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========================== MandelSquare 1.3 ========================== ====================================================================== Yet another Mandelbrot set exploration program written by Olaf `Olsen' Barthel. © Copyright 1991 by Olaf `Olsen' Barthel, Freeware, all rights reserved. No guarantee of any kind is made that the program described in this document is 100% reliable. You use this material on your own risk. ========================= A word of warning ========================== ====================================================================== `MandelSquare' is a very `demanding' program which will run only on Amiga systems equipped with expensive custom hardware (i.e. '881/'882 accelerator boards, 68020/30/40 processors and real fast ram), a plain A3000(T/UX) will do as well, but not quite as nicely as an A2000 with a GVP A3001 expansion board or an A3000(T/UX) fitted with an '040 card. Kickstart 2.x (v37.175 or higher) is required as well, any attempt to run this program on a plain A500/A2000 will fail. YOU HAVE BEEN WARNED! ============================= Background ============================= ====================================================================== I have been toying with this kind of program for a long time, I even started writing it on my ol' faithful A500 back in 1990. Since I don't have a great interest in mathematics (which currently causes `some' problems while studying computer science at university) I started this project to learn a bit about complex numbers and to shake off some of the trouble mentioned before. The first internal revisions of this program would simply calculate pictures dot by dot. This technique while accurate and precise takes quite a lot of time (see Thomas R. Wilcox' `MSE'). There are faster ways to calculate a picture, such as the recursive routine `MandelSquare' uses: the screen is divided into four areas; if the pixels in the four corners are of the same colour, the rectangle is filled in this colour, if not, the area is divided into four rectangles and the same procedure is applied again. This technique relies on the fact that the Mandelbrot set does not contain isolated points, each outline rests within a different outline, just like a babooshka puppet is contained in its mother puppet. `MandelSquare' uses a very simple form of this algorithm which requires that the rectangles are square, and that's how the child received a name... `MandelSquare' uses the standard z²+c algorithm to generate pictures, a numerical coprocessor or an '040 is required since the calculation is done in a fast hand-coded '881/'882 assembly language subroutine. While throughout the whole program double precision values (64 bits) are used for calculation, the '881/'882 assembly language subroutine uses extended precision (96 bits) to do its job. While I can and will not claim that `MandelSquare' is the fastest Mandelbrot set exploration program, I may say that it is the fastest program in respect to its accuracy and the algorithm employed. Colours are assigned to pixels based on a linear transition table which avoids the unpleasant look of broken colour ranges. Transition tables are created according to the screen resolution (32/16 colours). Except for the rectangle filling routines `MandelSquare' uses custom assembly language routines to do the picture rendering. The program still tries to be very careful not to disturb system imagery such as the menu bar and the pull down menus. The screen size depends on the text overscan settings of your machine. The following text assumes a resolution of 256 × 256 pixels (low resolution) and 512 × 512 pixels (high resolution). In late August I played with the idea of adding animation support to the program, and here it is: select the area you wish to zoom to and `MandelSquare' will generate a standard Anim-Opt-5 animation file while it zooms to the indicated spot. The animation file can be viewed using programs such as `ShowAnim', `DisplayAnim', `PPAnim', `Animagic', `The Director', `DPaint III/IV' and `MandelSquare' itself, of course. Many thanks to Gary Bonham and Jim Kent for releasing the anim file creation/delta compression and replay code to the public domain. At startup time `MandelSquare' tries to read a file called `MandelSquare.Title' which happens to be the standard Mandelbrot set picture where all explorations will start. If the named file cannot be found the program will generate the picture it needs, and you are advised to save it to disk under the name mentioned before. ============================= The menus ============================== ====================================================================== Following is a description of the functions and options associated with the pull down menus. Open Picture........... Opens a picture file in IFF-ILBM format created by `MandelSquare', reads and displays it. Since coordinates, number of iterations and screen width are saved with the picture you may continue exploring from the point where you saved it. Save Picture........... Saves the current picture under the last name a picture file was loaded. If no file name was loaded yet, you will be prompted to provide a file name. Save Picture As........ Saves the current picture under a name you have to provide. Priority............... This menu allows you to select the task priority `MandelSquare' will run under. While 0 is the standard priority the majority of tasks and processes will execute on your machine you may want to change this value to -5 to save processing time other tasks may wish to allocate or to +5 to make `MandelSquare' allocate more processing time than possibly available when running under priority 0. Replay Animation....... Will load and replay any animation file which meets the following conditions: - Since the replay routines do not open their own display (as most anim players do) it will use the `MandelSquare' screen for display. This means that any animation to be replayed must be recorded in the same resolution (width, height, depth) as the current screen. - The animation file must be compressed using delta mode 5. - There must be enough memory available to load the animation frames. Any animation which does not fit into memory will be truncated. If successfully loaded the animation will be played repeatedly. Press any key or mouse button to abort. Begin Animation........ After providing a file name to save the animation file under this will start the animation routine. The mouse pointer will change to a crosshair allowing you to select the area to zoom to. A requester will ask you to confirm the area size and positionm offer you reselect it (select `No' to do so) or to abort the animation (select `Abort'). If confirmed the animation will start. It can be aborted at any time by selecting the menu `End Animation'. After the animation has been rendered you will again be presented with the crosshair mouse pointer and the whole procedure starts again. Should you decide not to continue the animation just select a dummy area and click on the `Abort' button of the confirmation requester. The confirmation requester will also display the number of pictures to create in the animation when zooming to the selected spot. This value is based on the current `Scroll Amount' settings (see below). End Animation.......... Selecting this menu item will stop any animation creation currently in progress and close the animation file without including the current picture. Set Scroll Amount...... The moves and zooms performed when generating animations depend largely on a