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MANDELBROT MAGIC Version 3.1 USER'S MANUAL Left Coast Software P.O. Box 160601 Cupertino, CA 95016-0601 (408) 996-3130 June 1, 1989 Copyright 1989 Left Coast Software. All rights reserved. SOFTWARE LICENSE AGREEMENT Mandelbrot Magic is distributed as a shareware program. It is NOT a public domain program! However, we encourage you to copy the program for trial purposes. The program and all associated files can be freely copied and shared to allow others to try Mandelbrot Magic. You may upload this program and all associated files to any bulletin board system (BBS) or on-line computer service. You may not charge more than $10 to distribute Mandelbrot Magic in any form. If you try Mandelbrot Magic and decide to use it, you must register your copy. If you do not register your copy, you are not authorized to use the program beyond an initial evaluation period of thirty (30) days. By registering, Left Coast Software grants you a license to use the copyrighted computer program Mandelbrot Magic on a single computer, subject to the terms and conditions of this license. You agree not to (a) modify, disassemble, or decompile the program or (b) use this program on more than one terminal of a network, on a multi-user computer, on a time-sharing system, on a service bureau, or on any other system on which the program could be used (other than for trial purposes) by more than one person at a time. The registration fee for Mandelbrot Magic is $15. When you register, you will receive the most recent version of the program and will be placed on our mailing list to receive information on future upgrades to the program. In addition, you'll receive a copy of BackMAGIC, a memory resident program which generates fractal slides in the background while you work with other programs. BackMAGIC IS NOT A SHAREWARE PROGRAM! The only way you can obtain a legal copy of BackMAGIC is to register as a user of Mandelbrot Magic. To register for Mandelbrot Magic, send your checks to: LEFT COAST SOFTWARE P.O. BOX 160601 CUPERTINO, CA 95016-0601 (408) 996-3130 Users located outside the U.S. please send international money orders denominated in U.S. dollars. You may also register or order by phone. We accept VISA and MasterCard. A registration/order form is included at the end of this manual. THE PROGRAM ON THIS DISKETTE IS PROVIDED "AS IS". LEFT COAST SOFTWARE DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, AS TO THE PROGRAM OR ITS PERFORMANCE OR QUALITY, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT WILL LEFT COAST SOFTWARE BE LIABLE FOR ANY DAMAGES, INCLUDING WITHOUT LIMITATION DIRECT, INDIRECT, INCIDENTAL, SPECIAL OR CONSEQUENTIAL DAMAGES, LOST PROFITS OR LOST DATA, RESULTING FROM THE USE OF OR INABILITY TO USE THE PROGRAM. A WORD TO VERSION 2.0 USERS Although the name is the same as Mandelbrot Magic Version 2.0 and the program looks familiar, Mandelbrot Version 3.1 is essentially a completely new program. It has been completely rewritten to provide a host of new features and much greater performance. Our goal was to create the best program for creating, displaying and manipulating slides of the Mandelbrot and Julia Sets on an IBM PC. We think we have succeeded. Rather than list all of the changes, we suggest that you read the Version 3.1 manual in its entirety. It's not that long and this is the best way to understand all of the changes and new features. Unfortunately, the vast number of changes incorporated into Version 3.1 made it impractical to maintain compatibility with Version 2.0 files. Version 2.0 files will not work with Version 3.1; if you attempt to load a Version 2.0, you will get a critical error message, just as if you attempted to load a spreadsheet file into the program. We recognize that this incompatibility will cause grief for some users, especially those who have CGA adapters since you cannot use the new higher graphics resolutions provided in Version 3.1. We understand that recreating your favorite slides to work with Version 3.1 is a time consuming process and we apologize for the inconvenience. Fortunately, we have recently created BackMAGIC, a memory resident program which can generate slides in the background, while you use your computer for other purposes. Please refer to the manual for details on BackMAGIC. MANDELBROT MAGIC USER'S MANUAL TABLE OF CONTENTS SECTION PAGE ------- ---- 1. INTRODUCTION.......................................1 2. SYSTEM REQUIREMENTS................................2 2.1 GRAPHICS ADAPTERS.............................2 2.2 MEMORY REQUIREMENTS...........................3 2.3 COMPUTATIONAL SPEED...........................3 3. A BRIEF INTRODUCTION TO FRACTALS...................4 3.1 THE MANDELBROT SET.............................4 3.2 JULIA SETS.....................................5 3.3 SUGGESTED READINGS.............................6 3.4 VIDEOS.........................................6 4. USING MANDELBROT MAGIC..............................7 4.1 STARTING MANDELBROT MAGIC......................7 4.2 CONTROL PANEL..................................8 4.3 MESSAGES AND PROMPTS...........................8 4.4 LOADING A SLIDE................................8 4.5 DISPLAYING A SLIDE.............................8 4.5.1 Color Mode..............................9 4.5.1.1 Cyclic..........................9 4.5.1.2 Sectional.......................9 4.5.1.3 Equal Areas....................10 4.5.1.4 Assigned.......................10 4.5.2 Number of Regions (Size of Color Band).10 4.5.3 Number of Colors.......................10 4.5.4 Use Black as Color.....................11 4.5.5 Show Coordinates.......................11 4.6 CONTROLLING THE SLIDE DISPLAY.................11 4.6.1 Assigning Colors.......................12 4.6.2 Changing Palettes......................14 4.7 ANIMATING A SLIDE.............................15 4.8 CREATING NEW SLIDES...........................16 4.8.1 File/Pathname..........................16 4.8.2 Slide Type.............................16 4.8.3 Compressed.............................16 4.8.4 X (Real) and Y (Imaginary).............17 4.8.5 C Value (Julia)........................17 4.8.6 Slide Size.............................17 4.8.7 Number of Iterations...................18 4.8.8 Graphics Mode..........................19 4.8.9 Show Coordinates.......................19 4.8.10 The Grid Method........................20 4.9 ZOOMING IN ON A SLIDE.........................21 4.10 CALCULATING PARAMETERS........................22 4.11 CREATING A SLIDESHOW..........................22 4.12 PRESENTING A SLIDESHOW........................23 4.13 QUITTING......................................24 4.14 PRINTING SLIDES...............................24 SUGGESTED SLIDE PARAMETERS....................25 MANDELBROT SET.........................25 JULIA SETS.............................26 CUSTOMER SERVICE..............................27 OTHER LEFT COAST PROGRAMS.....................28 EXCHEQUER..............................28 PC-AREACODE............................29 BackMAGIC..............................29 ORDER/REGISTRATION FORM.......................30 COMMAND SUMMARY...............................31 1. INTRODUCTION Mandelbrot Magic generates color displays ("slides") of the Mandelbrot Set and Julia Sets on IBM PC-compatible computers with color graphics adapters. The Mandelbrot Set is perhaps the most famous of a fascinating group of mathematical structures known as fractals. Fractal geometry is a complicated mathematical field, but Mandelbrot Magic is easy to use and will automatically create spectacular slides when you specify a few simple parameters. With Mandelbrot Magic, you can create a new slide or load and view an existing slide from disk. The program runs on virtually any color graphics adapter and supports four different color modes from CGA (320 x 200 x 4 colors) to VGA (640 x 480 x 16 colors), depending on which adapter you use. Although the program offers three automatic coloring algorithms, the user has complete control over the color of any point as well as the color palette. Several different preprogrammed palettes are also provided. The program also features different "animation" techniques which make the features in the slide appear to move. One of the unique things about fractals is that they reveal more and more detail the closer you get and the small-scale details are similar to the large-scale details. With Mandelbrot Magic, you can graphically select any part of the slide to magnify. You can "zoom" in on various features of the fractal and reveal more detail. You can also create slideshows consisting of a sequence of up to 20 existing slides. This manual includes a list of suggested parameters for interesting slides and a list of suggested readings for those who want to explore the theoretical foundations of fractals in greater detail. 1 2. SYSTEM REQUIREMENTS Mandelbrot Magic runs on any IBM PC or PS/2-compatible computer with a minimum of 256k of memory, a color graphics adapter, a color monitor and a single floppy disk. A hard disk is not required but is recommended because the files used by this program are quite large (up to 310 k). A hard disk also reduces the time required to load existing slides from memory. Although an 80*87 math coprocessor is not required, it is recommended. Mandelbrot Magic automatically detects and uses the coprocessor if one is installed. 