farmsg.ASMۖ% DGROUPDATACODE_DATA farmsg_TEXT H H  _1 _helpmessageendtext} _helpmessageauthors  _helpmessagefractalsP m _plasmamessage _initifs߂ _helpmessagemoretext=} _goodbyemessageׁ _runningontarga_ _initifs3d{ c _helpmessagemain @ _helpmessagemenu _argerrormessaget _helpmessagevideo~ N _helpmessagexhair  _helpmessagetitle 73 _helpmessageformoreinfo _helpmessagemouse( ( _inversionmessage _helpmessage1 1 _helpmessagecmdline0 _helpmessagecycling 7 _helpmessagecreditsU  Ѡ  ΜQ        # '"( /+*0 a/24 468 9:< 9>>@ )CBD 8HFH oMJP ORT TVX XZ\ Z^` i^bd 6cfh  hjl jnp nrt pvx wtz| v~Ą yȆʠ  FRACTINT Version 14.0 ------------------ Primary Authors (this changes over time) ----------------- Bert Tyler - Compuserve (CIS) ID: [73477,433] BIX ID: btyler Timothy Wegner - CIS ID: [71320,675] Internet: twegner@mwunix.mitre.org Mark Peterson - CIS ID: [70441,3353] Pieter Branderhorst - CIS ID: [72611,2257] --------- Contributing Authors (SPACEBAR toggles scrolling off/on) ---------- Please press one of the Function Keys to select a video mode and begin an image (or press the >> F1 << (NOT the 'h') key now or at any other time for help) ... Michael Abrash - 360x480x256, 320x400x256 VGA video modes Kevin Allen - Finite attractor and bifurcation engine Steve Bennett - restore-from-disk logic Rob Beyer - [71021,2074] Barnsley IFS, Lorenz fractals Mike Burkey - 376x564x256, 400x564x256, and 832x612x256 VGA video modes John Bridges - [73307,606] superVGA support, 360x480x256 mode Brian Corbino - [71611,702] Tandy 1000  640x200x16 video mode Lee Crocker - [73407,2030] Fast Newton, Inversion, Decomposition.. Monte Davis - [71450,3542] Documentation Richard Finegold- [76701,153] 8/16/../256-Way Decomposition option Lawrence Gozum - [73437,2372] Tseng 640x400x256 Video Mode David Guenther - [70531,3525] Boundary Tracing algorithm Mike Kaufman - [71610,431] mouse support, other features Adrian Mariano - [theorem@blake.acs.washington.edu] Diffusion fractal type Chris Martin - Paintjet printer support Joe McLain - [75066,1257] TARGA Support, color-map files Bob Montgomery - [73357,3140] (Author of VPIC) Fast text I/O routines Bret Mulvey - plasma clouds Marc Reinig - [72410,77] Lots of 3D options Kyle Powell - [76704,12] 8514/A Support Matt Saucier - [72371,3101] Printer Support Herb Savage - [71640,455] 'inside=bof60', 'inside=bof61' options Lee Skinner - Tetrate, Spider, Mandelglass fractal types and more Dean Souleles - [75115,1671] Hercules Support Kurt Sowa - [73467,2 013] Color Printer Support Scott Taylor - [72401,410] KAM Torus, many trig function types Paul Varner - [73237,411] Floating-point fractal algorithms Dave Warker - Integer Mandelbrot Fractals concept Phil Wilson - [76247,3145] Distance Estimator, Bifurcation fractals Richard Wilton - Tweaked VGA Video modes ... Byte Magazine - Tweaked VGA Modes MS-Kermit - Keyboard Routines PC Magazine - Sound Routines PC Tech Journal - CPU, FPU Detectors The following help screens are available 1 - Commands available at the initial Credits Screen and main command level 2 - Commands available at the Color-Cycling command level 3 - Commands available at the Cross-Hair command level 4 - The SSTOOLS.INI file and Command-Line arguments 5 - Descriptions of currently available fractal types 6 - List of Available Video Modes and the keys that select them ( >>> and if you're at the initial Credits Screen, NO FRACTAL IMAGES are going to get drawn UNTIL Ѡ  AFTER you select a video mode <<< ) 7 - Contacting the authors / obtaining the latest versions of FRACTINT 8 - Using FRACTINT with a mouse Please press one of the above keys (or press ESCAPE to exit Help Mode) The useful keys you can hit while