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MANDELBROT COLORAMA COLOR GRAPHICS DEMO AND MANDELBROT PROGRAM TRIMARK ENGINEERING 12402 W. KINGSGATE DR. KNOXVILLE, TN 37922 EQUIPMENT REQUIRED IBM PC, XT, AT OR COMPATIBLE COMPUTER 256K MINIMUM MEMORY COLOR GRAPHICS OR COMPATIBLE ADAPTER COLOR MONITOR DESIRABLE MANDELBROT COLORAMA by Marshall Dudley TABLE OF CONTENTS 1.0 Introduction: MandelWhat?. . . . . . . . . . . . . . . . . 2 2.0 Display : A Picture is worth a thousand words. . . . . . . 3 2.1 Starting the Display Function . . . . . . . . . . . . 3 2.2 BreakPoints, Automatic Selection. . . . . . . . . . . 3 2.3 BreakPoints, Manual Selection . . . . . . . . . . . . 3 2.3.1 Banding, enable/disable, and top end . . . . . 3 2.3.2 BreakPoints 1 and 2. . . . . . . . . . . . . . 3 2.4 Color Redefinition. . . . . . . . . . . . . . . . . . 4 2.5 Changing the Palette and Background colors. . . . . . 4 2.6 Using the Window Function . . . . . . . . . . . . . . 4 2.6.1 PgUp & PgDn Keys - Window size adjustment. . . 4 2.6.2 Arrow Keys - Moving the window . . . . . 4 2.6.3 Home Key - No Window . . . . . . . . . 4 2.6.4 Ins & Del Key - Aspect Ratio Changes. . . . 4 2.6.5 End Key - Reading the Coordinates . . 5 2.7 Saving a VIEW of a picture . . . . . . . . . . . . . 5 2.8 Exiting the Display Function. . . . . . . . . . . . . 5 3.0 Loading a VIEW file . . . . . . . . . . . . . . . . . . . 5 4.0 Animation : Computer Store's Dream Demo. . . . . . . . . . 5 4.1 Starting the Animate. . . . . . . . . . . . . . . . . 5 4.2 Saving the Animate File . . . . . . . . . . . . . . . 6 4.3 Changing the Palette and Background . . . . . . . . . 6 4.4 Exiting the Animate Function. . . . . . . . . . . . . 6 5.0 Creating a new Mandelbrot Plot : Like Being an Explorer. . 6 5.1 Starting the Create . . . . . . . . . . . . . . . . . 6 5.2 Automatic Coordinates from Window function. . . . . . 6 5.3 Entering Coordinates. . . . . . . . . . . . . . . . . 7 5.4 Existing Filename Conflict. . . . . . . . . . . . . . 7 PAGE 1 OF 7 1.0 INTRODUCTION - MandelWhat? The Mandelbrot Set, named for Benoit B. Mandelbrot of IBM, is a beautiful mathematically derived map of points on the complex plane. The points that are in the set are much like islands on an infinite sheet of complex numbers. Along the boundaries of these islands, other points flee to infinity. Coloring these fleeting points according to their speed yields the beautiful plots called a Mandelbrot. Although the algorithm is relatively simple, each point on the plane may require several thousand multiplications and additions to determine its value. Like islands seen from an airplane, the shoreline is ragged and complicated. Also, as you zoom in on a point along the shore, the geometry changes but never becomes less complex. In fact, as you keep looking closer the complexity continues to grow, as many old shapes reappear and new ones come into view. Welcome to the field of Fractal Geometry. The full Mandelbrot lies within a region of -2 to .5 on the Real (X) axis and -1.25 to 1.25 on the Imaginary (Y) axis. This plot is stored on the disk as MANDEL.PIC. Increasing values are plotted as you go toward the right (Real) or up (Imaginary) the screen. Imaginary Axis | + | | Real Axis - _______________|_______________ + | | | | - This program allows you to examine the Mandelbrot region with such detail, the precision is hard to imagine. If the full Mandelbrot were the size of the earth, and you mapped it down to the smallest grain of sand, you would still be an order of magnitude from what this program can do. If everyone in the U.S. were to be generating Mandelbrot blow-ups, you could quickly find a region to explore which no one has ever seen before. In many ways, it carries the excitement of exploring a new island, cave or world. Yet you can do it without leaving your favorite computer. For more information about the Mandelbrot set, see the August 1985 issue of Scientific American. PAGE 2 OF 7 2.0 DISPLAY - A PICTURE IS WORTH A THOUSAND WORDS 2.1 STARTING THE DISPLAY To Display a Mandelbrot file, start the Mandelbrot program by entering SUPERMAN or SUPER-87(8087 version only) at the MSDOS prompt. After a short sign-on, the program will ask for the filename with which you will work. Enter the name of the .PIC file to be displayed, e. g., MANDEL, or MANDEL2. After a filename has been entered, a menu will appear. The display function is selection 3. Enter a "D" or a "3" and the display pro- gram will load the selected .PIC file. If the load is successful, then the coordinates of the plot are shown and you are asked whether you want to enter the Break- points manually, or let the computer select them. 2.2 AUTOMATIC BREAKPOINT SELECTION Entering an "A" will instruct the computer to generate the Breakpoints. The computer will attempt to set the upper limit of the Banding, Breakpoint 1 and Breakpoint 2 that provide the most esthetic display. The actual breakpoints are displayed to enable you to use them or change them in the Manual mode. 2.3 MANUAL BREAKPOINT SELECTION Entering an "M" will instruct the computer to allow you to enter your own upper limit to Banding and Breakpoints. Thus one map can provide thousands of possible pictures by simply changing the breakpoints. 