2.1 GRAPHICS ADAPTERS Mandelbrot Magic supports the CGA, MCGA, EGA or VGA graphics adapters and offers the following four standard graphics modes: Number of Number of Number of Mode X pixels Y pixels Colors ------------------------------------------------- CGA 320 200 4 EGA Low 640 200 16 EGA High 640 350 16 VGA 640 480 16 ------------------------------------------------- Mandelbrot Magic does not currently support any 256-color normal or extended mode on VGA adapters. Not all graphics adapters support all four standard graphics modes. The following chart show which modes are available on which adapters: Graphics Adapter -------------------------------------- Mode CGA MCGA EGA (64k) EGA VGA ------------------------------------------------- CGA X X X X X EGA Low X X X EGA High X X VGA X ------------------------------------------------- If you try to generate or display a slide in a mode not supported by your machine, Mandelbrot Magic will display an error message. Mandelbrot Magic also supports the extended EGA mode (640 by 480 pixels) of the Paradise Autoswitch 480 EGA card. You must have a Autoswitch 480 card to use this mode. WARNING: IF YOU TRY TO 2 GENERATE OR DISPLAY A SLIDE IN THIS MODE ON ANY OTHER EGA CARD, YOUR SYSTEM WILL CRASH!!! Slides generated in Paradise mode can be viewed on a computer with a VGA adapter but not vice versa. 2.2 MEMORY REQUIREMENTS Mandelbrot Magic itself requires approximately 120 K of RAM while running. However, additional memory is required to hold the slide. The amount of additional memory needed depends upon the number of pixels used in the slide which is a function of the graphics mode and the slide size. The total memory needed to run Mandelbrot Magic and to produce a full-size slide in each mode is: K-Bytes of Mode RAM Memory ------------------------- CGA 190 K EGA Low 250 K EGA High 350 K VGA 430 K Paradise EGA 430 K ------------------------- 2.3 COMPUTATIONAL SPEED Generating a fractal slide is an intensive computational task and will often take three or four hours on a standard PC. Some slides, however, can take up to 25 hours to generate. There are several ways to reduce the calculation time: o Use an 80*87 math coprocessor. Using a coprocessor will reduce the generation time by a factor of 3 to 5. o Buy a faster computer! o Reduce the size of the slide. Since Mandelbrot Magic must generate each point (pixel) in the slide, reducing the number of pixels in the slide reduces generation time proportionately. This is especially useful when exploring a particular area of the Mandelbrot or Julia Sets for the first time. o Use a lower graphics resolution. Mandelbrot Magic has several features which help reduce computing requirements. In addition to 80*87 support, the program takes advantage of certain symmetries in the Mandelbrot and Julia sets to reduce computation. You can also stop work on a slide then resume generation at a later time. Most importantly, registered users receive a copy of BackMAGIC, a memory resident program that generates Mandelbrot Magic slides while you run other programs! 3 3. A BRIEF INTRODUCTION TO FRACTALS Fractal geometry is one of the newest and most exciting fields of mathematics. It was essentially invented by Benoit Mandelbrot, an IBM research fellow. Fractal geometry has been used to create images and models of many different areas. From threedimensional landscapes in movies to accurate cross-sectional models of the heart, fractals are at the leading edge of research in many fields. One of the unique characteristics of fractals is that they reveal more and more detail the closer you get. Furthermore, the small scale details are similar to the large scale details. For example, consider a map of the coast of California with its jagged irregularities. If you look at a map of a smaller area such as a bay, you find that the edge of the bay has the same kind of shapes and irregularities as the California coast. Move closer to examine a one foot section of the shore and you again find that it has the same kind of shapes and irregularities. Although we will try to explain the basic concepts underlying the Mandelbrot and Julia Sets, we cannot begin to fully explain them. If you are interested in fractal theory (or just want to look at pretty pictures), please refer to the publications listed in Section 3.3. 3.1 THE MANDELBROT SET The Mandelbrot Set is perhaps the most famous of all fractals. It has been called "the most complicated object in mathematics." It was discovered by Benoit Mandelbrot during his work in fractal geometry. The Mandelbrot Set exhibits the same kind of repetitive detail at smaller and smaller scale unique to fractls. As you explore the Set, you will find innumerable miniature copies of the Set. Although many of these copies appear to be totally separate from the main Set, they are not. One interesting feature of the Set is that every point in the Set is connected. Each of these miniature sets is connected to the main body of the Set by a "thread" of points which are also in the Set. The Mandelbrot Set also includes an infinite number of kaleidescopic whirls and curlicues along the edge of the Set. The slides created by this program represent the plane of "complex" numbers. A complex number is made up of a real part and an imaginary part. An example of a complex number is 5 + 7i. The "5" is the real part and the "7i" is the imaginary part. The "i" in "7i" stands for the square root of -1. The term "imaginary" comes from the fact that the square root of -1 does not exist. Points which lie in the Mandelbrot Set have a real part between 0.50 and -2.00 and an imaginary part between 1.25 and -1.25. Each point (or pixel) on the slide represents a complex number. The real component of the number corresponds to the X dimension while the imaginary component lies along the Y dimension. 4 The Mandelbrot Set is generated by repeatedly performing a mathematical process on each point in the plane of complex numbers. A good description of this process appears in an article written by A.K. Dewdney which appeared in the August, 1985 issue of Scientific American: "Begin with the algebraic expression z2 [z squared] + c, where z is a complex number that is allowed to vary and c is [the complex number represented by a specific point]. Set z initially to be equal to the complex number 0. The square of z is then 0 and the result of adding c to z2 is just c. Now substitute this result for z in the expression z2 + c. The new sum is c2 [c squared] + c. Again substitute for z. The next sum is (c2 + c)2 + c. Continue the process, always making the output of the last step the input for the next one." After each iteration, the "size" of the resulting complex number is determined. The size can be thought of as simply the distance from the origin of the plane of complex numbers to the point which represents that complex number. The size is therefore equal to the square root of the sum of the squares of the real and imaginary parts of the complex number. (Got that?) As Dewdney describes: "The Mandelbrot set is the set of all complex numbers c for which the size of z2 + c is finite even after an indefinitely large number of iterations....A straightforward result in the theory of complex-number iterations guarantees that the iterations will drive z to infinity if and only if at some stage z reaches a size of 2 or greater." As a default, this program assumes that a specific point is in the Mandelbrot Set if the size is less than 2 after 1000 iterations. The color of each pixel reflects the number of iterations required for the size of z2 + c to reach 2. 3.2 JULIA SETS Benoit Mandelbrot discovered the Mandelbrot Set while investigating Julia Sets (named for the French mathematician Gaston Julia). Unlike the unique Mandelbrot Set, however, there are an infinite number of Julia Sets of many different types. Julia Sets are generated using essentially the same mathematical procedures as are used to generate the Mandelbrot Set. The only difference is that c is set to a constant and z is the value of the the complex number represented by a specific point in the display. Here's the fascinating part! The value of c determines what the associated Julia Set looks like. Mandelbrot discovered that the general shape of the Julia Set depends upon where c is in relation to the Mandelbrot Set. When c is far from the edge of the Mandelbrot Set, the result is much different than if c lies inside the Set. The most interesting Sets are produced when c lies very near the edge of the Mandelbrot Set. Mandelbrot Magic provides a very easy way to select these points and generate slides of interesting Julia Sets. 5 3.3 SUGGESTED READINGS If you are interested in the theory of fractals, the following books and articles are especially informative. The Dewdney article is the best introduction to the theory of fractals while Gleick's book is a readable account of the history of fractals and how they relate to the fascinating new field of chaos. Gleick's book is available in paperback in all serious bookstores. The Peitgen books can usually be found in large bookstores near major universities. Barnsley, Michael. Fractals Everywhere. San Diego: Academic Press, 1988. Dewdney, A.K. "Computer Recreations: A computer microscope zooms in for a look at the most complex object in mathematics", Scientific American (August 1985), pp. 16-20. Dewdney, A.K. "Computer Recreations: Of fractal mountains, graftal plants and other computer graphics at Pixar," Scientific American (November, 1987), pp. 14-20. Gleick, J. Chaos, Making a New Science. New York: Viking, 1987. Mandelbrot, Benoit B. The Fractal Geometry of Nature. New York: Freemant & Co., 1983. Peitgen, H.O. & Richter, P.H. The Beauty of Fractals. New York: Springer-Verlag, 1985. Peitgen, H.O. & Saupe, D. The Science of Fractal Images. New York: Springer-Verlag, 1988. If your theoretical interest in fractals and chaos is very