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COPYRIGHT 1988 BY DANIEL WOLF - ALL RIGHTS RESERVED MegageM Box 1785 Santa Maria, CA 93456 805 349 1104 July 23, 1988 HAMandel Documentation ***** What is HAMandel? HAMandel is a fractal image generating program for all Amiga computers. The remarkable features of HAMandel are a result of technology developments by Daniel Wolf Ph.D. which, for the first time, utilize the HAM graphics mode of the Amiga systems to create breathtaking images of Mandelbrot Sets and Julia Sets in up to 256 colors. Most Amiga owners have seen or used one of the many popular public domain programs for generating Mandelbrot Set images. Until the advent of HAMandel these images were restricted to the usual limited number of 16 or 32 Amiga colors. Those who've had an interest in fractal art have seen some of the beautiful published work in Scientific American (August, 1985) and The Beauty of Fractals (by Peitgen and Richter - Springer Verlag) and hungered for a fractal art program on the Amiga which can compute these images in hundreds of color shades. HAMandel's release is also timely in that its HAM images can now be used as 'clip art' with the new generation of HAM paint packages, such as Digi-Paint and Photon Paint. By combining the results of your work with HAMandel and the 'brush-wrapping' feature of Photon Paint you can create highly artistic renditions of fractal images 'wrapped' around spheres and other shapes. The HAMandel images are rendered in a standard HAM (Hold And Modify) graphics mode on the Amiga using 6 bit-planes. HAMandel always uses the maximum graphical resolution of HAM, that is 320x400 pixels (interlaced screen). HAMandel is a full-featured, multi-tasking, Intuition-based program. It has the familiar Amiga user-interaction standard including: Four pull-down Menus with Keyboard alternatives Select Mandelbrot or Julia Sets and HAM shading control Save and Load images as IFF files (with coordinates) Iterations per point of 15, 31, 63, 127, 255, 511, or 1023 ZOOM by 2x, 4x, 8x, or 16x - Reset and Default X,Y and ColorCycle DRAW, PAUSE and toggle the title bar on/off HAM 320x400 Interlace screen for maximum detail up to 256 colors Auxiliary window on the WorkBench screen shows the X,Y values and current file path name ZOOM-IN windows have a 'CANCEL' gadget (marked with a !) in case you change your mind and wish to select a different ZOOM Program operation from CLI or WorkBench Icon CLI control allows pre-selection of X and Y coordinates as well as Width so you can directly 'dive' into interesting parts of the Mandelbrot Set or you can begin with the usual full Mandelbrot Set 'default' settings. WorkBench ICON control automatically loads an image of the full Mandelbrot Set at the 'default' settings. Full Amiga Multi-tasking. The program will exit if a low memory condition occurs. Its designed with error-checking and crash- resistance in mind! All hand-crafted in 68000 Assembly Language using the techniques described in Compute!'s AMIGA MACHINE LANGUAGE PROGRAMMING GUIDE, which was also written by Dr. Wolf (with Doug Leavitt, the creator of the ASM68010 speedy assembler for the Amiga). Intuitive ease of use. Zooming only requires you 'PAUSE' the drawing and move a ZOOM window's drag bar until the window is over the area you want to ZOOM. Then just click the 'close' gadget on the ZOOM window and select DRAW on a menu. Coordinates are displayed at all times so you can make records of your fractal explorations. Coordinates saved as text files. Julia Sets aren't available on most Amiga Mandelbrot programs. They are very beautiful and you can easily switch back and forth between Mandelbrot and Julia Sets with HAMandel. Compatibility with ALL AMIGA SYSTEMS with at least 512K memory. No expansion memory is required, but HAMandel will work just fine with expansion memory systems. It will use expansion memory whenever possible to minimize its impact on limited CHIP memory resources. FAST. That means the arithmetic does not use Floating Point routines, which can be slow on some Amigas. The fixed-point arithmetic in HAMandel is about twice as fast as floating point with only a slight sacrifice of accuracy. That means nice pictures in from 2 minutes to an hour or so instead of overnight waits with other programs. The techniques for fixed-point arithmetic were taught to Dr. Wolf by Mark Riley, another fractal art enthusiast, who developed them after being introduced to the Mandelbrot Set by Dr. Wolf. Mr. Riley is well known in the Amiga music community for his sophisticated SONIX program as well as his contributions