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Text File | 1990-11-12 | 13.9 KB | 370 lines

----------------------------------------------------------------------------- Version history v0.50 First numbered version. Most bugs I've found are fixed. v0.60 Workbench interface added. v1.00 First public release. ----------------------------------------------------------------------------- BUGS - Not very smart handling of AUTOCRAWL - If invoked with too little memory, 56 bytes will mysteriously disappear - Window title bar may get trashed if moved too high ----------------------------------------------------------------------------- Copying licence: This program is copyright 1990 by Hannu Helminen. However, you may freely distribute it provided that this package is left intact and no charge is taken. You are also licenced to use parts of the code in your programs provided that 1) New versions are clearly marked as such 2) You give credit where credit is due (me) I will not guarantee anything about this program. It seems quite reliable to me, though. ----------------------------------------------------------------------------- Package includes: mandel Main proggie mandel.doc This file iff.library Used when saving pictures. Place in libs: directory. source/gui.asm Graphical user interface source/brot.asm This takes care of the actual drawing source/pipe.asm A package of fifo routines, as needed by brot source/macros.i General macros source/mbrot.i brot-specific include file, including my own structure source/iff.i Needed to use iff.library ----------------------------------------------------------------------------- OVERVIEW There are quite a few Mandelbrot programs for Amiga, perhaps to the extent that I should have named my program "yamb" instead of "mandel". (Yet Another MandelBrot) I hope though that there are enough reasons to satisfy the existence of this program. Namely, it was designed with three goals in mind: first, speed. Secondly, speed. And last but not least, speed. Of course, most Mandelbrot programs draw nice-looking pictures, if only you can wait for ten minutes or even more for them to be complete. Increase the number of iterations and you will have to wait for hours, unless you are one of those lucky guys with a 60-MHz 68040-equipped A3000's... The main reason for that slowness is the floating point math most programs use. The first version of this program was quite ugly: coded partly in Basic, partly in 68000 machine language, it was a mess of a code. Its optimized core used 32-bit fixed point math but was still relatively slow. After writing it, I forgot it for years. Then someone in alt.fractals told about a new algorithm called contour crawling that produces fast images of Mandelbrot set. I adopted the idea and rewrote the program to use it, this time completely in machine language. It turned out to be fast (within minutes); that is because it does not need to iterate all pixels. And the drawing was visually attractive, so it suits well for interactive use. After imploying a 16-bit iteration for lower resolutions, I found I had written the fastest Mandelbrot program I had ever seen. (Ok, forget that little transputer...) I cannot pretend to have seen even all Amiga ones, though, so there may already be a faster one. If so, please tell me that all this code was in vain. USAGE Start from CLI by typing `mandel', or click the icon in Workbench. The program will then immediately begin to draw the Mandelbrot set. Various options exists, however, to modify how, where and when the image will be drawn. Use CTRL-C to abort a draw in progress, and another CTRL-C to abort the program. From CLI: Enter the options after the command, e.g. mandel -i1000 -j -sram:Picture Type `mandel ?' to see a brief summary of the options. From Workbench: Select mandel icon, select `info' from the `Workbench' menu and enter options in the TOOL TYPES array, e.g. I=100 FLAGS=j SAVE=ram:Picture The options are listed below. # is a shorthand for a number. CLI WorkBench -x# X=# These determine the point (z = x + yi) in the complex -y# Y=# plane you will see right in the center of your monitor. They are in the range -4 to 4. -m# M=# This is a logarithmic quantity that represents the magnification of the image. 2^(-m) determines the distance between two lo-res pixels in complex plane. Default is 6, maximum is 29. -i# I=# Iterations. Self-explanatory? No? The greater the number, the more accurate pictures mandel will draw. For further information, refer to APPENDIX A. The maximum number of iterations is 65535. -jx# JX=# These determine a constant (c = jx + jy i) that is used -jy# JY=# when iterating a Julia set. Each c will produce a different set. See APPENDIX A. These, too, have a range from -4 to 4. -sname SAVE=name This determines a filename for saved pictures. If mandel is operated interactively (g flag is set), the user can save pictures by pressing CTRL S. The standard filename is `mandel.picture', but can be overridden by this option. If many pictures are saved, a number is added at the end to distinguish the files from each other. If mandel is in non-interactive use (x flag is set), this options specifies that the image must be saved upon exit, and determines the name for it. Note: if this option does not exists, no image will be saved. -l FLAGS=l Normally mandel determines itself whether it should use -h FLAGS=h 16 or 32 bits of precision, as denoded by (a). There -a FLAGS=a are certain, limited circumstances when you need to set the precision explicitely to 16 (l) or 32 (h) bits. In particular, Julia sets that have a complex structure near origo may produce inaccurate images unless 32 bits are used. -c FLAGS=c You can enable (c) or disable (w) the crawling if you -w FLAGS=w wish, default is (p), which means to crawl whenever -p FLAGS=p possible. Currently non-connected Julia sets are not crawled because they *could* produce inaccurate results. Future versions might add more sanity checks to this. -x FLAGS=x When the (x) flag is used, the programs exits -g FLAGS=g immediately after the first image is drawn. Default is (g) which means to prompt the user with a requester-like window (See below). The x flag