strong, you should also contact Clifford Pickover of IBM and request information on the Journal of Chaos and Graphics. He will send you information on how to obtain back copies along with issues of other papers. Many of these are available for free from IBM. His address: Clifford A. Pickover IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598 3.4 VIDEOS Media Magic sells three interesting videotapes with fractal images -- "Fractal Fantasy", "Frontiers of Chaos" and "Nothing But Zooms" -- along with books, calendars and other assorted fractal-related items. Their address: Media Magic P.O. Box 2069 Mill Valley, CA 94942 (415) 381-4224 6 4. USING MANDELBROT MAGIC Before using Mandelbrot Magic, be sure to make at least one backup copy on a floppy diskette and store it in a safe place. If you want to run Mandelbrot Magic off of your hard disk, copy all of the program files to an appropriate directory. If you want to be able to run Mandelbrot Magic from any directory, make sure that you add the name of the directory containing MM.EXE to your DOS path. Refer to the DOS manual for details on the PATH command if you are unfamiliar with how to do this. So where do you start with Mandelbrot Magic and just what the heck do you do with it? Well, there are several slides on the distribution diskette. Three of these slides (M1*.PIC) show the entire Mandelbrot Set at three different resolutions (i.e. graphics modes). You will undoubtedly want to explore the Mandelbrot Set by magnifying certain parts of this slide. Working from these slides, you can use the program's Zoom function to select areas or you can enter the coordinates of the area directly (there is a list of some interesting values at the end of this manual). Then you make slides of the new areas and zoom in on them, etc, etc... Although there is only one Mandelbrot Set, there are an infinite number of Julia Sets. So you can approach the exploration of this type of fractal in two ways: (1) you can produce large-scale pictures of lots and lots of Julia Sets or (2) you can zoom in on slides of interesting Julia Sets and explore their features in greater detail. In practice, you will undoubtedly do both. This program comes with several sample slides. Two of these (M1_CGA.PIC and M1_EGA.PIC) are complete and can be displayed immediately. The others are incomplete; you can finish them by loading the appropriate file into the program (F9), then pressing F8 to finish creating them. 4.1 STARTING MANDELBROT MAGIC To run Mandelbrot Magic, move to the directory with MM.EXE and type: MM then hit <Return>. Assuming you have the proper graphics adapter, the title screen will be displayed. Next, a shareware information screen will be displayed. When you press a key, this disappears and the main Control Panel appears. If you do not have an acceptable graphics adapter, the program will refuse to run. If you want, you can avoid the title screen and shareware information screen by starting Mandelbrot Magic by typing either: MM Q or MM /Q then pressing <Return>. You can enter an upper or lower case "Q". 7 4.2 CONTROL PANEL The Control Panel is used to enter all of the parameters used while creating or displaying slides. The parameters for each slide are stored with that slide. Specific functions such as loading files, displaying slides or creating new slides are invoked by pressing the Function keys (F1 through F10). The Control Panel is divided into two sections -- a parameters section on top and a function key menu on the bottom. The top section contains two types of fields -- data fields where you will enter values for use in generating and displaying slides and status fields which just display information. The arrow keys, Home, End and <Return> can be used to move among the data fields. When entering data, pressing <Backspace> will delete the last character or digit. Each of the fields is described below. 4.3 MESSAGES AND PROMPTS Error messages and prompts appear in boxes in the middle of the screen. Most messages and prompts can be cancelled by pressing <Esc>. Prompts which require a Yes or No answer have a default value which are shown in brackets [ ] after the prompt. When a default value is shown, pressing any key except the opposite of the default will use the default value. For example, if the default is "Y" then you must press "N" or "n" to override the default. 4.4 LOADING A SLIDE You can load an existing slide by simply typing the name of the file containing the slide in the Filename field, then pressing F9. Mandelbrot Magic verifies that the slide exists, checks that the slide can be displayed on your computer, then loads the slide into memory and displays its parameters on the Control Panel. The time required to load a file depends upon both the size of the file (as determined by its resolution and its size) and whether the file was compressed during creation (See Section 4.8.3). 4.5 DISPLAYING A SLIDE Once you have loaded a slide (or created a new one), you can display it by pressing F10. You can also display a slide by pressing F1, F5, F6 or F7. If you press on of these other keys, the slide will be displayed just as if you pressed F10. However, the function associated with these keys (as described below) is invoked immediately once the slide is displayed. When you press F10, the screen will be cleared and Mandelbrot Magic will display the slide. Since each pixel must be drawn individually, displaying a slide can take as long as 20 seconds. The time required to display a slide depends upon the number of pixels (as determined by graphics mode and slide size) and the speed of your computer. 8 You can control how the slide is displayed by entering appropriate values for the following parameters: 4.5.1 Color Mode Mandelbrot Magic provides complete control over the colors of your slide by allowing you to modify the color assignments (i.e. which color number is assigned to which pixel) and the color palette (i.e. which actual color is assigned to each color number). As described in Section 3, the color of each point is based upon the number of iterations required for the size of the point to exceed a certain limit. Of course, all pixels which have identical values (i.e. number of iterations) will be the same color at all times. Mandelbrot Magic provides four separate mechanisms for assigning colors to individual pixels in a slide. Select a color mode by highlighting the color mode field on the Control Panel and pressing the <Space> bar to cycle through these four choices. Once the slide is displayed, you can redisplay the slide with a different color mode by pressing F10 in conjunction with another key. The key combination for each mode is listed after the name of the color mode in the following descriptions: 4.5.1.1 Cyclic (Ctrl-F10) If you select the Cyclic color mode, Mandelbrot Magic will assign color numbers to various iteration values according to a regular cycle. For example, pixels with values of 1 will be colored with color number 1, pixels with values of 2 will be colored with color number 2,... pixels with values of 15 will be colored with color number 15, etc. When Mandelbrot Magic runs out of colors, it simply starts over again. When you select this mode, you should also input the number of colors to be used in the slide and the width of the color band. In the preceding example, the color band width is 1. If you set the band width to 3, then pixels with values of 1, 2 or 3 will be colored with color number 1, pixels with values of 4, 5, or 6 will be color with color number 2, etc. 4.5.1.2 Sectional (Shift-F10) When you select the Sectional color mode, Mandelbrot Magic divides the total range of possible pixel values (from 1 to the maximum number of iterations) and divides into equal sections. All pixels within a certain range would then be colored with the same color. For example, if you have a slide with a maximum iteration count of 1000 and divide it into 50 sections, then all pixels with values from 1 to 20 will be colored with color number 1, all pixels from 21 to 40 will be colored with color number 2, etc. When you select this color mode, you must also input the number of color regions since this controls how many sections are used. 9 Although the Sectional and Cyclic color modes are conceptually different, they can usually be used to produce identical results. For example, if you have a slide with a maximum iteration count and divide it into 50 sections using the Sectional mode, you can achieve the same result by using the Cyclic mode with a bandwidth of 20 (1000 divided by 50). 4.5.1.3 Equal Areas (F10) When the Equal Areas mode is chosen, Mandelbrot Magic will divide the slide into separate color regions of approximately equal size. You must therefore enter the number of color regions on the Control Panel when you select this mode. This mode often produces the best visual results. Since most slides have areas where the pixel values vary widely, the Cyclic and Sectional mode will make these areas appear very speckled. In some cases, virtually all detail is lost. The Equal Areas mode can avoid this problem. 4.5.1.4 Assigned (Alt-F10) Mandelbrot Magic also allows you to assign any color to any pixel value by pressing F5. The mechanism for doing this is described in detail in Section 4.6.1 - Assigning Colors. If you select this mode, Mandelbrot Magic will first display the slide using the Sectional color mode. You can then assign colors as you choose. Although the Assigned mode requires the most work, it is extremely useful precisely because it allows you to assign colors on a point by point basis. Thus, you have complete control over how the slide will look. 4.5.2 Number of Regions (Size of Color Band) This parameter controls how many separate color regions will appear on the slide. The maximum number of regions is 99 and the minimum number is 1. Depending upon the Color Mode and the characteristics of the slide itself, the actual number of color regions you see at any give time may be less than the number you entered. In the Cyclic mode, this field is used to input the size of the color band rather than the number of regions. For example, if you enter "5" then the color will change every 5 steps. 