this program is running (the commands marked with an '*' are also available at the credits screen) are: * F1 or ? HELP! (Enter help mode and display this screen) * F2,F3,F4,F5... Select a new Video Mode and THEN Redraw (see the Video-modes HELP screens for the full modes list) * t or T Select a new fractal type and parameters * x or X Set any of a number of options ('eXtensions') PageUp, PageDown Shrink or Expand the Zoom Box Cursor Keys Pan (Move) the Zoom Box across the screen Ctrl-Cursor Keys Fast-Pan the Zoom Box (may require an enhanced keyboard) End or Enter Redraw the Screen or area inside the Zoom Box Tab Display the current fractal image information Home Redraw Previous screen (you can 'back out' recursively) s or S Save the current screen image to disk (restart with 'r') * r or R or 3 or o Restart from a saved (or .GIF) file ('3' or 'o' for 3-D) Hit any of these keys while drawing a fractal to immediately do the command. If the screen finishes before you hit a key, it will beep and wait for you. The useful keys you can hit while this program is running (the commands marked with an '*' are also available at the credits screen) are: p or P Print the screen (command-line options set printer type) c or C or + or - Enter Color-Cycling Mode (see Color-Cycling Help screen) Spacebar Mandelbrot/Julia Set toggle (read FRACTINT.DOC first) * Delete or Esc Stop the program and return to MSDOS * Insert Restart the program (at the credits screen) * d or D Shell to DOS (type 'exit' at the DOS prompt to return) o or O toggles 'orbits' # option on and off during image generation Ctrl- Enter 'Zoom-out' - expands the image so that your current image is positioned inside the current zoom-box location. Ctrl- Pad+/Pad- Rotate the Zoom Box Ctrl- PgUp/PgDn Change Zoom Box vertical size (change its aspect ratio) Ctrl- Home/End Change Zoom Box shape Ctrl- Ins/Del Change Zoom Box color Hit any of these keys while drawing a fractal to immediately do the command. If the screen finishes before you hit a key, it will beep and wait for you. The useful keys you can hit while this program is running (the commands marked with an '*' are also available at the credits screen) are: b or B Add the current fractal description to FRABATCH.BAT * 1 or 2 or g Select Single-Pass, Dual-Pass, or Solid-Guessing mode < or > Lower or Raise the Iteration Limit (display with Tab key) * f or F toggle the floating-point algorithm option ON or OFF. * n or N or l  or L Select Normal (the default) or Logarithmic Palettes i or I apply inversion to the current fractal image q or Q apply Decomposition (2, 4, .. 256-way) to the current fractal image. See FRACTINT.DOC for details. a or A Convert the current image into a fractal 'starfield' (the 'astrologer' option). * e or E Edit the parameters for the Barnsley IFS fractal-types (this option ONLY affects Barnsley IFS and IFS3D fractals) Hit any of these keys while drawing a fractal to immediately do the command. If the screen finishes before you hit a key, it will beep and wait for you. Command Keys that are available in Color-Cycling mode (which is the mode you are in if you have hit the 'c' key and are now paused in Color-Cycling mode with a white overscan (border) area, or you hit the '+' or '-' keys and the the colors are now cycling on your screen). Commands marked with an '*' are available only on  VGA systems (the others also work on EGA systems). F1 or ? HELP! (Enter help mode and display this screen) + or - (re)-set the direction of the color-cycling Right/Left Arrow (re)-set the direction of the color-cycling (just like +/-) Up/Down Arrow SpeedUp/SlowDown the color cycling process F2 thru F10 Select