EigenPC: Software Surprise

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Text File | 1991-06-16 | 13.8 KB | 283 lines

"Fractal Designer v3.30 by Doug Nelson May 5, 1991" (submitted to the public domain) can generate unique fractal designs. The number of IFS designs is limited only by the amount of time spent using Fdesign. The designs can be saved to .GIF files or printed on an HP Laserjet or Epson compatible printer. Hardware Requirements o A very-MicroSoft-compatible mouse is required (some clones haven't worked). Also, an 80x87 coprocessor greatly speeds up the generation of images. To give you an idea of the coprocessor's speed --- an 8 MHz XT with coprocessor is faster than a 20 MHz 386 without coprocessor. EGA or VGA graphics are required, but VGA is much better because the pixel size is square. You'll also need 350k bytes of free memory when invoking Fdesign (less if you don't use the Virtual Screen plot). o Your printer must be able to receive commands for one of these: HP Laser Jet II P --- the best pictures Epson 24 pin compatible --- I used an LQ-1000 for testing Epson 9 pin compatible --- I used an early FX series model Running the program o To view a fractal (no mouse required) from the command line: C> fdesign sierpink or C> for %1 in (*.trn) do fdesign %1 to view all .TRN files in the directory o The mouse is the main input device. Hit the mouse button for the top menu (without a coprocessor you may have to hold the mouse button down until the menu appears). For interactive design, type "fdesign" return and you'll get the Top Menu screen: - Normal Plot - plots (to the screen) the current fractal in EGA or VGA 16 colors. - Edit Transformations screen - allows you to change the description of the fractal (edit triangle transformations). If there are at least two transformation triangles, a small fractal image is displayed in the upper right corner and will change concurrently with your edits. * Scratch Everything - cleans the workspace. Then you specify a reference triangle and input transformation triangles until your right mouse button ends the input. * Add a Triangle - you input three points defining an additional triangle. * Delete a Triangle - you select a triangle to delete. * Adjust a Triangle - allows you to move a single vertex of a triangle. First select a triangle by finding an unambiguous edge of the triangle and click left. Then click on the corner you wish to move. Now you may move the cursor to the new position and click left. The fractal image in the upper right updates with your edits. You may continue to click left and watch the fractal change in the upper right corner. When you're satisfied, click the right mouse button. * Grat is on/off - clicking on this will toggle the "on/off". If grat is off, you may place triangle vertices between dots. If grat is on, the closest graticule will be used to place the vertex. * Main Menu - return to plot fractal on the big screen. - Load file screen - loads a transformation (.TRN) file. You may click left on a filename to preview the fractal in that file. When you see the one you want, click right. You will be thrown into the Edit Transformations Screen. If you want a big screen image, click on "Main Menu" immediately. I have included several .TRN files which you may load, display and modify. - Save file - save the current transformations to a file. Type in the filename (without extension) that you wish to save the transformations to. If the filename already exists, you will be prompted for an ok. Saving to another subdirectory or disk is not supported. - Alternate display - plots in 16 colors, but starts with color 1 and increments the color every time a pixel is re-plotted. - Print - Prints the filename, the current screen, the Edit Transformations and IFS codes. This is intended as a way to document your fractals. - Virtual Screen Print - Use this to create high-res pictures on a printer. * Plot 1000000 points - Plots to a virtual screen (1504x1200) a million points. I've found a million to be adequate for most images. This number will increase if you have already zoomed on the image. This number is only a recommendation by a very dumb algorithm. * Plot N points - Again, this plots to the virtual screen as many points as you specify. It occasionally happens that you may need to plot 20 million points to get a full picture. You specify the number of points in thousands (5000 means 5 million). * Print - prints the virtual screen to your printer on LPT1. * Return - gets you back to the top menu. - IFS codes (FRACTINT) - This allows transfering files to/from Fractint. * Write a FRACTINT file --- computes IFS codes for FRACTINT's screen size and writes an ascii file with an extension of .IFS. # FRACTINT viewing is accomplished with the following command line: FRACTINT type=ifs ifs=myfile.ifs video=F4 You would, of course, replace 'F4' with your own video mode preference from the help screens. * Read a FRACTINT file --- computes triangle transformations from the IFS codes. You may then edit the transformations as with any Fdesign file. You may then opt to save the result as a .IFS file (for FRACTINT viewing). * IFS codes for this screen --- these are a,b,c,d,e,f,p used to generate the main display. Note that no scaling to the display is required --- the IFS codes are already scaled for it. - Zoom in - Brings up a zoom box. The box may be moved by moving the mouse. The size of the box may be changed by holding the left mouse button and moving the mouse up or down. To accept the zoom box, press both mouse buttons, or type any key. Multiple zooms are allowed, but the computation time required increases with every zoom. - Zoom reset - reset to the original full-sized image. - Save to .GIF - copies the screen to a .GIF formatted file. - Quit - returns you to DOS. Basic Fractal Education o Not all fractals can be generated by this program. IFS stands for Iterative Function System, just one method of generating fractals. The IFS codes define a space which has a "fractional" dimension. This space has a "shape", the images that this program generates. At least two IFS codes are required to generate a fractal. Each IFS code is derived from an affine transformation, which can be described as mapping one triangle into another (in the same 2D space). o The triangle transformations: In the edit screen, a reference triangle is shown, and any number (up to 32) of transformation triangles are shown. A transformation triangle maps "from" the reference triangle "to" the transformation triangle itself. These mappings are called affine transformations, which means they move points closer together. To enforce the affinity requirement, the A-B side of the transformation triangle must be shorter than or equal to the A-B side of the reference triangle (the same is true of the B-C and A-C sides). However, a transformation triangle may not have all three sides equal to the reference triangle. The program will display an error message if you attempt to input a non-Affine transformation triangle (you can re-define the reference triangle with the "Scratch Everything" command). o Random IFS Algorithm - A beginning point is selected which is on the fractal. - A transformation triangle (IFS code) is randomly selected. - The selected transformation is applied to the current point and the new point is plotted. - One point out of millions has been plotted. - Now go back to randomly select a transformation triangle (may or may not be the same as the transformation just applied). - That's all there is to it. Amazingly simple isn't it? The problems are in the user interface. - A point on the attractor (the fractal) may be thought of as having a coordinate consisting of the history of IFS code numbers required to get there. - Even though the transformations are randomly selected, the resultant image is the same (by mathematical proof). Given infinite time, the resultant image has infinite detail, so the algorithm repeats until you interrupt with a mouse click. o The references will give you everything you ever wanted to know on the theoretical basis for these images. Tips on Building Fractals o Experiment with only two transformation triangles. There is a lot a of creativity in some of those two triangle transformations. Then add a triangle and experiment with various rotations and scalings. o Start with one of the example files and adjust a corner and watch the progress. o When adding a triangle, start with a small triangle and adjust its corners while watching the fractal in the upper right corner. o Make the colored regions "just touching" in the small edit plot to create interesting connections. o To me, creating fractals seems like a very intuitive process. I've designed the user interface to facilitate a quick design cycle. Revisions o v3.30 - .IFS file format change to be compatibility with Fractint after rev 15: Some minor user interface changes were made. In-line assembler if 80287 or better coprocessor is present. The R250 algorithm (see Doctor Dobb's Journal, May 1991) becomes the random number generator. o v3.08 - more enhancements: GIF file saving was added. IFS codes display and FRACTINT interface were added. Zooming support on main screen and "virtual screen print" was added. Up to 32 triangle transformations are allowed. A command line option to view .TRN files was added. Color codes now exclude WHITE, DARKGREY, and BLACK. Two video "modes" available: 1) normal plot --- this color codes the triangle transformations (or IFS codes), and 2) alternate display --- increments the color code every time a pixel is re-plotted (shows density). o v2.05 - lots of enhancements: A bug that caused a floating point domain error has been removed. Three printer types are supported. A "virtual screen" has been added with 1504x1200 resolution (used only for printing). File menu now shows a little plot from the filename you click on. 256 color plotting was added (and subsequently removed). You may turn off the graticule spacing when adjusting triangle transformations. Menus have been "cleaned up". o v1.00 - added the 'small plot' to the Modify screen and the 'adjust triangle' command. o v0.01 - the first distributed copy of FDESIGN. Known Problems o Sometimes the probabilities are not computed correctly when adding an Fdesign design to a Fractint .IFS file. Some adjustment of the last parameter on each line may be necessary for Fractint (this is the probability setting). However, the total of the last parameters must add up to 1.0. o Sometimes an .IFS file design will read in correctly --- however, it may not display perfectly in the "small plot" mode (as when editing the triangle transformation). I currently have no fix for this. o An extremely rare floating point error occurs which I've been unable to track down. References o An excellent reference is "Fractals Everywhere" by Michael Barnsley. o BYTE magazine, January 1988. o A good reference is "The Science of Fractal Images" by M.F. Barnsley, R.L. Devaney, B.B. Mandlebrot, H.-O. Peitgen, D. Saupe, and R.F. Voss with contributions by Y. Fisher and M. McGuire. o Thanks to Bert Tyler [73477,433] (CIS) and Lee Daniel Crocker [73407,2030] (CIS) for their .GIF encoder. Send comments or suggestions to: Doug Nelson 3640 Old Denton Rd #2405 Carrollton, TX 75007 Compuserve ID 70431,3374 (my address may change, but not my compuserve ID)