4.5.3 Number of Colors This parameter selects how many different colors will be used in the slide. The maximum is determined by the graphics mode selected while generating the slide. For the CGA mode, the maximum number of colors is 4 while it is 16 in EGA and VGA modes. 10 4.5.4 Use Black As Color This value controls whether Mandelbrot Magic will use the background color (which is black by default but can be changed) in displaying the slide. The background color is ALWAYS used to color the Mandelbrot Set or Julia Set itself (i.e. those points which have values equal to the maximum number of iterations). If you set this parameter to YES, then the background color will appear in other places in the slide as well. The default value is NO. The practical effect of using black as a color is to insert bands of black into the slide. 4.5.5 Show Coordinates If this parameter is set to YES when displaying a slide, then maximum and minimum X and Y coordinates will be shown on the slide. If it is set to YES while creating a slide, then Mandelbrot Magic will also display the elapsed time since the slide was started in hours and minutes (e.g. 3:17) and the percent of the slide that is complete. When you are done viewing the slide, press <Esc> to return to the Control Panel (you will be prompted to confirm this step). You cannot display a slide with a graphics mode different from the one used when it was created. The mode (and thus the resolution) is determined during the creation of the slide. If you enter a different mode, Mandelbrot Magic just ignores the information. 4.6 CONTROLLING THE SLIDE DISPLAY Once you have displayed a slide, you can control many aspects of the display. As discussed above, you can redisplay the slide with a different color mode (without returning to the Control Panel) by pressing one of the following keys: F10 Redisplays the slide using the Equal Areas color mode. Ctrl-F10 Redisplays the slide using the Cyclic color mode. Shift-F10 Redisplays the slide using the Sectional color mode. Alt-F10 Redisplays the slide using the Assigned color mode. Prior to redisplaying a slide, you can change the number of regions (or width of the colorband with the Cyclic method) without returning to the Control Panel by pressing Alt-N. A data input box will pop up on the screen; simply enter the new number and press <Return>. Press <Esc> if you decide not to change this number. You can also control the palette by pressing the following keys: B or b Cycles the background color (which is used to color the Mandelbrot or Julia Set itself) through all possible combinations. 11 P or p In EGA or VGA mode, cycles through 10 predefined color palettes. In CGA mode, cycles through four predefined palettes. Home Restores the palette to the default values. End In EGA or VGA mode, generates a random palette out of all possible colors. In CGA mode, selects a new background color at random. Up "Rotates" the palette upward (i.e. the colors shift toward higher pixel values). Down "Rotates" the palette downward (i.e. the colors shift toward lower pixel values). PgUp Continuously rotates the palette upward. This is similar to holding the Up Arrow key down continuously. PgDn Continuously rotates the palette downward. This is similar to holding the Down Arrow key down continuously. + Increases the delay between successive rotations of the palette when either PgUp or PgDn is pressed. In other words, it slows down the display. - Decrease the delay between successive rotations of the palette when either PgUp or PgDn is pressed. In other words, it speeds up the display. After pressing "+" or "-", you must press PgUp or PgDn again to restart the palette rotation. 4.6.1 Assigning Colors When you select the Assigned color mode, Mandelbrot Magic will display the slide using the colors you choose. To make the actual color assignments, press F5 while a slide is displayed. A Color Window will appear at the bottom of the slide. If you press F5 from the Control Panel, the slide will first be displayed, then the Color Window will appear. You can also access the Color Window from the Palette Window directly by pressing F5 (See following Section). The Color Window displays a relative frequency graph for the slide. The X axis of the graph shows all of the pixel values from 1 to 250 (see Section 4.8.7 for a more complete discussion of pixel values). The pixel value is simply the number of iterations required before a pixel exceeds the limit for inclusion in either a the Mandelbrot or a Julia Set. The Y axis of the chart plots the number of pixels in the slide which have the corresponding pixel value. The range of the Y axis is from 0 to 1.0, where 1.0 represents the maximum number of pixels for any 12 single pixel value (excluding the limit value). If there are no points with a specific pixel value, then no line is plotted for that point. Note that there is a minimum plot height for any value which has a non-zero number of pixels. Thus, a value with 1 pixel might appear to be the same as a value with 100 pixels. This is done to improve the readability of the chart and has little practical impact upon the chart. At the bottom of the graph is an arrow which points to the current pixel value. You can move the arrow using the following keys: Left Arrow Moves the Arrow one pixel to the left. Right Arrow Moves the arrow one pixel to the right. Home Moves the arrow to the left hand edge of the chart (i.e. a pixel value of 1). End Moves the arrow to the right hand edge of the chart (i.e. a pixel value of 250). Once you have selected a specific pixel value, you can change its value with the following keys: Up Arrow Increases the color number of that pixel value by 1. <Return> <Space> + Down Arrow Decreases the color number of that pixel value by 1. - Finally, you can "paint" adjacent areas of the graph by using the Left and Right Arrow keys in combination with the Ctrl Key: Ctrl-Right Moves the Arrow one pixel to the right and "drags" the current color to the new pixel. Ctrl-Left Moves the Arrow one pixel to the left and "drags" the current color to the new pixel. Note that this window can only be used to assign colors, not palettes. For example, if you keep pressing the up arrow, you will cycle through the 16 current colors in the palette rather than the maximum of 64 colors which is available on an EGA or VGA. You can, however, go directly to the Palette Window (see following Section) by pressing F6. You can return to the Color Window by pressing F5. Press <Esc> to close the Color Window and return to the slide. In addition to assigning colors, the relative frequency graph also provides useful information for generating slides. Specifically, it will show you how many pixels were close to the limit on iterations for that slide. If there is a large mass of pixels at the right hand 13 end of the graph, this suggests that you should use a larger number of iterations to reveal more detail. Conversely, you should use fewer iteration (and save time) if most of the points are at the left hand side of the graph. 4.6.2 Changing Palettes Although the EGA and VGA adapters can only display 16 colors at a time, these colors can be chosen from a total of 64 different colors. The current selection of 16 colors out of these 64 options is called the current palette. (In EGA low resolution mode of 640 x 200 pixels, there are only 16 possible colors. The current palette can thus include all available colors, although this is not mandatory). Mandelbrot Magic provides several ways to alter the current palette. Changes to the palette are reflected immediately on the slide. You can change the color palette by pressing B, P, Home and End as discussed in Section 4.6. In addition, you can achieve total control over the color palette by pressing F6 while a slide is displayed. A Palette Window will appear at the top of the slide. If you press F6 from the Control Panel, the slide will first be displayed, then the Palette Window will appear. You can also access the Palette Window from the Color Window by pressing F6 (see preceding section). Please note that because of the CGA's design, you cannot change the color palette when displaying a slide generated at CGA resolution (even if you have an EGA or VGA). You can only cycle through the four pre-programmed palettes by pressing "P". The Palette Window displays 16 color blocks which represent the 16 current colors in the palette. The leftmost block shows color number 0 while the rightmost block shows color 15. (Color 0 is the background color). Below the color blocks is an arrow which points to the current color. You can move the arrow to select a different color by using the following keys: Left Arrow Moves the Arrow one block to the left. Right Arrow Moves the arrow one block to the right. Home Moves the arrow to the first color (0). End Moves the arrow to the last color (15). Once you have selected a specific color, you can change its value with the following keys: Up Arrow Increments the current color by 1. <Return> <Space> + PgUp Increments the current color by 8. 