to AX Magazine. HAMandel draws the full Mandelbrot Set with 63 iterations per point in: (default settings X=-2.25, Y=-1.5, Width=3.0) 105 seconds on Amiga 1000 with Hurricane 68020 14MHz Board 371 seconds on Amiga 2000 with no accelerator board With 255 iterations per point, the times are: 273 seconds on Amiga 1000 with Hurricane 68020 14MHz Board ***** USING HAMandel You can start HAMandel two ways: DoubleClick the WorkBench Icon or Type HAMandel (return) in a CLI Whichever way you start, HAMandel always begins using 255 iterations per point (IPP) for up to 256 colors in the image. Once the program is running, you can PAUSE and set IPP differently if you wish. ***** WORKBENCH STARTUP When HAMandel is started from the WorkBench it automatically attempts to load in an IFF image of the full Mandelbrot Set (X=-2.25, Y=-1.5, Width=3.0, 255 IPP - up to 256 colors). The 'default' image is stored on the HAMandel disk in the Pics directory. Its full path name is: HAMandel:Pics/Pic0 If HAMandel finds an image with this file name, it loads it and displays it on the main HAM screen. If this image can't be found, HAMandel sets itself to the default values (X,Y,W, and IPP) noted above and PAUSEs with a blank screen. The coordinate values for the initial image are also loaded at the same time, from a file named: HAMandel:Pics/Pic0.XYW If HAMandel successfully loads the Pic0 and Pic0.XYW files when it starts up, it goes directly into PAUSE mode. You can then begin your ZOOM-in explorations of the Mandelbrot Set. (You may find it interesting to look at an .XYW file using the CLI 'Type' command.) ***** CLI STARTUP You can exercise a good deal of control using the CLI. Here are some examples: CLI COMMAND RESULTS HAMandel ? Shows usage format and example, then quits HAMandel Same as WB startup (loads Pic0 file and PAUSEs) HAMandel -2.25,-1.5 Uses X,Y (width=3.0, 255 IPP), begins drawing HAMandel -.8633,.2716,.00046 Uses X,Y,W (255 IPP), begins drawing HAMandel -2.25 Shows usage format and example, then quits HAMandel f Hamandel:pics/pic3 Starts using designated image file and coords. HAMandel F df1:pics/pic2 Starts using designated image file and coords. HAMandel df1:pics/pic1 Shows usage formate and examples, then quits When you start HAMandel from the CLI you can simply use the default starting picture, or either 2 or 3 parameters which control the X,Y starting point (lower left corner of the screen) and 'width'. We always recommend using all 3 parameters. If you use only 1, then HAMandel senses an error (you must give both X and Y values if you want to select a starting point). If you use only 2, HAMandel automatically selects 3.0 as the width value. If you use all 3, you have the most control; its like 'pre-zooming' on a region. This can be a time-saver if you're doing lots of Mandelbrot exploring. In summary, from the CLI you can just type HAMandel to start up with the usual starting pic loaded from disk or you can type HAMandel plus some coordinate information to begin drawing at whatever point you wish. Your other alternative is to use the 'f' or 'F' parameter followed by a space and a file name (remember that a corresponding .XYW file will also be loaded for the X, Y, and W values). The 'f' parameters let you start HAMandel with any image file as the starting point for your zoom and color explorations. LIMITATION: Don't try to use more than 4 or 5 digits to specify a floating point value. The software can handle up to 8 significant digits on input, but you'll get bad results if you use a width value less than about .00002 . That value represents a magnification of 75,000 in linear dimension or about five billion in the square dimensions. When HAMandel draws with Default Settings the program begins drawing the full Set as quickly as possible. It may take a few seconds before it is obvious that anything is happening, since the dark colors at the edges of this image are pretty low contrast to the black background chosen for aesthetic reasons. During the drawing with Defaults, the full Mandelbrot set is drawn simul- taneously from the top and bottom of the screen. All other drawings of the Mandelbrot and Julia sets take place only from bottom to top. The special situation in the Default mode is that the Mandelbrot Set is symmetric at the center (which is the center of the screen in this case), so HAMandel is smart enough to recognize that and cut the drawing time in half by drawing the top and bottom simultaneously. ***** DRAW MODE AND PAUSE MODE - TITLE BAR MESSAGES HAMandel has two main modes of operation. In DRAW mode, it is busy computing and