Short--Medium--Long (randomly-generated) color bands 1 thru 9 Cycle through 'nn' colors between screen updates (default=1) Enter Randomly (re)-select all new colors [TRY THIS ONE!] Spacebar Pause until another key is hit (the overscan area is set to white as a visual indicator of a Color-Cycling pause) * SF1 thru AF10 Pause and re-set the Palette to one of 30 fixed sequences * r or g or b or force a pause and Lower (lower case) or Raise (upper case) * R or G or B the Red, Green, or Blue component of the fractal image Command Keys that are available in Color-Cycling mode (which is the mode you are iX n if you have hit the 'c' key and are now paused in Color-Cycling mode with a white overscan (border) area, or you hit the '+' or '-' keys and the the colors are now cycling on your screen). Commands marked with an '*' are available only on VGA systems (the others also work on EGA systems). d or D or a or A pause and load the palette from DEFAULT.MAP or ALTERN.MAP m or M pause, prompt for a palette map filename (default filetype is .MAP), and load the palette from that map file s or S pause, prompt for a palette map filename (default filetype is .MAP), and save the palette to that map file * x or X Enter Cross-hair palette-manipulation mode, where you can modify the screen colors a palette at a time (see the Cross-Hair Help screen for details) (any other key) Exit Color-Cycling and return to main command level Command Keys that are available in Cross-Hair mode (which is the mode you are i #n if you have hit the 'x' key in Color-Cycling mode and are now looking at a screen with a white overscan (border) area and a Cross-Hair cursor on the screen). Cross-Hair mode is available only on VGA systems. F1 or ? HELP! (Enter help mode and display this screen) Cursor Keys Move the cross-hair cursor around the screen. The Control-Cursor keys move the cross-hair around faster. A mouse can also be used to move around. r or g or b or Lower (lower case) or Raise (upper case) the Red, Green, R or G or B or Blue component of the palette color of the pixel in the center of the Cross-Hair cursor (and all of the other pixels that use the same palette value) + or - Change the RGB values of the palette of the pixel in the center of the Cross-Hair cursor (and all of its sister pixels) to that of the next higher (or lower) palette value. UР 'seful for 'erasing' bands of color. Command Keys that are available in Cross-Hair mode (which is the mode you are in if you have hit the 'x' key in Color-Cycling mode and are now looking at a screen with a white overscan (border) area and a Cross-Hair cursor on the screen). Cross-Hair mode is available only on VGA systems. Ctrl-Ins Change the palette value (color) of the Cross-Hair or Ctrl-Del Cursor. Useful when the cursor gets 'lost'. Holding down the Right mouse-button and moving the mouse forward or backward also changes the cursor color. Enter, Ctrl-Enter, the other keys used for Zoom Box functions, and the equivalent mouse buttons, all do nothing in Cross-Hair mode. (any other key) Exit Cross-Hair mode and return to Color-Cycling mode Using FRACTINT with a Mouse Left Button: Brings up and sizes the Zoom Box. While holding down the left button, push the mouse forward to shrink v +the Zoom Box, and pull it back to expand it. Double-clicking the left button performs the Zoom. Right Button: While holding the right button held down, move the mouse from side to side to 'rotate' the Zoom Box. Move the mouse forward or back to change the Zoom Box color. Double-clicking the right button performs a 'Zoom-Out'. Both Buttons: (or the middle button, if you have three of them) While holding down both