14 Down Arrow Decrements the current color by 1. - PgDn Decrements the current color by 8. Mandelbrot Magic's color spectrum does not correspond to the sequence of the EGA's default palette or to the octal numbers often used to refer to its colors. All of the available colors are arranged a crude, linear spectrum which runs from black to gray to purple to blue to green to yellow to red to white. When you change one of the palette colors, you are moving through this linear sequence. When you reach one end, you automatically start over at the other end. This spectrum groups all similar colors together and makes it easy to find the color you want. You can also access the Color Window from the Palette Window by pressing F5. Pressing F6 again returns you to the Palette Window. Press <Esc> to return to the slide display. 4.7 ANIMATING A SLIDE Pressing F7 while a slide is displayed "animates" the slide so that it is redisplayed continuously. After each pass, the color "map" which Mandelbrot Magic uses to determine the color of each pixel is modified. As a result, different areas of the slide will appear to "grow". This effect is most interesting on fast computers, at lower resolutions, and with a relatively small number of color regions (less than 8). It is also interesting to let the animation run for an hour or two and check it occasionally since you will see a wide range of color assignments. You can control the animation with the following keys: Up Animates the slide in the "up" direction, i.e. colors move toward higher pixel values. Down Animates the slide in the "down" direction, i.e. colors move toward lower pixel values. + Increases the delay between slide displays, thus slowing the animation down. - Decreases the delay between slide displays, thus speeding the animation up. <Esc> Stops the animation. Unless you have an incredibly fast computer, you will almost certainly not want to slow down the animation process. As a default, Mandelbrot Magic runs the animation at the fastest possible speed. Finally, when you press <Esc>, the animation stops immediately. You will probably want to redisplay the slide by pressing one of the F10 key combinations. 15 4.8 CREATING NEW SLIDES This is the heart of Mandelbrot Magic. Unfortunately, generating a slide is an extremely intensive computational task. Even a CGA-mode slide contains 64,000 pixels, each of which must be calculated independently. A VGA-mode slide contains over 300,000 pixels! Furthermore, the calculations required to produce a slide utilize floating point arithmetic which greatly increases the computation time. It can take up to 25 hours to generate a reasonably complex slide on a standard IBM PC without a math coprocessor. There are two ways to minimize the inconvenience of long processing times. First, you can create the slides at night or during some other time when you do not need your computer, then display them at a later time. Alternatively, you can register for Mandelbrot Magic and get a copy of BackMAGIC, our memory resident program that generates slides in the background while you use your computer for other purposes. (Note: Mandelbrot Magic, like many graphics programs, is incompatible with many screen blankers. Once the screen is blanked, your system may freeze. This is generally not a problem while viewing a slide since you will probably press a key often enough to keep the screen blanker from clearing the screen. It is a problem while generating slides, however, so you should deactivate any screen blanker while creating a slide). You can create a new slide by entering the following parameters, then pressing F8 or Alt-F8 (See Section 4.8.10): 4.8.1 File/Pathname This is simply the name of the file which will store the values used in the slide. Any DOS-acceptable filename can be used and you can use any extension. If you want to store the slide in a directory/ disk different from the current disk/directory, simply enter the complete pathname (i.e. a:\fractals\slide1.pic). 4.8.2 Slide Type There are two different Slide Types: Mandelbrot and Julia Set. Press the <Space> bar to toggle between these two values. 4.8.3 Compressed Since Mandelbrot Magic must store a separate value for each pixel in the slide, the slide files can become quite large. For example, a VGA mode slide (640 by 480 pixels) uses over 307 K of disk space. If you want, Mandelbrot Magic will automatically compress this data as it generates the slide. Press <Space> to select the option you want. You can typically reduce the size of the file by 40 to 70 percent. In addition, compressed files often load faster than uncompressed files. Once you set this parameter, you cannot change the type of 16 the slide file. Once a slide is compressed, it must remain compressed and vice versa. Mandelbrot Magic uses a proprietary data compression scheme tailored to the unique characteristics of its slide files. You can also use a commerical data compression program to compress a slide files (even if it is already compressed using Mandelbrot Magic). If you use a standalone compression program, you must first decompress the file before you can load it into Mandelbrot Magic. 4.8.4 X (Real) and Y (Imaginary) The maximum and minimum values for X and Y determine the part of the Mandelbrot or Julia Set which will be displayed on the slide. As discussed in Section 3, X refers to the real component of the complex number plane and Y refers to the imaginary component of the complex number plan. The maximum acceptable value is 9.9999... while the minimum value is -9.9999.... The entire Mandelbrot Set lies within the range of X equals -2.5 to 1.0 and Y equals -1.5 to 1.5. These are essentially the default values for the program which appear when you first start Mandelbrot Magic. Similary, the range of X equals -2.0 to 2.0 and Y equals -1.5 to 1.5 will usually display all of a Julia Set. Mandelbrot Magic provides a way to enter these values automatically (See Section 4.10). When you enter values for X and Y, the difference between the maximum and minimum values will be displayed on the Control Panel. This is designed as an aid to help you enter appropriate values. Mandelbrot Magic also provides two other functions to aid in the selection of proper X and Y parameters. These are the Zoom function (See Section 4.4.9) and the Calculate Parameters function (See Section 4.10). 4.8.5 C Value (Julia) If you want to create a slide of a Julia Set, you must also enter a seed value (C) for the Set. This seed value has both a real (X) and imaginary (Y) component since it represents a point in the complex number plane. When creating a Mandelbrot Set slide, Mandelbrot Magic ignores these parameters. 4.8.6 Slide Size Mandelbrot Magic usually creates a slide which fills the entire display screen. You can create smaller slides by changing the X and Y dimensions of the slide. To change the slide size, enter the size of each dimension (in percent) in the appropriate field. Do not enter the number of pixels; Mandelbrot Magic automatically determines how many pixels will be in the slide. The values you enter for X and Y cannot be used to set the slide size; Mandelbrot Magic always uses the slide size parameters to set slide size and then automatically 17 centers the area which you specified with the X and Y values in the middle of the slide. Why would you want to make a slide that didn't fill the entire screen? A smaller slide takes less time to calculate, which can be handy when you are just looking for interesting areas. Or you might want to create a small slide first to verify that all your other parameters are correct before generating a full size slide. Or you might want to focus on a particular feature in a Set which has a much different aspect ratio than your screen. 4.8.7 Number of Iterations As discussed in Section 3, points lie in the Mandelbrot set or a Julia set only if their "size" does not exceed a preset limit after a certain number of iterations. This data field determines how many times the program will perform the mathematical process described in Section 3. The maximum number of iterations is the default value of 1000. This is a rather arbitrary number; theoretically, the calculation should be performed an infinite number of times. This is impractical, however, and using a smaller number can cut processing time significantly. This is especially important if large sections of your slide are in the Set. We recommend that you start with an iteration count of 100 and increase it only as warranted. Although a small number of iterations can increase processing time significantly, a value which is too small creates other problems. Specifically, many points which are not actually in the Set will be treated as though they are in the Set. If there are too many such points, the resolution of the slide deteriorates and you begin to lose features. There are two easy ways to tell if you are using too few iterations. First, there will be more black areas (i.e. points that are in the Set) on the slide than you would expect. Second, you can view the relative frequency graph in the Colors Window (see Section 4.6.1). If most of the pixels are near the right hand side of the graph, you probably need to increase the number of iterations. Although Mandelbrot Magic can calculate up to 1000 iterations, Mandelbrot Magic does not store values higher than 250. It automatically scales the resulting pixel values (1 to 1000) into the range of 1 to 250. For example, if you use 750 iterations, all of the resulting pixel values will be divided by 3 before they are stored. In practice, you shouldn't notice the scaling if you choose the number of iterations wisely. For example, you should not choose iteration values which are slightly higher than 250, 500 or 750 since these are the scaling cutoffs and you will lose a lot of resolution. 