drawing your image. In PAUSE mode, it is ready for user interaction with the menus. DRAW MODE - When in DRAW mode, most of the menus are 'ghosted' so you can't use them. Only PAUSE and NOBAR options can be selected in DRAW mode. DRAW mode also is obviously detectable from the message on the title/menu bar. The DRAW mode 'message' says: Drawing Mandelbrot - PAUSE to stop or Drawing Julia - PAUSE to stop PAUSE MODE - When in PAUSE mode, all of the menus options are available (except PAUSE itself, which is 'ghosted'). All the usual menu option selection is done during PAUSE mode. PAUSE mode is also obviously detectable from the message on the title/menu bar. The PAUSE mode 'message' says: HAMandel stopped - DRAW to restart PAUSE mode is also automatically engaged when the drawing is finished (drawing reaches the top of the screen). When drawing is finished, PAUSE mode is engaged and the program presents its title 'message' on the menu/title bar: HAMandel v1.0 ©1988 by Daniel Wolf ***** HAMANDEL'S EXTRA WINDOW In addition to the main HAM screen you immediately see when HAMandel starts, there is another AUXILIARY WINDOW on the Workbench Screen. To see it, pull the HAM screen down in the usual way with the mouse by grabbing its title bar. The little window on the Workbench screen shows the coordinates of the current image and a file name (you can modify this string gadget to supply file path names of your own for loading and saving images, see below). ***** CONTROLLING HAMandel - THE FOUR MENUS Once HAMandel is under way, you'll be able to interact through the four pull-down menus. If HAMandel is in its DRAW mode, the first thing you MUST do to interact with the menus is to get the drawing to PAUSE. Even while HAMandel is drawing, you can examine the menus: Press the mouse menu button and bring the mouse pointer up to the title bar - then you'll see the menus. IMPORTANT While in DRAW mode, HAMandel checks to see if you make a menu selection at the end of each line it is drawing (when the drawing process reaches the right hand edge of the screen). If HAMandel is busily involved in DRAW mode, it may appear that it doesn't respond to your request for PAUSE mode (see immediately below) for a few seconds. Be patient. If you select PAUSE on the CONTROL MENU (while in DRAW mode) it may take a few seconds to respond. Control of PAUSE mode and DRAW mode is important, so lets look at the last menu first. ***** CONTROL MENU - DRAW, PAUSE, NOBAR (far right on the menu bar) DRAW (RIGHT AMIGA - D) You should see a checkmark next to the DRAW option in the CONTROL menu. That means HAMandel is in DRAW mode (it should be obvious). While HAMandel is drawing, the DRAW menu item is 'ghosted' (you can't select DRAW while HAMandel is already in that mode). Note also that when HAMandel is drawing, the other three menus are all totally ghosted. You can't do anything with the menus until you get HAMandel to PAUSE! PAUSE (RIGHT AMIGA - P) This menu item is not ghosted. Whenever HAMandel is drawing, you can select this menu item to get it to PAUSE. Once you have HAMandel in the PAUSE mode, then PAUSE will become ghosted and DRAW will become available. Its natural. When drawing you can PAUSE, when paused you can restart the DRAW mode. Once you have made HAMandel PAUSE, all the other menus become un-ghosted so you can control all of the features of HAMandel when you are in the PAUSE mode. IMPORTANT Be sure you know how to work with the PAUSE and DRAW items in the CONTROL menu before you go on. NOBAR (RIGHT AMIGA - N) This menu item is never ghosted. If you select it once, the menu/title bar at the top of the screen will disappear as soon as possible. When you select this item again the menu/title bar will reappear as soon as possible. You can 'toggle' the menu/title bar using this option at any time. If you want to 'pull the screen down' or use the screen's front/back gadgets you need to have the menu/title bar showing. If you just want to see the maximum fractal image, you can use this option to 'hide' the bar. ***** PROJECT MENU - MANDELBROT, JULIA, SHADE RED, SHADE GRN, SHADE BLU, SAVE, LOAD, QUIT NOTE - This menu is completely ghosted during DRAW mode. To use it you must select the PAUSE mode. Once you have learned to switch HAMandel to the PAUSE mode there are a variety of options on this menu which give you a lot of flexible control of HAMandel's fractal drawing and HAM coloring shades. JULIA/FATOU (RIGHT AMIGA - J) When in the PAUSE mode you can select the Julia Set and then restart the program by selecting DRAW. HAMandel will create the Julia/Fatou Set corresponding to