buttons, move the mouse up and down to stretch/shrink the height of the Zoom Box, or side to side to 'squish' the Zoom Box into a non-rectangular shape. Zoom and Pan using the mouse typically consists of pushing in the left button, sizing the zoom box, letting go of the button, panning to the general area, then double-clicking the left button to perform the Zoom. If FRACTINT locates a file called 'SSTOOLS.INI' in the DOS PATH, it reads initialization variables from it. T /hese variables can also be initialized on the command-line as arguments, or from other files referenced on the command line using an '@' notation. The variables currently available are: @filename Read more cmd-line arguments from 'filename' (this option only available on the command-line) [filename=]filename Start with this saved file (one saved by FRACTINT or a generic GIF file [treated as a plasma cloud]) ('filename=' is mandatory inside '@' or .INI files) savename=filename Save files using this name (instead of FRACT001) video=xxx Begin with this video mode (Example: Video=F2) See the video-modes HELP screen for a full list type=fractaltype Perform this Fractal Type (Default = mandel) See the fractaltypes HELP screen for a full list params=xxx[/xxx[/xxx]]... Begin with these extra Parameter values 3 (Examples: params=4 params=-0.480/0.626) corners=xmin/xmax/ymin/ymax[/x3rd/y3rd] Begin with these X, Y Coordinates (Example: corners=-0.739/-0.736/0.288/0.291) The initialization variables available, and their formats are: passes=x (x = 1, 2, g, or b) Select Single-Pass, Dual-Pass, Solid-Guessing or the Boundary-Tracing drawing algorithms potential=nn[/nn[/nn]] Continuous Potential options (see FRACTINT.DOC) logmap=yes|old Maps logarithm of iteration to color. Updated calculation in version 14; 'old' selects old method. maxiter=nnn Maximum number of iterations (default = 150) iterincr=nnn Iteration inc/decrement stepsize (default = 50) inside=nnn Fractal interior color (inside=0 for black) outside=nnn Fractal exterior color (forces two-color images) finattract=yes Look for finite attractor in julia types map=filenc 7ame (VGA or TARGA) get the color map from 'filename' warn=yes Tells FRACTINT to avoid over-writing existing files batch=yes Batch mode run (display image, save-to-disk, exit) savetime=nnn Autosave image every nnn minutes of calculation batch=config Batch mode run to generate a 'fractint.cfg' file cyclelimit=nnn color-cycler speed-limit (1 to 256, default = 55) float=yes For most functions changes from integer math to fp The initialization variables available, and their formats are: preview=yes Turns on 3D 'preview' default mode showbox=yes Turns on 3D 'showbox' default mode sphere=yes Turns on 3D sphere mode longitude=nn/nn Longitude minumim and maximum latitude=nn/nn Latitude minimum and maximum radius=nn Radius scale factor rotation=nn[/nn[/nn]] Rotation abount x,y, and z axes scalexyz=nn/nn/nn X,  ;Y, and Z scale facytors roughness=nn Same as Z scale factor waterline=nn Colors this number and below will be 'inside' color filltype=nn 3D filltype perspective=nn Perspective viewer distance (100 is at the edge) xyshift=nn/nn Shift image in x and y directions (alters viewpoint) lightsource=nn/nn/nn The coordinates of the light source vector smoothing=nn Smooths rough images in light source mode invert=nn/nn/nn Turns on inversion - turns images 'inside out'. transparent=mm/nn Sets colors 'mm' to 'nn as transparent The initialization variables available, and their formats are: coarse=nnn Sets Preview 'coarseness' default value stereo=nnn Sets Stereo (R/B 3D) option: 0 = none, 1 = alternate, 2 = superimpose, 3 = photo interocular=nnn Sets 