN.INI", exit Windows and restart Windows so
that the change in "WIN.INI" can take effect.
Fractal Paint User's Manual/23
Fractal Paint Registration; CardFractal Paint
Registration Card;
Fractal Paint is shareware, so if you use this program
please send $25.00. Without some sort of financial support
from users, work on this program will not be possible. If
you send in the $25.00 you will receive a registered next
version of the program absolutely free. Also, we have a
forum on the ComputerSmiths BBS only for registered Fractal
Paint users.
Please fill out this card, enclose a cheque for $25.00
and mail it immediately to:
Fractal Paint Registration
International ComputerSmiths
3726 West Broadway
Vancouver, B.C.
V6R 2C1
Canada
Product: Fractal Paint Version: 1.0 Registration Number:
Name: ___________________________________________________
Company: ___________________________________________________
Title: ___________________________________________________
Address: ___________________________________________________
___________________________________________________
City: _______________ Province/State: _____________________
Country: ____________ Postal/Zip Code: ____________________
Telephone:( ) __________
Computer Type: AT Comp 286 [ ] AT Comp 386 [ ] PS/2 [ ]
Diskette Size: 5 1/4" [ ] 3 1/2" [ ]
Other: _________________________________________
1. Introduction to Fractal
Paint 1
1.1 Installation 1
1.2 Introduction to
Fractals 2
2. The Menus 3
2.1 The File Menu 3
2.2 The Edit Menu 4
2.3 The View 5
2.4 The Program Menu 6
2.5 The Draw 7
2.6 The Tools 11
2.7 The Options 11
2.8 Help 12
3. Fractal Programming
Language 12
4. A Tutorial 14
4.1 Basic Drawing 14
4.2 Defining and Drawing
Fractals 15
5. A Guide to the Enclosed
Samples 16
6. Support for Fractal Paint 16
7. References 17
Appendix A
Updating WIN.INI 18
Fractal Paint Registration
Card 19
TURN 13
2 X 6 TURNTO 13
3 X 6 Turtle 8
4 X 6 Tutorial 14
Actual Size 6 Undo 4
Basic Drawing 14 View 5
Clear 5, 14 WIN.INI 18
Copy 5
Cut 5
Define Base Shape 7
Define L-systems 7
Draw 7
Edit 6
Edit Text & Text Style 9
ELLI 13
Evolve 9
Exit 4
Fit in Window 5
FRAC 13
FRACDEF 13
Fractal 11
Fractal Programming Language 12
Help 12
Installation 1
LINE 13, 14
Line Style 10
LINETO 13
LSTYLE 14
LSYS 13
LSYSDEF 13
MOVE 13
MOVETO 13
New 3
Open 3
Options 11
Page 6
Paste 5
PATTERN 14
Patterns 10
Print 4, 6
Program Menu 6
RECT 13
Registration 19
RNDR 13
Rulers 11
Run 6
Samples 16
Save 3
Save As 4
Show toolbox 11
Support for Fractal Paint 16
TEXT 13, 14
Tools 11
TSTYLE 14