the coordinates of the lower-left corner of the screen. Usually J/F Sets are fast to calculate and they are always symmetric. They are also quite interesting. When you are in an interesting region of the Mandelbrot Set, PAUSE and select JULIA/FATOU and restart the DRAW mode. The resulting J/F set usually 'looks like' the same region in the Mandelbrot Set, but with a beautiful symmetry. HAMandel always draws 'full' Julia/Fatou Sets, that is, you can't ZOOM in on the Julia Sets. There is one Julia/Fatou Set for each possible lower-left hand corner point in the Mandelbrot Set. Its as if each point in the Mandelbrot Set has a complete two dimension picture hidden within that one point, that is the Julia Set for that point. If the lower left corner point on a Mandelbrot picture is 'inside' the Mandelbrot Set (in a large 'black' area) then the Julia Set will look a certain way. If the point is 'outside' the Mandelbrot Set, the Julia Set will look different. The best points to use for Julia Sets are those in which you are 'close' to the edge of the Mandelbrot Set. To most effectifely utilize this menu option, first get yourself to a nice area in the Mandelbrot set, then PAUSE, select JULIA/FATOU and restart DRAW. When the Julia Set is complete you can return to this menu and de-select this item, then restart DRAW. HAMandel will re-draw the Mandelbrot Set exactly where you left off to explore the Julia Set. There is no change of coordinates when you switch between Mandelbrot and Julia Sets. The Julia Sets let you look at the '3rd and 4th dimensions' of the Mandelbrot Set with a minimum of fuss or interruption. SHADE RED (RIGHT AMIGA - R) Selecting this option during PAUSE mode will immediately shift the HAM drawing algorithm from its current state (default is SHADE BLU - see below) to a RED shading mode. The dominant colors for this mode are shades of GREEN, with the minor shades in RED. SHADE GRN (RIGHT AMIGA - G) Selecting this option during PAUSE mode will imediately shift the HAM drawing algorithm from its current state to a GREEN shading mode. The dominant colors for this mode are shades of BLUE, with the minor shades in GREEN. SHADE BLU (RIGHT AMIGA - B) Selecting this option during PAUSE mode will imediately shift the HAM drawing algorithm from its current state to a BLUE shading mode. The dominant colors for this mode are shades of RED and YELLOW with minor shades in BLUE. This is the default setting and when HAMandel begins you can see a checkmark next to this 'active' option. LOAD (RIGHT AMIGA - L) Selecting this option during PAUSE mode will save the current picture according to the file path name shown in the PATH string gadget of the auxiliary Workbench screen window (see above, HAMandel's Extra Window) SAVE (RIGHT AMIGA - S) Selecting this option during PAUSE mode will load a previously saved image according to the file path name shown in the PATH string gadget of the auxiliary Workbench screen window (see above, HAMandel's Extra Window) QUIT (RIGHT AMIGA - Q) Selecting this option during PAUSE mode will exit the program! ***** DEPTH MENU - 15, 31, 63, 127, 255, 511, 1023 NOTE - This menu is completely ghosted during DRAW mode. To use it you must select the PAUSE mode. This menu controls the number of iterations per point (IPP), which is related both to the 'accuracy' and detail of the Mandelbrot Set image as well as to the maximum number of colors used in drawing. 15 (RIGHT AMIGA - 4) During PAUSE mode you can select 15 IPP. This can be a timesaver of you just need to quickly draw a portion of an image. This is not recommended for high quality pictures, but is present as a convenience only. 31 (RIGHT AMIGA - 5) During PAUSE mode you can select 31 IPP. This can be a timesaver of you just need to quickly draw a portion of an image. This is not recommended for high quality pictures, but is present as a convenience only. It may work just fine for some Julia Set images. 