magic value which can be adjusted when selecting this menu item. The `scroll amount' controls how many pixels long a move or zoom may actually be. Any distance longer than this value will be truncated and move/zoom will be scaled approriately. This assures that moves and zooms will always execute at the same `speed'. (It took me about a month to discover this method of operation :-) Include Frame.......... When zooming into an area `MandelSquare' will draw a square around the area to zoom to if this options is in effect. This frame actually shows you where you are going to in the Mandelbrot set and may remind you of Charles Eames' famous `Powers of Ten' film/slide show. Include Coordinates.... If this option is in effect the coordinates and screen size of each picture to be added to an animation file will be printed into the lower left corner of the image before it is saved. Change Resolution...... `MandelSquare' operates in two different resolutions: low resolution (256 × 256, 32 colours) and high resolution (512 × 512, 16 colours). Selecting this menu item will toggle between both resolutions. Note that you will lose your current picture if you change the resolution. `MandelSquare' will immediately start recalculating the previous picture in the current resolution. About.................. Shows a small `author' requester. Quit................... Terminates the program. Magnify................ This menu item lets you select an area on screen using the mouse `MandelSquare' will magnify to screen size. Note that the resolution of the routines employed by `MandelSquare' is limited and after a certain number of magnifications the pictures generated will look blurred or coarse, but the program is guaranteed to perform reliably up to screen resolutions of 1E-13 (0.0000000000001). Detail................. If changing the number of iterations to be used for picture generation, the user may want to explore the new patterns and colours hidden inside the areas of the picture `MandelSquare' has left black. `MandelSquare' will check each black pixel in the selected area and recalculate its colour. Recalculate............ The algorithm employed by `MandelSquare' is by no means perfect: it will sometimes fill rectangles which it should not and truncate imagery. This happens rarely enough, but the resulting picture can be corrected by selecting selecting this menu item and by marking the area to be recalculated. Each pixel of the selected area will be recalculated and set accordingly. If the area selected is as wide as the whole screen a special mode will be used to render the pixels into fast ram. As soon as a line is complete it will be copied from the fast ram line buffer to the corresponding line on screen. This is especially useful if `MandelSquare' is running in high resolution mode in which the display memory does not respond quite as fast as real fast memory. Precise Calculation.... If this option is in effect `MandelSquare' will calculate the colours of all pixels on the margins of a square which is to be filled in a single colour. If these pixels all match the same colour the square will be filled as usual, if not the square will be divided into four smaller squares and the calculation will proceed. While this method is more precise than the standard way it avoids rendering errors and is recommended to use when generating animations. As a drawback it is slower than the standard method of calculation. Coordinates............ This menu item will open a control panel in which the screen coordinates and size can be adjusted manually by typing the approriate floating point numbers. Palette................ Selecting this menu item will open a palette control panel in which three sliders are to shift the red/green/blue colour tables the screen palette is made of. Each colour table represents the positive part of a sine wave spread across 32/16 colors ranging from 0 to 15. Move the sliders to create more or less interesting colour effects. Spectral Colours....... If in effect this option causes `MandelSquare' to use a special palette of 75 spectral colours instead of the 32/16 colour palette to be adjusted by the palette control panel. Since not all 75 colours will fit on the screen at one time, only a small part will be visible. Which part to be displayed can be adjusted using the left and right cursor keys. Toggle Calculation..... Use this menu item to abort any calculation currently in progress. If no calculation is currently running, it will be restarted. 32-16384............... The number of iterations to be used when generating a picture. The higher this number, the longer the calculation will take and the more patterns will be revealed in otherwise black areas of the screen. ============================ Special keys ============================ ====================================================================== Just like many other programs of this kind `MandelSquare' supports colour cycling. The following keys control the cycling process: Tab.................... Stops or restarts the colour cycling. Cursor up.............. Starts the cycling in forward direction. Cursor down............ Starts the cycling in reverse direction. Cursor left............ Cycles the colour palette one entry backward. Cursor right........... Cycles the colour palette one entry forward. ========================== Author's Request ========================== ====================================================================== Since I don't expect Commodore to sell more A3000(T/UX) machines, GVP to sell more A3001 boards and PP&S, RCS and ACD to sell more '040 cards just because I happened to create `MandelSquare' I am releasing this program and the accompanying source code as Freeware. The program may not be sold for more than DM 5,- (3$ US) or the equivalent in the local country's currency, but it may be copied for free as long as my copyright remains untouched. If you like this program, send me copy of the animations or pictures you created with it, a picture postcard of your home town would be nice, too. My `physical' address is: Olaf Barthel Brabeckstrasse 35 D-3000 Hannover 71 Federal Republic of Germany My email adresses are: Z-Net: O.BARTHEL@A-Link-H Usenet: o.barthel@a-link-h.zer.sub.org cbmvax.commodore.com!cbmehq!sourcery!olsen Comments and suggestions how to improve this program are generally appreciated! ============ Revision history (most recent change first) ============= ====================================================================== 1.3 Added the animation replay feature, removed the crosshair mouse pointer, the colour transition tables are now generated in a much simpler way than before, some basic calculation logics have been modified to permit faster execution. 1.2 The calculation routine was slightly rewritten to allow for earlier termination (old code used to go through the more complicated calculations before actually noticing that it was time to terminate). The `precise' calculation code should work much faster now since the precalculation will now terminate as soon as an odd pixel is encountered. The animation code now sports much smoother camera zooms. Old code used to bounce & accelerate when coming closer to the selected square, the new code will always appear to approach the square at the same speed. The zoom speed may be set to a custom value and the zoom code actually precalculates the number of frames to calculate before reaching the selected square. I also added an option to have a box displayed around the selected square whilst rendering the single frames (for the `Powers of Ten' effect). 1.1 First public release.