18 4.8.8 Graphics Mode Mandelbrot Magic supports five different graphics mode as discussed in Section 2. To select one of these modes, highlight this field on the Control Panel and press the <Space> bar repeatedly until you see that mode. Once a slide is generated, its graphics mode cannot be changed. When it is displayed, it will automatically be displayed in the proper mode. 4.8.9 Show Coordinates When this parameter is toggled to YES, the X and Y coordinates for the slide will be displayed. During generation, the elapsed time and the percentage of slide saved to disk will also be displayed after each column of pixels is displayed. Unfortunately, there is no direct correlation between the elapsed time, the percentage of pixels already calculated, and the total generation time. When you press F8 after entering the preceding parameters, Mandelbrot Magic verifies that your computer supports the graphics mode selected, that there is sufficient RAM to generate the slide, that the file does not already exist, and that there is sufficient disk space to store the slide. Since Mandelbrot Magic cannot determine how large a compressed slide file will be in advance, it assumes that the slide file will not be compressed when it checks for disk space. As Mandelbrot Magic generates a slide, it displays each pixel as it finishes calculating that pixel. You can therefore see the status of the slide at any time. The slide will originally be displayed with an arbitrary color mapping. Depending on the area you are viewing, this original display may not be particularly appealing. Mandelbrot Magic also takes advantage of certain symmetries in the Mandelbrot and Julia Sets to reduce the calculation time. Consequently, certain parts of a slide may be displayed almost instantaneously. When a slide is finished, you can return to the Control Panel by pressing <Esc> or you can display the slide immediately by pressing one of the F10 combination keys. You cannot utilize any of the display functions until you redisplay the slide. Mandelbrot Magic allows you to stop generating a slide at any time by pressing <Esc>. You will be asked to confirm that you want to quit. When you halt a slide, only the data for current column is lost and you can restart the slide at a later time. If you want Mandelbrot Magic to work on a partially completed slide, simply load that slide file (by entering the filename and pressing F9), then press F8. Mandelbrot Magic will restore all of the parameters used when you started the slide and will start generating the slide where it stopped. 19 A number of incomplete slide files are included with this program. These files all have the extension ".PIC". To complete them, simply enter their names, press F9 to load, then press F8. 4.8.10 The Grid Method With Version 3.1, we have implemented a new slide generation algorithm which can GREATLY reduce calculation times, especially if you do not have a math coprocessor. This algorithm is based upon the following concept: If you enclose an area of a slide with points have the same iteration value, then every point within that area has the same value. Although we do not know if this has been proved mathematically yet, it makes sense intuitively and it generates slides correctly (at least during our tests). The new algorithm works by overlaying a series of successively smaller grids on the slide. After each grid is produced, each square of the grid is check to see if all the points on its perimeter are equal. If so, then the entire square is filled with that value. When the last grid is produced, Mandelbrot Magic starts generating the slide with the normal algorithm. This method can substantially reduce the time required to produce a slide. Furthermore, the time savings are exponential; the longer it takes to produce a slide, the greater the percentage savings. Our tests indicate that this method does not save much time on slides which can be generated in less than 20 minutes (on an XT with an 8087). On most slides, the new method saves 20 to 40 percent. On really complex slides, the savings can be astounding. One slide which took 27 hours to produce (with an 8087) with the standard method took just 5 hours with the new method! Likewise, the savings when NOT using an 8087 are impressive (often 50 to 80 percent). To use this grid method, create the slide by pressing Alt-F8. To bypass the new method and create a slide with the normal algorithm, just press F8. If you want to stop a slide, press ESC. If you are using the new method, Mandelbrot Magic will start generating the slide with the old method. Press ESC again if you want to stop the slide entirely and return to the Control Panel. Note that the two methods are interchangeable -- you can start a slide with one method, stop it, then resume calculation with the other method. There is one disadvantage to this new method. Mandelbrot Magic does not save any of the slide data to disk while it is using the new method. No data is saved until the grid process is completed and Mandelbrot Magic starts generating the slide one row at a time. The percent complete indicator on the screen represents the percentage of the slide which has been saved to disk, not the percentage that has been calculated. Consequently, you should probably not use this new method if you know that you will not be able to finish the slide or at least complete a large part of it. 20 4.9 ZOOMING IN ON A SLIDE The best part of using Mandelbrot Magic is simply exploring the various sets. When you display a Set at large scale, you will invariably see an area of the slide that you would like to "zoom" in on or enlarge. Mandelbrot Magic provides a very convenient way to do this via its Zoom function. The Zoom function is invoked by pressing F1 whenever you see a slide or from the Control Panel (in which case the slide will first be displayed). When F1 is pressed, a cursor appears in the middle of the slide. With certain color combinations, the cursor does not stand out too well, but it is there. To use the Zoom function, you move the cursor to one corner of the area you want to enlarge, and press <Return> to select that location as one corner of the area. When you move the cursor again, a "rubberband" Zoom box appears. You can stretch this box with the arrow keys to enclose exactly the area you want to enlarge, then press <Return> again to select the area within the box for zooming. After you have selected one corner of the zoom box, you can make any other corner of the box the "active" corner by pressing Home, End, PgUp or PgDn. For example, pressing Home makes the upper-left corner of the box the active corner. Pressing the arrow keys will move this corner. The following keys move the cursor: Arrow Keys Moves the cursor one pixel in the appropriate direction. Shift-Arrow Keys Moves the cursor twenty (20) pixels (10 in CGA mode) in the appropriate direction. Home When the crosshair cursor is displayed, these End keys move the cursor to the corresponding corner PgUp of the slide (e.g. Home moves to upper-left PgDn corner). When a zoom box is displayed, these keys make the corresponding corner of the zoom box the "active" corner. If you decide you would rather zoom in on different area of the slide, repeat the process. Press <Esc> to cancel the zoom function. As you move the cursor around the slide, you will notice a number on the left hand side of the screen. This number is simply the value of the pixel which is at the center of the cursor. Thus, the Zoom function can also be used simply to understand the slide better. If you want to generate a slide of the zoom area, simply return to the Control Panel, supply a new filename and other appropriate parameters, then press F8 or Alt-F8 to create the slide. You do not need to worry about whether the area you selected with the Zoom function fits the slide size. Mandelbrot Magic automatically centers the area you selected within the new slide and calculates appropriate 21 X and Y values so you never lose any of the Zoom area. The Zoom function can also be used to select C values for generating Julia Sets. When you are zooming in on a slide of the Mandelbrot Set, the first location you select with the cursor is also used as the C value on the Control Panel. The value of C has a significant impact upon the shape and complexity of the corresponding Julia Set. The most interesting Julia Sets are generated when you select a C value which is very near the edge of the Mandelbrot Set. Thus, you can display a slide of the Mandelbrot Set, select a C value with the Zoom function, then return to the Control Panel and generate a slide of a Julia Set which uses that C value. However, the X and Y parameters selected off of the Mandelbrot Set slide will almost certainly be inappropriate for the Julia Set slide. The Calculate Parameters function (see next section) can help with this problem. 