63 (RIGHT AMIGA - 6) During PAUSE mode you can select 63 IPP. This can be a timesaver of you just need to quickly draw a portion of an image. An IPP of 63 is OK when drawing the full Mandelbrot Set. 127 (RIGHT AMIGA - 7) During PAUSE mode you can select 127 IPP. This is a good setting for many Mandelbrot and Julia images and will give you up to 128 colors. RECOMMENDED SETTING FOR MEDIUM ZOOM MANDELBROT SETS AND MOST JULIA SETS. 255 (RIGHT AMIGA - 8) During PAUSE mode you can select 255 IPP. This is the maximum available for HAMandel and its use gives you the most beautiful images possible with HAMandel with up to 256 colors. You should use this IPP setting whenever you are working with significant magnifications since there is a curious relationship between the size of a Mandelbrot Set region and the number of colors you're likely to see. The smaller the region, the better off you'll be with this setting. The drawback is that 255 IPP is the slowest possible drawing speed. You'll see that effect if you (foolishly) include large sections of the 'black' areas (that is, areas that are really 'inside' the Mandelbrot Set - they are pretty uninteresting since they're all black). When you've selected a region for ZOOMing that is near the 'border' of the Mandelbrot Set, you'll get the best results with this setting. Using an IPP setting of 255 lets HAMandel really shine; the extra time is usually worth the wait because the beauty of the finished images can be breathtaking. There is a neat relationship between maximum colors and maximum detail in the picture. HIGHLY RECOMMENDED FOR THE MOST BEAUTIFUL IMAGES. This is the default value when HAMandel starts, note the checkmark on the menu. 511 (RIGHT AMIGA - 9) During PAUSE mode you can select 511 IPP. This is a good setting for many Mandelbrot and will give you up to 256 colors. RECOMMENDED SETTING FOR HIGH ZOOM MANDELBROT SETS. 1023 (RIGHT AMIGA - A) During PAUSE mode you can select 1023 IPP. This is a good setting for many Mandelbrot images and will give you up to 256 colors. RECOMMENDED SETTING FOR HIGH ZOOM MANDELBROT SETS. ***** OPTIONS MENU - ZOOM 2X, 4X, 8X, 16X, COLOROLL, DEFAULT XY, RESET XY NOTE - This menu is completely ghosted during DRAW mode. To use it you must select the PAUSE mode. ZOOM is restricted to Mandelbrot Set images. You cannot ZOOM in on Julia Sets (perhaps in a future version of HAMandel). The OPTIONS menu gives you control of ZOOMing, color cycling, and 'resetting' the coordinates (so you don't have to exit the program to re-start drawing an image from a blank screen). ZOOM 2X (RIGHT AMIGA - 0) ZOOM 4X (RIGHT AMIGA - 1) ZOOM 8X (RIGHT AMIGA - 2) ZOOM 16X (RIGHT AMIGA - 3) Zooming is what makes the Mandelbrot set interesting. The Mandelbrot Set can be enlarged INDEFINITELY and will always continue to show interesting detail. Mathematicians have concluded that this is one feature which helps make it the most complex mathematical object known (July 1988). Zooming with HAMandel is fast and easy. HAMandel is limited to magnifications of about 50-75,000 in order to get the math of the fractal shape evaluation to match the 256 color mode use on the HAM screen. If you attempt a ZOOM which would result in a Width value too small for the math to handle, the ZOOM window will quickly close itself. Try ZOOMing with one of the smaller ZOOM values. If none of the ZOOM windows works, its because no further ZOOM is possible. Select the ZOOM value you wish while you've got HAMandel in PAUSE mode. A special ZOOM window will appear on top of the HAM image on the screen. You can do this even when the picture is only partly completed. HAMandel knows where you are on the screen even if part of the screen is still blank. Just move the ZOOM window around on the screen until it covers the area you wish to enlarge. Then simply click on the 'close window' gadget of the ZOOM window and restart the DRAW mode. HAMandel will automatically calculate the new coordinate of the lower left corner (wherever you left the lower left corner of the ZOOM window) and begin drawing your ZOOMed Mandelbrot Image. The ZOOM windows overlay a HAM screen and can cause a rather strange appearance with massive streaks of color extending from the ZOOM window's right edge to the right edge of the screen. DON'T WORRY. When you close the ZOOM window (or click its ! CANCEL gadget) the screen will be restored OK. IMPORTANT - ESCAPING FROM A ZOOM WINDOW WITHOUT CAUSING ANY EFFECTS AT ALL You may find that you really want a different ZOOM factor after the ZOOM window is already on the screen. Or even that you don't want to ZOOM after all. You can 'exit' from the ZOOM window by clicking on the ! gadget instead of the 'close window' gadget. Then if you restart the DRAW mode, HAMandel will simply continue where it left off. If you click on the ! gadget its as if you never even asked for a ZOOM. You can immediately select a different ZOOM. VERY IMPORTANT - ZOOM ONLY WORKS ONCE DURING PAUSE MODE Once you do select a ZOOM window, position it, and click its 'close window' gadget you are committed. You can't select ZOOM again until you restart DRAW and then PAUSE again. It would be quite bizarre if this were not true. At this time, the menu doesn't 'ghost', but the program internally forbids you from re-selecting