3D Interocular distance default value converge=nnn Sets 3D Convergence defaul+ ?t value crop=nnn/nnn/nnn/nnn Sets 3D red-left, red-right, blue-left, and blue-right cropping default valuess bright=nnn/nnn Sets 3D red and blue brightness defaults, xyadjust=nnn/nnn Sets 3D X and Y adjustment defaults, rseed=nnnnn Forces reproducable Plasma Clouds. The 'rseed=' value is listed as part of the display decomp=nn[/nnnnn] 'Decomposition' toggle. First value 2 to 256, 2nd is bailout limit. See FRACTINT.DOC for details biomorph=nnn Turns on Biomorph Coloring (try with the mansinzexpd and Julsinzexpd fractal types) bailout=nnnn Use this as the iteration bailout value (rather than the default value of [for most fractal types] 4.0) distest=nnn Turns on Distance Estimator Method, see FRACTINT.DOC for details ifs=filename ߠ CDefine an IFS map for the Barnsley IFS fractals Read the IFS section of FRACTINT.DOC for details symmetry=xxxx Force symmetry to None, Xaxis, Yaxis, XYaxis, Origin, or Pi symmetry. Useful for debugging. formulafile=filename Find the 'type=formula' fractals in this file instead of the default file (FRACTINT.FRM). formulaname=formulaname Have the 'type=formula' fractals use this formula (instead of the first one in the file). printer=type[/res[/lpt#]] Set the printer type (HP-Laserjet, IBM, Epson, or, Color [Star Micronix]), dots/inch, and port# (1-3 for LPTn, 11-14 for COMn) askvideo=no Disable 'Is This Mode OK?' prompt if you have a FRACTINT.CFG file restricted to legal video modes. ; indicates the rest of the line is a comment ( GIE, 'fractint type=plasma ; use plasma clouds') sound=off (nobody ever plays with fractals at work, do they?) function=fn1/fn2/fn3/fn4 Allows specification of transcendental functions with types using variable functions. Possible values are sin, cos, sinh, cosh, exp, log, and sqr. periodicity=[no|show|nnn] Controls periodicity checking. 'no' turns checking off; entering a number nnn controls the tightness of checking (1 is default, higher is more stringent) 'show' or a neg value colors 'caught' points white. center-mag=[Xctr/Yctr/Mag] Allows an alternative method of entering corners. With no parameters causes 'b' command to output 'center-mag=' instead of corners. randomize=nnn smoothes 3d color transitions between elevations fullcolor=yes allows creation of full color . KTGA image with light source fill types. See the Docs. ambient=nnn sets depth of shadows and contrast when using light source fill types haze=nnn sets amount of haze for distant objct if fullcolor=1 lightname=filename file name which will be used to save the full color files with full color option. gif87a=yes Forces Fractint to save all GIF files in the older GIF87a format (with no FRACTINT extension blocks) initorbit=nnn/nnn Sets the value used to initialize Mandelbrot orbits to the given complex number (real and imag parts). initorbit=pixel Sets the value used to initialize Mandelbrot orbits to the complex number corresponding to the screen pixel. This is the default for most types. mandel = 'Classic' Mandelbrot fB Oractals using 32-bit integer math for speed. z(0) = 0; z(n+1) = z(n)^2 + C, where C = Xcoord + i * Ycoord. Two optional params: real and imaginary pertibations of z(0). julia = 'Classic' Julia set fractals using 32-bit integer math for speed. z(0) = Xcoord + i * Ycoord; z(n+1) = z(n)^2 + C. Two params required: real and imaginary parts of C. newton, = Newton Domains-of-attraction (only the coloring schemes are newtbasin different). First param: the power (from 3 to 10) of the eqn. If param=4, the eqn is z(n+1) = (3*z(n)^4+1)/(4*z(n)^3). Second param is flag to turn on alternating stripes in basin mode. complexnewton, = Newton's fractal type extended to complex numbers. complexbasin Calculates roots of z^a + b, where both 'a' and 'b' complex. lambda = Classic Lambda fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = Lambda*z(n)*(1 - z(n)^2). Two params: real, imaginary parts of Lamb Sda. 