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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 1.06 May. 12, 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