another ZOOM until its reasonable to do so. Were this not true, you might be in the position of ZOOMing 'blind'. ALSO IMPORTANT - LIMITED DRAG BAR SIZE ON ZOOM 16X WINDOW When you select the smaller ZOOM windows (ZOOM 8X or ZOOM 16X) the window is so small that the whole title of the window, NEWXY, may not be completely visible. The ZOOM 16X window is so small that there is only a very small portion of drag bar available next to the 'close window' gadget. BE CAREFUL when moving the ZOOM 16X window; be sure to position your mouse pointer in the drag bar area so you don't hit the 'close window' gadget inadvertently and freeze in a zoom you don't want. COLOROLL (RIGHT AMIGA - C) During PAUSE mode you can request a color cycling mode. This can be very beautiful with finished images (its a little strange with partially completed images to see a large portion of blank screen cycling its color). The color cycling is limited to about 10 seconds, after which the colors are restored to their starting points and you're back where you started. If you wish to extend the duration of the coloroll, simply move the mouse pointer to the far left edge of the screen during the coloroll. As long as you leave the mouse pointer at the far left edge, the coloroll will continue. To get it to stop, just move the mouse pointer away from the left edge and it will halt in a few seconds. DEFAULT XY (RIGHT AMIGA - Z) During PAUSE mode you can select this option which forces HAMandel to 'start over from the beginning'. It will force the program to draw the full Mandelbrot Set from the beginning, just as if you exited the program and restarted it using HAMandel or from the WorkBench. This can prevent you from having to exit the program and re-start it if you get lost somewhere in the complex plane. If you simply set the name HAMandel:pics/pic0 in the PATH string gadget of the auxiliary window and then PAUSE to LOAD, you'll get the same picture. This menu item is for convenience and completeness only. RESET XY (RIGHT AMIGA - Y) During PAUSE mode you can select this option to assure that the screen is cleared when you reactivate DRAW. This is very useful. For example, say you PAUSE and change the IPP setting, then restart DRAW. Your resulting image will have portions with two different IPP settings. The same reasoning applies to PAUSEing to change SHADES (RED, GRN, or BLU). DRAW is pretty smart. It knows how to continue just where you left off. If you select this option then DRAW will start the whole screen over with your new IPP or COLOR setting. IMPORTANT For best results, after you PAUSE to change IPP (DEPTH MENU) or SHADE colors, it is WISE to select RESET XY before you reactivate DRAW. This completes the presentation of HAMandel menu operation. MORE ABOUT THE AUXILIARY WINDOW The small window on the Workbench screen contains 4 string gadgets. Three of them show the X, Y, and W(idth) numbers in ASCII Decimal. The other shows the current File Path Name used for LOAD and SAVE operations. You can alter the PATH name string gadget to set up LOAD and SAVE for your own file naming requirements. Remember the HAMandel disk has Pic0, Pic1, etc. in its PICS directory so you can use them as starting points for your Mandelbrot Set explorations, too. WE RECOMMEND LEAVING THE X, Y, AND W STRING GADGETS ALONE. THESE THREE STRING GADGETS MAY BE EXPLOITED IN FUTURE RELEASES OF HAMandel. MORE ABOUT LOADING AND SAVING IMAGES - THE .XYW COORDINATE FILES For each image you LOAD or SAVE, there is a small extra file, called the .XYW file, which contains the X, Y, and W values for that image. The extra .XYW file is a short ASCII text file. For example, the initial default image file is HAMandel/Pics/Pic0. That file has the actual IFF image file. There is another file called HAMandel/Pics/Pic0.XYW which has the X, Y, and W values. HAMandel always saves the .XYW file during a SAVE operation and always tries to find the .XYW file during a LOAD operation. Try doing a SAVE operation (during PAUSE mode) with a file name of your own choice. Then examine (using the CLI) the directory in which you saved the image. You should find the file name and also an identical one with the .XYW extension tacked on. The .XYW file is 34 bytes long. In summary, SAVE and LOAD always work with two files. First is the actual IFF image file with its name in the PATH string gadget of the auxiliary window. Second is the coordinate file which has the same name as the image file, but with the .XYW extension. Whenever you do a SAVE, both files are saved. Whenever you do a LOAD, both files are loaded. NOTE - HAM SCREEN