4.10 CALCULATING PARAMETERS After slide generation time, the biggest headache in producing slides is entering accurate X and Y values. The Zoom function, along with Mandelbrot Magic's ability to automatically center a zoom area within a new slide, can minimize this problem. However, there will be times when you need help with calculating parameters and Mandelbrot Magic provides that help via the F2 key. The Calculate Parameters function is used by highlighting a specific field on the Control Panel, then pressing F2. The result varies with the location of the cursor. If one of the X or Y values is highlighted, Mandelbrot Magic will automatically recalculate that value using the three other X and Y values as well as the slide size parameters. If one of the slide size fields is highlighted, Mandelbrot Magic will automatically calculate the correct slide size using the maximum and minimum X and Y values already entered. This allows you to have a slide contain just the area which you selected with the Zoom function. Although the program first tries to adjust the highlighted parameter, it will sometimes adjust both slide dimensions if necessary to fit the X and Y values which were entered. If the Type of Slide field is highlighted, pressing the F2 key will reset the X and Y parameters to the default values for that type of slide (Mandelbrot or Julia). The default values will produce a slide which contains the entire set. This is especially useful when generating a slide of a new Julia Set for the first time. 4.11 CREATING A SLIDESHOW With Mandelbrot Magic, you can create a "slideshow" of up to 20 existing slides. If you press F3, you will be prompted for the name of the slideshow file. This can be any DOS-acceptable file/pathname. 22 When you enter a filename and press <Return>, Mandelbrot Magic first checks to see if this file already exists. If it does, that file will be loaded so you can edit it. Otherwise, a new slideshow file is created. A new screen appears which is used to enter the names of up to 20 existing slide files. In addition to the filename, enter the other parameters which you want to be used when the slide is displayed such as number of color regions, number of colors, the color mode, and whether you want to use black as a color. You may use the arrow keys to move around the input screen. The Home, End, PgUp and PgDn keys also move the cursor around the screen. When you are done entering data, press <Esc> to return to the Control Panel. The updated/new slideshow will automatically be stored in the slideshow file. You can then run the slideshow at any time in the future by pressing the F4 function key. Three sample slideshows are included with this program. These slideshows have the name "DEMO.*" where "*" is either CGA, E64, or EGA (for the applicable adapters). You can run these slideshows directly. However, some of the slides included in the slideshows have not been finished yet. If you run the slideshow with an incomplete slide, Mandelbrot Magic will not load the slide and will sound a beep. 4.12 PRESENTING A SLIDESHOW Pressing the F4 function key presents a previously created slideshow. When you press F4, you will be prompted for the name of the slideshow file you want to present. If the file exists, the program will then load and display the first slide listed in the slideshow file. This slide will originally be displayed using the parameters stored for it in the slideshow file. Once displayed, however, you can manipulate colors and palettes freely or redisplay the slide using one of the F10 key combinations (F10, Ctrl-F10, Alt-F10, Shift-F10). In short, you can do anything you can do when you display a single slide. When you are finished with a slide, press <Esc> to load and view the next slide immediately. Mandelbrot Magic will ask you to confirm that you want to advance before it destroys the current slide. Continue advancing through the slideshow until it is complete. When the slideshow is finished, you will be returned to the main screen. You can also end the slideshow and return to the main screen at any time by pressing Alt-Q. If Mandelbrot Magic cannot load one of the slide files, the program will sound a beep. Simply press <Esc> to continue. 23 4.13 QUITTING You can only quit Mandelbrot Magic from the main Control Panel. If you press <Esc>, you will exit from the program and return to DOS. You will be asked to confirm that you do, in fact, want to quit. If you want to quit while a slide is displayed, first return to the Control Panel by pressing <Esc> and confirming that you want to end the display. Then press <Esc> again. 4.14 PRINTING SLIDES Mandelbrot Magic currently has no built-in capability to print copies of a slide. However, a rudimentary printout can be obtained of slides by using the GRAPHICS.COM program provided with DOS. This program can be loaded as part of your AUTOEXEC.BAT file. Once loaded, slides can be printed by pressing <SHIFT> and <Prt Sc> simultaneously. The GRAPHICS.COM program supplied as part of DOS 4.x will produce printouts of slides in any graphics mode (CGA, EGA, VGA). Earlier versions of GRAPHICS.COM do not work with EGA or VGA mode slides and will only produce printouts of CGA mode slides. The DOS 4.x version of GRAPHICS.COM does not normally work with earlier versions of DOS. This is a problem for users who purchased DOS 4.x but have decided (for whatever reason) not to use it. However, you can allegedly patch the new version of GRAPHICS.COM so it will work with earlier DOS versions. See PC Magazine, April 25, 1989, page 315 for details. Left Coast has not tested this patch and assumes no responsibility for the results if you try it. 24 SUGGESTED SLIDE PARAMETERS Almost any part of the Mandelbrot or Julia Sets can produce innumerable interesting slides. As you explore these sets, you will undoubtedly discover areas that interest you and merit further exploration. The Sets are so complicated and Mandelbrot Magic can zoom in so close that in all probability, you'll soon be looking at a part of the set that literally no one else has discovered. However, here are some parameters for interesting areas to explore. Depending upon how you obtained Mandelbrot Magic, slide files for all or some of these combinations of parameters may be included with the program. Many of the slides have been started but are not complete. To complete a slide, enter its name, press F9 to load the file, then press F8 to complete the slide. The actual parameters for a specific slide may vary from those listed below because of Mandelbrot Magic's automatic centering algorithms. Most of the slide files distributed with the program are for EGA adapters/modes. To create slides for different graphics modes, load the appropriate file, give the file a new name, change the appropriate parameters, then press F8 to create a new slide. MANDELBROT SETS The first set of parameters will display the entire Mandelbrot Set. Name X (Minimum) X (Maximum) Y (Maximum) Y (Minimum) ===================================================================== M1.PIC -2.00000000 0.50000000 1.25000000 -1.25000000 M2.PIC -0.25000000 0.05000000 1.10000000 0.80000000 M3.PIC -0.17500000 -0.14500000 1.05000000 1.02000000 M4.PIC -1.25800000 -1.24850000 0.03000000 0.02050000 M5.PIC -0.95000000 -0.88333000 0.30000000 0.23333000 M6.PIC -0.71300000 -0.40820000 0.71429000 0.40949000 M7.PIC -0.75104000 -0.74080000 0.11536000 0.10511000 M8.PIC -0.74553800 -0.74505400 0.11323600 0.11275200 M9.PIC -0.74543560 -0.74542150 0.11301390 0.11299980 M10.PIC -1.25402400 -1.25286100 0.04712500 0.04596200 25 JULIA SETS This list shows the C values for interesting Julia Sets. To display an entire set, use the following values for X and Y. To enter these values automatically, highlight the Type of Slide field and press F2. X Y ---- ----- Minimum: -2.0 -1.50 Maximum: 2.0 1.5 C VALUES ---------------------------- Name X Y ======================================= J1.PIC 0.27334000 0.00742000 J2.PIC -1.25000000 0.00000000 J3.PIC -0.11000000 0.65570000 J4.PIC 0.11031000 -0.67037000 J5.PIC -0.19400000 0.65570000 J6.PIC -0.15652000 1.03225000 J7.PIC -0.74543000 0.11301000 J8.PIC 0.32000000 0.04300000 J9.PIC -0.12375000 0.56508000 J10.PIC -0.39054000 0.58679000 J11.PIC -0.11000000 0.67000000 26 CUSTOMER SERVICE Left Coast provides free technical support for Mandelbrot Magic. If you require technical support, please call us at (408) 996-3130 between 9:00 A.M. and 5:00 P.M. Pacific time (12:00 Noon to 8:00 P.M. Eastern time). You may also write us at: Left Coast Software P.O. Box 160601 Cupertino, CA 95016-0601 You may also send us a message on CompuServe (71160,756). It may take us a several days to respond to CompuServe messages. You may obtain the most recent version of the program from CompuServe, the Source, or GEnie. New versions are uploaded to these services almost immediately after their release. The next major change to Mandelbrot Magic is not scheduled until early 1990. The major anticipated change in the program will be support for the Super VGA mode (assuming it does become a standard) and other extended EGA and VGA modes. We thank you for supporting Mandelbrot Magic. If you have suggestions for how to improve the program, please write us. We love hearing from our customers. 