2.3.1 BANDING - Banding is the name given to the area away from the BLACK region which alternates between two colors. The most striking pictures usually have banding up to the point where the bands would become overly complicated. Entering a "0" for TOP of BANDING will disable banding. 2.3.2 BREAKPOINTS - The two Breakpoints define the position of the transition betweeen colors. The area between the TOP of BANDING and the Mandelbrot (BLACK) region is divided into three colors. The First breakpoint will define the end of the color above the TOP of BANDING level. The Second Breakpoint will define the transition between Breakpoint 1 and the Mandelbrot region. As the numbers increase, the transition lines move in TOWARD the Mandelbrot. Lower numbers push the colors out toward the border. When experimenting, use the numbers given in the AUTOMATIC selection as starting points. PAGE 3 OF 7 2.4 COLOR REDEFINITION The default mode is for Yellow to be next to the Black Mandelbrot, followed by Red, then Green. After the Breakpoints have been selected, the computer will allow you to change the default sequence by entering a "C" for Colors. Enter the first character of the color wanted next to the Mandelbrot, then the second color. The third color will be selected automatically by process of elimination. 2.5 PALETTE AND BACKGROUND The Palette of colors for the area surrounding the Mandelbrot may be changed with the Palette command. Entering a "P" will allow the choice of 4 different palettes. Although a different palette may be selected, the Color function of section 2.4 will still respond only to RED, GREEN and YELLOW. Entering a "B" will change the BACKGROUND color. This is the color of the Mandelbrot itself, which normally is shown as black. 2.6 THE WINDOW FUNCTIONS The window function allows you to move a window over a region of interest which you want to blow up (create). After windowing in an interesting area, exit the function with an 'E' and go to (C)reate. The co- ordinates for the next creation will already be loaded. Simply return carriage through them to leave unchanged. 2.6.1 PgUp & PgDn - The PgUP key will increase the size of the window region each time it is pressed. Since the window size is zero at the beginning of the Display, this key must be pressed at least once to even see the window. The PgDn key will decrease the size of the window each time it is pressed. If the window size goes to zero, then the window disappears from the screen. 2.6.2 ARROW - The Arrow keys allow the window to be moved throughout the Picture. The directions should be obvious. 2.6.3 HOME - The Home key returns the window to the exact center of the screen and decreases the size to zero. 2.6.4 Ins & Del - The Ins key increases the aspect ratio of the window. The Del key decreases the Aspect ratio of the window. PAGE 4 OF 7 2.6.5 END - The End key will give the coordinates of the window in the upper left hand corner of the screen. Thus, the window can be moved to several interesting areas and the exact co- ordinates noted for each. Note that it is not necessary to record the coordinates for a region of interest if you want to immediately create the blowup. Exiting the display mode and entering the Create will automatically move the desired coordinates to Create. 2.7 SAVING A VIEW A view may be saved by entering an "S" when viewing a picture. A picture file can be viewed many ways by varying the breakpoints. A view only stores what is on the screen, including the window and coordinates if they are visible. The view will be stored as the filename.VEW. Since more than one view of any given picture may be worth storing, the computer will wait 3 seconds for any additional characters you may wish to be appended onto the filename when storing the view. If any characters are entered during this time they must be followed by a carriage return before the store will begin. 