LIMITATIONS - MENU OPERATION AND POSSIBLE DAMAGE TO THE IMAGE When HAMandel is drawing the full Mandelbrot Set (from both top and bottom of the screen), activation of menus using the mouse and pointer may cause some damage to the image. This only occurs when the drawing process is actually drawing through the area where a menu strip is showing at the same time. You can avoid this damage easily; just wait a few seconds during the drawing until it proceeds part way 'down' the screen past the bottom edge of the menu strips. You can always prevent any damage by just using the Keyboard Alternative commands shown for each menu option. When you activate menus, they project down the screen in the HAM area and appear to cause massive streaks. Don't worry, those streaks only appear when the menu is actually being used. They will vanish when you release the mouse menu button and won't damage your image. The menu/title bar itself (for reasons not yet well understood) is always damaging to the very top few lines of the image. Intuition's way of handling the title bar on a HAM screen apparently prevents those few lines of the screen from behaving exactly like the remainder of the screen. You will note (even with NOBAR active) that the top few lines of the screen have a different appearance than the rest of the screen. MegageM is working to provide a way of preventing this in a future release of HAMandel. Dr. Wolf wished to avoid the need to move to another screen to control the menus. You only need to get to the WorkBench screen to change the file PATH name using its string gadget in the Auxiliary Window. The HAM graphics mode on the Amiga has some limitations built-in. It is not possible to have arbitrary colors immediately next to one another in adjacent pixels under most circumstances. Programmers and HAM paint package users are aware of this limitation which can sometimes cause streaks of a few pixels length (horizontal lines). HAMandel uses special techniques to avoid these built-in limitations as much as possible. Each SHADE option (SHADE RED, SHADE GRN, and SHADE BLU) has its own color palette of 16 colors which have been very carefully chosen to avoid streaking. We don't recommend you change them, but you may be able to improve your pictures and even eliminate a few streaks (when they do occur) by using a color palette program on your finished image. Dr. Wolf has had some success with ANYTIME from DISCOVERY SOFTWARE. This color palette program lets you alter any of the 16 palette colors while viewing the results directly on the image. It won't always give good results and Dr. Wolf recommends you take care when changing palette colors. Always do your palette color changing AFTER the image is complete and you have saved it to disk. Then load it into a HAM paint program to modify it to your heart's desire. Another color modifying program is COLOURS on one of the Fred Fish disks. ***** What IS the Mandelbrot Set, Anyway? To really get a handle on the Mandelbrot set, you should first know a few facts: 1. Benoit Mandelbrot is a mathematician who works for IBM. He discovered the Mandelbrot Set in 1980. 2. The Mandelbrot Set exists in a region of the 'complex plane' (where distance in the y direction is multiplied by i [the square root of -1]) centered around the 0,0 point. The 'whole thing' lies between -2.25 and +0.75 on the x (real) axis and between -1.5 and +1.5 on the y (imaginary) axis. You can draw a little x,y coordinate grid and then draw a box using those coordinates to get an idea of 'where the Mandelbrot Set lives'. 3. To make an image of the Mandelbrot Set, you set up a screen layout of, say, 320x400 pixels and let the leftmost border pixels correspond to x = -2.25 (and rightmost border pixels are set to x = +0.75). Then each pixel along a horizontal line on the screen has a certain x value. For the y direction, set the bottommost line of pixels to a y value of -1.5 (and topmost line to y = +1.5). Now each horizontal line of pixels on the screen layout has a different y value. Each pixel combination on the screen has a unique x,y position on the coordinate grid. The x value of the 14th pixel from the left is: -2.25 + 14 * (3/320) The y value of the 139th pixel from the bottom is: -1.5 + 139 * (3/400) If our left and bottom borders moved elsewhere in the coordinate grid, these formulas would change accordingly. In general, the x value of the nth pixel in a row is: x val. of leftmost border + n * (width of grid/screenwidth) and the y value of the nth pixel from the bottom is: y val. of bottommost border + n * (height of grid/screenheight) Now, we