'Julia' variant of Mandellambda mandellambda= 'Mandelbrot-Equivalent' for the lambda fractal. z(0) = .5; lambda = Xcoord + i * Ycoord; z(n+1) = lambda*z(n)*(1 - z(n)^2). Parameters are pertubations of z(0). Types taken from Michael Barnsley's 'Fractals Everywhere' barnsleym1 = Alternative 'Mandelbrot'. z(0) = Xcoord + i * Ycoord; z(n+1) = (z-1)*C if Real(z) >= 0, else = (z+1)*modulus(C)/C, where C = Xcoord + i * Ycoord. Params are pertubations of z(0). barnsleyj1 = 'Julia' corresponding to barnsleym1. z(0) = Xcoord + i * Ycoord; z(n+1) = (z-1)*C if Real(z) >= 0, else = (z+1)*modulus(C)/C. Two params required: real and imaginary parts of C. barnsleym2 = Another alternative 'Mandelbrot'. z(0) = 0; z(n+1) = (z-1)*C if Real(z)*Imag(C) + real(C)*imag(z) >= 0, else z(n+1) = (z+1)*C, where C = Xcoord + i * Ycoord. Parameters are pertubations of z(0). barnsleyj2 = 'Julia' corresponding to Wbarnsleym2. z(0) = Xcoord + i * Ycoord; z(n+1) = (z-1)*C if Real(z)*Imag(C) + real(C)*imag(z) >= 0, else = z(n+1) = (z+1)*C. Two params: real and imaginary parts of C. barnsleym3,= Another Barnsley 'Mandelbrot', 'Julia' pair. barnsleyj3 See FRACTINT.DOC for details. Barnsley types (continued) sierpinski = Sierpinski gasket - a Julia set that produces a 'Swiss cheese triangle'. z(n+1) = (2*x,2*y -1) if y > .5; else (2*x-1,2*y) if (x > .5); else (2*x,2*y). No parameters. ifs = Barnsley IFS Fractal (a fern unless an alternate IFS map has been defined using the 'ifs=' command-line option). ifs3d = Barnsley 3D IFS Fractal (a fern unless an alternate IFS map has been defined using the 'ifs3d=' command-line option). Mark Peterson's Types marksmandel= A variant of the mandel-lambda fractal. z(0) = 0; z(n+1) = ((Xcoord+i*Ycoord)^exp)*z(n) + (Xcoord+i*Ycoord). Parameters are pertubations of  [z(0). marksjulia = A variant of the julia-lambda fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = (z(0)^exp)*z(n) + z(0). cmplxmarksjul, = The above two types generalized with 'exp' a complex rather cmplxmarksmand than a real number julibrot = 'Julibrot' 4-dimensional fractals. Read FRACTINT.DOC for an description of these fractals (and a description of the prompts involved in invoking them). unity = Mark Peterson's 'Unity' fractal type. Truly Wierd - See FRACTINT.DOC for the description of this one! formula = Formula interpreter - write your own formulas as text files! See FRACTINT.DOC for instructions on using this one. lambdafn = lambda-fn fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = lambda * fn(z(n)). Two params: real, imag portions of lambda. 'Julia' variant of Mandelfn. 'fn' is a variable function, and may be one of sin, cos, sinh, cosh, exp, log, or sqr. mandelfn = 'MandeѠ _lbrot-Equivalent' for the lambda-fn fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = z(0)*fn(z(n)). Parameters are pertubations of z(0). 