2.8 EXIT Exit the Display by entering an 'E'. This will return you to the main Menu. 3.0 LOADING A VIEW FILE The VIEW file stored in paragraph 2.7 may be recalled from the main menu by entering either a "5" or an "L". It will display the view stored including any onscreen messages, windows, or coordinates visible when stored. The VEW file is useful since it only requires 16K of disk space and loads very quickly. The time to analyze and generate breakpoints is also saved. 4.0 ANIMATION - THE COMPUTER STORE'S DREAM DEMO 4.1 STARTING THE ANIMATE From the MAIN MENU enter a "1" or an "A" to start the Animation. See section 2.1 on how to bring up the MAIN MENU. You will be given a choice of using three or four colors in the animate and of animating the picture toweard or away from the center region. If an Animation file (.ANI) is found, it will be read, and Animation will begin immediately. Otherwise, a Picture (.PIC) file will be retrieved and converted to an animation file. This process takes about 3 minutes. PAGE 5 OF 7 4.2 SAVING THE ANIMATE FILE Upon completing generation of an .ANI file from a .PIC file, the computer will ask if you want to save the .ANI file. Since an .ANI file will typically be from 80 to 128K long, you should make certain sufficient disk space is available. A message of "UNABLE TO WRITE FILE" is an indication of a full disk. 4.3 PALETTE, BACKGROUND COLORS and SPEED As with the DISPLAY function, the Palette (colors) can be changed by entering a "P", and the backgound color can be changed by entering a "B". Since the Computer is very busy with the animate, it can only check for inputs about every three seconds. However it will process all pending instructions during each inquiry. Enter a 0 through 9 will vary the speed of the ANIMATE. 4.4 EXITING As with the DISPLAY mode, exiting the function is done by entering an "E". This can be done either while generating an .ANI file from a .PIC file, or while the actual animate is being performed. 5.0 CREATING A NEW MANDELBROT PLOT - LIKE BEING AN EXPLORER 5.1 STARTING THE CREATE Enter the Create function by either entering a "2" or a "C" from the MAIN MENU. Refer to 2.4 to get to the MENU. You may want to change the filename which is in the MAIN MENU. This is done by entering either a "0" or an "F". The create function will present a second menu. The CREATE function will typically take about 8 to 12 hours when MANDEL is used. If MANDEL87 is used, the create time is typically 10 to 15 minutes. However, you MUST have an 8087 installed when running the 8087 version or your system will crash. 5.2 AUTOMATIC COORDINATES The coordinates of the section to be blown up will be shown if you have previously windowed an area in the Display mode. If you want to use these coordinates, then simply enter a carriage return for each. PAGE 6 OF 7 5.3 ENTERING THE COORDINATES If you haven't windowed an area of interest, then the coordinates displayed will be the coordinates of the last Picture displayed. If nothing has been displayed, then the coordinates will be the default coordinates for the entire Mandelbrot. In either case, you will need to enter the coordinates for the desired Mandelbrot. Remember, the Lower Real defines the left side, the upper real the right side. The Lower Imaginary defines the bottom and the Upper Imaginary defines the top. Reversing of the coordinates will reverse the picture generated. The file to which the Mandelbrot will be written will be displayed at the bottom and cannot be changed here. 5.4 FILENAME CONFLICTS If the file selected already exists, then the computer will ask if you wish to erase the old file. A response of "N" will return you to the MAIN MENU. If you make a mistake setting up the Create, it can be aborted after it starts by entering an "E". When aborted, any files with the same name are not erased even if you previously answered with a "Y". (C) COPYRIGHT 1985 by Marshall Dudley Feel free to copy and upload the public domain versions of SUPERMAN. The source code and 8087 versions of SUPERMAN are not public domain and duplication, except for the express purpose of backup is expressly prohibited. This is true whether you received the software on disk or it was transmitted to you via Modem. No warranty, either implicit or implied, is made for this software. No liability shall be assumed for direct or consequential damage caused by this software. Our only guarantee is that there are no intentional bugs, and if any fatal errors are found, the disk will be replaced free of charge. TriMark Engineering 12402 W. Kingsgate Dr. Knoxville, Tn. 37922 Compuserve ID# 72416,3357 PAGE 7 OF 7