need to make a test for each pixel and give the pixel a color depending on the results of the test. The 'test' tells whether that point in the coordinate grid is 'in' the Mandelbrot Set. The Test Each pixel has a certain x and y value (x is somewhere between -2.25 and +.75, while y is between -1.5 and +1.5) which we must use in the test. In the Mandelbrot Set Test, these numbers are treated mathematically as if they were 'complex' numbers. A complex number has a REAL part and an IMAGINARY part. In our test, the x value is the REAL and the y value is the IMAGINARY. Now here is the heart of the test: Take the x,y values of the point and create a new x,y combination in the following way: new x = x^2 - y^2 + x(point) new y = 2xy + y(point) Each time new x and new y are created, they replace the pre-existing x and y but NOT the x(point) and y(point) which remain as constant for each pixel. Also find the 'size' of the new combination in the following way: size = new x^2 + new y^2 Now check if size is > 4 (same thing as checking if square root of size is > 2). For those who understand complex numbers, we start with z = x + iy and we get new z = z^2 + z(point). The size of new z is z^2. That accomplishes the test. The test checks to see if, when you change x and y into newx and newy, the size of the combination of newx and newy is larger than 4. If it is, then if you then make new new x and new new y the size will certainly only grow larger. What we are looking for is how many time we can make a new x and a new y (starting with x and y from the coordinate grid points for a pixel on the screen) without letting the 'size' of the result blast off to infinity. Every pixel on the screen has a number associated with it. That number says how many times you can do the test before the 'size' gets bigger than 4. From that number we can give the pixel a color. Usually a Mandelbrot Set program not only relates the screen's grid of pixels into x,y values for the test, but also sets a limit on how many times the test will be done before quitting. A point on the coordinate grid is 'in' the Mandelbrot Set if you can do the test an infinite number of times. We, however, are mortal and cannot afford to check even a 320x400 array of pixels more than about 1000 times each to get a picture in some reasonable time. HAMandel's grid is 320x400 (128,000 pixels) with a maximum 'limit' of 1023 tests per pixel (iterations per point). If a point 'survives' the test up to the 'limit' (depth value) then we simply assume that point is 'in' the Mandelbrot Set and assign it a black color. Once the cycle of tests and size checking is done up to a 'limit' number of times for each pixel, then each pixel should have a color related to the number of times it 'survied' the test and the entire screen of colored pixels IS the image of the Mandelbrot Set for the selected region of the coordinate grid representing the 'complex' plane. 4. For every point in the Mandelbrot Set there is a corresponding Julia Set. The formula is almost identical, but a single x(point) and y(point) are used throught the scan through all pixels. The entire grid is scanned like the Mandelbrot Set, but instead of changing x(point) and y(point) with each new pixels x and y values, the x(point) and y(point) are pre-chosen and fixed throughout the entire screen of pixels. That is, for each point in the Mandelbrot Set you can set x(point) and y(point) constant and scan through all the pixels to arrive at the image of the Julia Set for x(point) and y(point) - so long as you scan over a grid from about -3 to 3 (REAL) and -3 to 3 (IMAGINARY). 5. If you wish to read some great books on the Mandlebrot Set and other fractals, try: The Fractal Geometry of Nature by B. Mandelbrot (Freeman) The Beauty of Fractals by O. Peitgen (Springer) The Science of Fractal Images by O. Peitgen (Springer) The last one has numerous algorithm descriptions in pseudocode for ambitious programmers. 6. Fractal means FRACTionAL Dimension. Fractals are oddballs of geometry. We think of lines as one-dimensional, planes as two- dimensional, and solids as three-dimensional. Fractals occupy the 'spaces' between these whole numbers of dimensions. A highly complicated folded line could begin to look as if it 'fills up' a sheet of paper (a plane). Then the line sort of is between 1 and 2 dimensions. A coastline of an island has the property that its length depends on how 'finely' you measure it. These two kinds of lines are fractals. The first book (above) really goes into this definition and how you can estimate the actual fractional dimension of a fractal.