27 OTHER LEFT COAST PROGRAMS Left Coast Software sells other two popular programs for the PC -- Exchequer and PC-Areacode. We also distribute copies of BackMAGIC to registered users of Mandelbrot Magic. To order any Left Coast product, call 408-996-3130 or use the order form on the next page. We accept VISA and MasterCard. EXCHEQUER (Version 2.05) Exchequer is an easy-to-use check writing and checkbook management program for IBM PC-compatible computers. It is designed primarily for home users and small businesses wishing to automate and simplify the process of paying their bills. In addition, it provides a number of reporting options. For example, it allows the user to sort and print checkbook data by category or by payee. Exchequer provides the following features and functions: * Exchequer can pay all of your regular monthly bills with as few as two keystrokes! * Exchequer's check register looks and works just like a regular checkbook register. * Exchequer makes balancing your checkbook easy by automatically finding all uncleared checks and deposits. * Exchequer works with virtually all types of continuous-feed checks. The user has complete control over the check layout. * Exchequer supports an unlimited number of accounts. * Exchequer's check register can store over 4000 transactions. An archiving function saves the oldest transactions to a separate file (e.g. at year's end), thus making room for more transactions. * Exchequer can memorize all up to 255 predefined transactions (checks, withdrawals, deposits, service charges, etc.) These transactions can be easily recalled and used when paying bills. * Exchequer can assign a transaction to 255 user-defined categories. Reporting functions allow the user to sort the check register by category, making tax preparation a breeze! * Exchequer can split any transaction amount up to 10 ways and assign it to separate categories. * Exchequer offers a wide variety of reports which facilitate record keeping and expense analysis. Reports can be sent to the printer, the screen or to a file. 28 Exchequer runs on any IBM PC, XT, AT or PS/2 compatible computer running MS-DOS or PC-DOS Version 2.0 or higher. It works with any graphics adapter. Exchequer requires approximately 200 K of available memory (after installation of any memory-resident programs). Exchequer can be operated quite easily with just one floppy-disk drive. The program will work with any printer which handles continuous-feed checks. Exchequer is just $49.95 plus $3.00 shipping and handling. California residents please add sales tax. PC-AREACODE PC-Areacode is a useful utility program which can find the areacode for virtually any city in the U.S. and Canada in less than two seconds on a 4.77 Mhz PC and a floppy drive. It contains almost 15,000 city names in its built-in database. You can either browse through the cities in its database or type in the name of a city you want to locate. You can even type in an areacode and PC-Areacode will tell you what state it serves. PC-Areacode can run as either a standalone program or as a memory-resident utility. PC-Areacode runs on any IBM PC, XT, AT or PS/2 compatible computer running DOS 2.0 or higher. PC-Areacode is just $49.95 plus $3.00 shipping and handling. California residents please add sales tax. BackMAGIC BackMAGIC is a memory resident program which can be used to calculate fractal images for viewing with Mandelbrot Magic in the background while you run other programs on your computer. BackMAGIC solves the major problem encountered when exploring the Mandelbrot and Julia Sets -- the long calculation times required to generate images. BackMAGIC is compatible with virtually all other standalone and memory resident programs. Unlike Mandelbrot Magic, BackMAGIC does not require a specific graphics adapter. BackMAGIC will work with any video adapter, including all monochrome adapters. Thus, you can generate slides on virtually any machine for later viewing on the machine of your choice. BackMAGIC is a complementary program to Mandelbrot Magic and you must have a copy of Mandelbrot Magic to use BackMAGIC. Although Mandelbrot Magic is a shareware program, BackMAGIC is not a shareware program. The only way to get a legal copy of BackMAGIC is to register as a user of Mandelbrot Magic. 29 ORDER/REGISTRATION FORM If you want to register for Mandelbrot Magic, simply order the appro- priate number of copies of the program. You may also order/register by phone by calling (408) 996-3130. Ship to: Bill to (if different): _________________________ ___________________________ _________________________ ___________________________ _________________________ ___________________________ _________________________ ___________________________ Payment Method (please circle one): VISA MC Check COD Credit Card Number:_________________ Expiration Date: _______ Name on card (if different): ____________________________________ Signature (if using credit card): _______________________________ PLEASE SHIP ME THE FOLLOWING: _____ copies of Mandelbrot Magic at $15.00 = ____________________ (includes BackMAGIC) _____ copies of Exchequer at $49.95 = ____________________ _____ copies of PC-Areacode at $49.95 = ____________________ California Residents Add Sales Tax = ____________________________ Shipping/Handling (per order) 3.00 Add $11.00 for Federal Express ____________________________ TOTAL: ____________________________ Send form to: Left Coast Software P.O. Box 160601 Cupertino, CA 95016-0601 30 COMMAND SUMMARY Commands available at the Control Panel level are flush left. Available sub-commands for each major command are indented. +------------------------------------------------------------------+ | | | F1 Selects a ZOOM area (or C Value). | | | | Arrow Keys Move the cursor/corner 1 pixel. | | | | Shift-Arrow Keys Move the cursor/corner 20 pixels. | | | | <Return> Sets current location as corner of | | zoom box. | | | | <Esc> Cancels the zoom function. | | | | Home When the crosshair cursor is | | End displayed, these keys move the cursor | | PgUp to the corresponding corner of the | | PgDn slide (e.g. Home moves to upper-left | | corner). When a zoom box is | | displayed, these keys make the | | corresponding corner of the zoom box | | the "active" corner. | | | +------------------------------------------------------------------+ | | | F2 CALCULATES parameters | | | +------------------------------------------------------------------+ | | | F3 CREATES (or edits) a slideshow file | | | | Arrow Keys Move cursor one column or row. | | | | Home Moves cursor to upper lefthand field. | | | | End Moves cursor to lower righthand field. | | | | PgUp Moves cursor to top row of column. | | | | PgDn Moves cursor to bottom row of column. | | | | <Return> Advances cursor. | | | | <Backspace> Deletes last character in data field. | | | | <Esc> Saves the slideshow file. | | | +------------------------------------------------------------------+ 31 +------------------------------------------------------------------+ | | | F4 PRESENTS an existing slideshow file. | | | | All display commands are active. | | | | Alt-Q Cancels the slideshow and returns to | | Control Panel. | | | +------------------------------------------------------------------+ | | | F5 Activates COLORS Window | | | | Left Arrow Move the arrow one space left. | | | | Right Arrow Moves the arrow one space right. | | | | Home Moves the arrow to far left edge. | | | | End Moves the arrow to far right edge. | | | | Up Arrow Increases the color number of current | | <Return> pixel value by 1. | | <Space>,'+' | | | | Down Arrow Decreases the color number of current | | - pixel value by 1. | | | | Ctrl-Right Drags the current color to the right. | | | | Ctrl-Left Drags the current color to the left. | | | | F6 Activates Palette Window. | | | | <Esc> Closes the Colors Window. | | | +------------------------------------------------------------------+ | | | F6 Activates PALETTE Window | | | | Left Arrow Moves the arrow one block left. | | | | Right Arrow Moves the arrow one block right. | | | | Home Moves the arrow to the first color. | | | | End Moves the arrow to the last color. | | | | Up Arrow Increments the current color by 1. | | <Return> | | <Space>,'+' | | | +------------------------------------------------------------------+ 32 +------------------------------------------------------------------+ | | | F6 (continued) | | | | PgUp Increments the current color by 8. | | | | Down Arrow Decrements the current color by 1. | | - | | | | PgDn Decrements the current color by 8. | | | | P,p Cycles through predefined Palettes. | | | | F5 Actives COLORS Window. | | | | <Esc> Closes PALETTE Window. | | | +------------------------------------------------------------------+ | | | F7 ANIMATES an existing slide | | | | Up Arrow Animates the slide in up direction. | | | | Down Arrow Animates the slide in down direction. | | | | + Increases the delay between displays. | | | | - Decreases the delay between displays. | | | | <Esc> Stops the animation. | | | +------------------------------------------------------------------+ | | | F8 CREATES a new slide | | | | <Esc> Cancels slide generation process. | | | | Alt-F8 CREATES a new slide using the Grid | | Method. | | | | <Esc> Cancels the Grid Method. | | | +------------------------------------------------------------------+ | | | F9 LOADS an existing slide | | | +------------------------------------------------------------------+ 33 +------------------------------------------------------------------+ | | | F10 DISPLAYS an existing slide | | | | F1 Activates ZOOM function. | | | | F5 Activates COLORS Window. | | | | F6 Activates PALETTE Window. | | | | F7 Animates the slide. | | | | F10 Redisplays using Equal Areas mode. | | | | Ctrl-F10 Redisplays using Cyclic mode. | | | | Shift-F10 Redisplays using Sectional mode. | | | | Alt-F10 Redisplays using Assigned mode. | | | | Alt-N Pops up input window to change | | Number of Color Regions. | | | | P or p Cycles through predefined palettes. | | | | Home Restores the default palette. | | | | End Generates random palette. | | | | Up Rotates the palette upward. | | | | Down Rotates the palette downward. | | | | PgUp Continuously rotates palette upward. | | | | PgDn Continuously rotates palette downward. | | | | + Increases the delay between | | successive rotations of palette. | | | | - Decreases the delay between | | successive rotations of palette. | | | | <Esc> Cancels the display and returns to | | Control Panel. | | | +------------------------------------------------------------------+ | | | <Esc> Exits Mandelbrot Magic and returns to | | DOS. | | | +------------------------------------------------------------------+ 34 35