is intented for non-interactive use, for example continuous zooms that are achieved via scripts. -m FLAGS=m Whether you want to draw Julia (j) or Mandelbrot (m) -j FLAGS=j sets. See APPENDIX A. NOTE: In Workbench, if multiple FLAGS are used, they *must* be combined in a single FLAGS entry, e.g. FLAGS=apgx In CLI, flags *must not* be combined, so do not try `-apgx' instead of `-a -p -g -x'. GRAPHICAL USER INTERFACE When mandel is invoked with the -g option, after the first image is drawn, a requester-like window will pop in. A grid will also be displayed, indicating the centerpoint and borders of the next image. Screen title bar will show coordinates of the mouse position. You can then set the centerpoint by clicking in the image or entering a value in the string gadgets labeled `X' and `Y'. Magnification and iterations can be set in the gadgets `M' and `I', respectively. A new quantity can be set using the `Z' gadget: zooming. As its name implies, this determines which portion of the current image will be shown in the next one. This is a signed number that will be added to magnification, thus set z=0 for 100% zooming, z=1 for 50%, z=-1 for 200% etc. This can also be set by pressing the right mouse button and moving it over the image. The program draws images in one of three modes: ZOOM, DRAW and RESET. ZOOM means zooming to the size shown by the grid. DRAW will take the numbers from the requester and draw according to them (used for example to redraw the same picture, or to quickly enter a very deep magnification level) As setting zoom in DRAW mode makes as little sense as setting magnification in ZOOM mode, these modifications will immediately change the draw mode, too. The third mode, RESET, will return the magnification and centerpoint to normal. The mode can be changed by respective gadgets. Clicking MAND or JULIA will change the set type to Mandelbrot or Julia. The magical constant c for Julia sets (See APPENDIX A) can be set as follows: Make sure you are in MAND mode. Then select the point c by either clicking on the image or entering it in the X/Y-gadgets. Then click JULIA gadget and select whatever centerpoint you wish your image to have. Alas, window close gadget only removes the requester window, screen title and grid in order to let you view the image. Normal operation is resumed by pressing either mouse button. Quit the program by double-clicking the QUIT gadget or draw a new set by double-clicking either in the image or one of the gadgets ZOOM, DRAW, RESET. AUTHOR Hannu "The DM" Helminen Perkkiö 85900 REISJÄRVI FINLAND dm@stekt.oulu.fi (for the next few years, I hope) THANKS Thanks to T. Saarinen for extensive beta-testing 'LS' Hautamäki for not-so-extensive testing J.M. Jarre who was in great help during long nights of programming B. Mandelbrot who invented the set that carries his name APPENDIX A: A mathematical definition of Mandelbrot and Julia sets. A point z = x + y i is said to be in the Mandelbrot set if 0 2 z = z + c does not go to ±oo (infinity) when n -> oo n+1 n ____ where c = z . ( i = ,/ -1 so z, c are complex numbers ) 0 A point z = x + y i is said to be in the Julia set c if 0 2 z = z + c does not -> oo when n -> oo n+1 n NOTE: There are an infinite number of Julia sets, each corresponding to one value of c. c is also related to a point in the Mandelbrot set. (originally the Mandelbrot set was the set of c's that will produce a *connected* Julia set.) Note also that the Julia set looks similar to the surroundings of that point in the Mandelbrot set from which the Julia set was derived. Becausese these calculations would take a considerable amount of time with any contemporary computer, they are approximated by a finite number of iterations (typically 100 or more). An usual test for a point z going to infinity is to test whether or not | z | < 2. And since few computers can calculate with complex numbers, we can rewrite the equation (z -> z² + c) in a C-ish style program using only real variables z = x + y i: i = max_iterations; while (i > 0 && x² + y² < 4) { tmpx = x² - y² + x0; tmpy = 2 x y + y0; x = tmpx; y = tmpy; i--; } if (i=0) inside (); else outside(); If you are a first-time user of any Mandelbrot program, I might suggest that you study the edge of the black area, because that is where the most interesting parts of the set are. (The coloured areas do not actually belong to the set, and the interior is, of course, all black...) APPENDIX B: The contour crawling method This method works by finding an edge of an area of uniform color, then crawling its way through the edge until starting point is reached. The interior is then assumed to be of same color. This is of course true for the ideal set, but because the image is sampled to a finite set of pixels, errors *may* occur. (Haven't seen one so far, though.) Non-connected Julia sets must not be crawled in the strict mathematical sense. However, most of the time mandel produces correct pictures even then. So it is quite safe to use the -c option of mandel. APPENDIX C: Compilation Assuming you have a68k v2.61 or higher and blink, the following steps are needed to compile a working executable of mandel: a68k gui.asm -q500 -iinclude: a68k brot.asm -q200 -iinclude: a68k pipe.asm -q100 blink gui.o brot.o pipe.o to mandel lib amiga.lib where include: is assigned to standard assembly include directory. NOTE: if you have a68k v2.42, gadget arrow images will not be marked as going to CHIP ram. This will give you strange-looking images unless: 0) You have only CHIP ram (poor chap) 1) You use FastMemFirst, FixHunk, ATOM etc. kludges 2) Modify the code: allocate some CHIP-mem and CopyMem() the images there. This is a kludge, however. 3) Get v2.62 somewhere (e.g. disk 314 from Fred Fish's wonderful collection.) APPENDIX D: How to use brot with your own programs? Just pass the address of a valid mb-structure in a0 (see mbrot.i), `jsr MandelBrot' and `XREF MandelBrot' somewhere in your code and (b)link your proggie with brot.o and pipe.o. The RastPort you use *must* have valid TmpRas and AreaInfo structures attached to it. AreaInfo should carry as many vectors as possible (no more than 6553, however, since that seems to be a maximum)