'fn' is a variable function. mandel4 = Fourth-power 'Mandelbrot' fractals using 32-bit integer math. z(0) = 0; z(n+1) = z(n)^4 + C, where C = Xcoord + i * Ycoord. Two optional params: real and imaginary parts of z(0) (if not 0). julia4 = Fourth-power Julia set fractals using 32-bit integer math. z(0) = Xcoord + i * Ycoord; z(n+1) = z(n)^4 + C. Two params required: real and imaginary parts of C. test = 'test' point letting us (and you!) easily add fractal types. Currently, the 'Distance Estimator' M'brot/Julia Set algorithm. two optional parameters - if none given, uses the M'brot Set If given, they are the the same as the Julia Set parameters. plasma = plasma clouds - random, cloud-like formations. Requires four or more color cs. One param: 'graininess' (.5 to 50, default = 2) julfn+zsqrd= Julia Biomorph fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = fn(z(n)) + z(n)^2 + C. Two params: real, imag portions of C. manfn+zsqrd= 'Mandelbrot-Equivalent' for the Julfn+zsqrd fractal. z(0) = Xcoord + i * Ycoord0; z(n+1) = fn(z(n)) + z(n)^2 + (Xcoord + i * Ycoord). Parameters are pertubations of z(0). manzpower = 'Mandelbrot-Equivalent' for julzpower. z(n+1) = z(n)^m + C. Parameters are real and imaginary pertubations, exponent m. julzpower = Juliazpower fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = z(n)^m + C. Three params: real, imag portions of C, exponent m. manzzpwr = 'Mandelbrot-Equivalent' for the julzzpwr fractal. Use the Space-bar to select julzzpwr fractals a/la Mandel/Julia. z(n+1) = z(n)^z(n) + z(n)^m + C. Parameters are real pertubation, imaginary pertubation, and exponent m. julzzpwr = z(0) = Xcoord + i * g Ycoord; z(n+1) = z(n)^z(n) + z(n)^m + C. Three params: real, imag portions C, and the exponent m. manfn+exp = 'Mandelbrot-Equivalent' for the julfn+exp fractal. Use the Space-bar to select julfn+exp fractals a/la Mandel/Julia. z(n+1) = fn(z(n)) + e^z(n) + C. Parameters are real pertubation, and imaginary pertubation of z(0). julfn+exp = julia fn+exp fractal. z(0) = Xcoord + i * Ycoord; z(n+1) = fn(z(n)) + e^z(n) + C. Two params: real, imag portions C. popcorn = orbits of x(n+1) = x(n) - h*sin(y(n) + tan(3*y(n)) and y(n+1) = y(n) - h*sin(x(n) + tan(3*x(n)) plotted for EACH screen pixel and superimposed. popcornjul= Julia set from popcorn formula. z(0) = Xcoord + i * Ycoord. Orbit calculated as in popcorn. bifurcation = 'Bifurcation' fractal. Pictoral representation of a population growth model. Let P = new population, p = oldpopulation, r = growth rate. T khe model is: P = p + r*p*(1-p). biflambda = Bifurcation variation: model is: P = r*p*(1-p)P. bif+sinpi = Bifurcation variation: model is: P = p + r*sin(PI*p). bif=sinpi = Vifurcation variation: model is: P = r*sin(PI*p). lorenz = Lorenz attractor - orbit in three dimensions defined by: xnew = x + (-a*x*dt) + (a*y*dt) ynew = y + (b*x*dt) - (y*dt) - (z*x*dt) znew = z + (-c*z*dt) + (x*y*dt) Parameters are dt, a, b, and c. lorenz3d = 3D Lorenz attractor with 3D perspective. rossler3D = Orbit in three dimensions defined by: xnew = x - y*dt - z*dt ynew = y + x*dt + a*y*dt znew = z + b*dt + x*z*dt - c*z*dt Parameters are dt, a, b, and c. henon = Orbit in two dimensions defined by: xnew = 1 + y - a*x*x ynew = b*x Parameters are a and b pickover = Orbit in three dimensions defined by: xnew = sin(a*y) - z*cos(b*x) yn7 oew = z*sin(c*x) - cos(d*y) znew = sin(x) Parameters are a, b, c, and d. gingerbread = Orbit in two dimensions defined by: x <- 1 - y + |x| y <- x diffusion = Diffusion Limited Aggregation. Randomly moving points accumulate. One param: border width (default 10) Scott Taylor/Lee Skinner fractal types - 'fn' can be replaced by sin,cos, etc. fn(z*z) = z(0) = Xcoord + i * Ycoord; z(n+1) = fn(z(n)*z(n)) fn*fn = z(0) = Xcoord + i * Ycoord; z(n+1) = fn(n)*fn(n) fn*z+z = z(0) = Xcoord + i * Ycoord; z(n+1) = p1*fn(z(n))+p2*z(n) Parameters are real and imaginary components of p1 and p2. fn+fn = z(0) = Xcoord + i * Ycoord; z(n+1) = p1*fn1(z(n))+p2*fn2(z(n)) Parameters are real and imaginary components of p1 and p2. sqr(1/fn) = z(0) = Xcoord + i * Ycoord; z(n+1) = (1/fn(z(n))*(1/fn(z(n)) sqr(fn) = z(0) = Xcoord + i * Ycoord; z(n+1) = fn(z(n))*fn(z(n)) spider = c(0) = z(0) = Xcoord + i * Ycoord; z( sn+1) = z(n)*z(n) + c(n); c(n+1) = c(n)/2 + z(n+1) manowar = c = z1(0) = z(0) = Xcoord + i*Ycoord; z(n+1) = z(n)^2 + z1(n) + c; z1(n+1) = z(n); tetrate = z(0) = c = Xcoord + i * Ycoord; z(n+1) = c^z(n) kamtorus = series of orbits superimposed. x(0) = y(0) = orbit/3; x(n+1) = x(n)*cos(a) + (x(n)*x(n)-y(n))*sin(a) y(n+1) = x(n)*sin(a) - (x(n)*x(n)-y(n))*cos(a) After each orbit, 'orbit' is incremented by a step size. Parmeters are a, step size, stop value for 'orbit', and points per orbit. kamtorus3d= Same as kamtorus but in 3D with 'orbit' the z dimension. magnetj1 = z(0) = Xcoord + i * Ycoord; / z(n)^2 + (c-1) \ z(n+1) = | --------------- | ^ 2 \ 2*z(n) + (c-2) / Parameters are real and imaginary parts of c. magnetm1 = 'Mandelbrot' variant with c = Xcoord + i * Ycoord and z(0) = 0. Orbit formula same as magnetj1 w Parameters are pertubations of z(0). magnetj2 = z(0) = Xcoord + i * Ycoord; / z(n)^3 + 3*(C-1)*z(n) + (C-1)*(C-2) \ z(n+1) = | -------------------------------------------- | ^ 2 \ 3*(z(n)^2) + 3*(C-2)*z(n) + (C-1)*(C-2) - 1 / Parameters are real and imaginary parts of c. magnetm2 = 'Mandelbrot' variant with c = Xcoord + i * Ycoord and z(0) = 0. Orbit formula same as magnetj2 Parameters are pertubations of z(0). Virtually all of the FRACTINT authors can be found on the Compuserve network in the COMART ('COMputer ART') forum in S 15 ('Fractals'). Several of us can also be found on BIX in the GRAPHIC.DISP/FRACTALS area. In addition, several of the authors have agreed to the listing of their home addresses at the end of the FRACTINT.DOC file. New versions of FRACTINT are uploaded (as self-extracting archive files) to the Compuserve and BIX networks, and make their way to other system {s from those points. The latest version of the program can usually be found in the following locations: FRAINT.EXE - (Executable/Docs) Compuserve: COMART DL 15 and IBMNEW DL 5 BIX: GRAPHIC.DISP/LISTINGS and IBM.PC/LISTINGS FRASRC.EXE - (Complete Source) Compuserve: COMART DL 15 BIX: GRAPHIC.DISP/LISTINGS and IBM.PC/LISTINGS (What's the latest version? Well, THIS one was, way back when we uploaded it!) >>ANOTHER HELP PAGE IS AVAILABLE<< -- Press the ENTER key to see it. Press ESCAPE to exit Help mode, or F1 to see the help menu. Pressing any other key passes that keypress back to your program. (Notation: F1, SF1, CF1, AF1 == Normal-, Shift-, Control- or Alt-F1) 'B' after #-of-colors means video access is via the BIOS (s-l-o-w-l-y) >>ANOTHER HELP PAGE IS AVAILABLE<< -- Press the ENTER key to see it. Press ESCAPE to exit Help mode, or F1 to see the help menu. Pressing any other key passes that keypress back to your program. FRACTINT RunningH On TrueVision TARGA Card I'm sorry, but because of their random-screen-access algorithms, Plasma Clouds, Diffusion and Barnsley IFS fractal images cannot be created using a Disk-based 'Video' mode. Also, Plasma Clouds can currently only be run in a 4-or-more-color video mode (and color-cycled only on VGA adapters [or EGA adapters in their 640x350x16 mode]). Either press a function key (like F2 thru F5) that selects one of those modes, or press the 't' key to select a new fractal type. (see the Startup Help screens or FRACTINT.DOC for a complete argument list with descriptions): Thank You for using FRACTINT Please enter inversion parameters that apply. Note that the inversion option requires a fixed radius and center for zooming to make sense - if you want to zoom, do not use default values, but specify radius and center #> #k>Ga> ?)\=)\>>u> G>)\= O    _ ? Q8> #L L>L> > L? )\=LL> L>L> > L? )\=. Kl     ? UW~+ۊ t < tC| t˴@ !r = t3G  غ @!뺸 _]ۜ v{ / t