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HR@#`zvgCGGA^ pp,08gH F gF g&& ] m&feHUKa*_Nup*`p-`p.` p/`p+`p,`& fRHPa&"_HUa6RLa*_HSy|ZaLNuHSa - fH$_Nu y^:X^>oN^>nn#^:BRy|ZEHRK"y^: 9^> nN 9^> c2$""" "v eC Cg\Ukxg8JBk^20"#^:g  f`  f&_NuJBk^ a" `JBk^"2aB`JBj^H f"HQHP0(N$W$RH`2Q  _"_$X4BPY"2gHRB]%(\$@$2g@]e$HQ/0NB$_$RS@H2Q"_L` 1A$BHRA%L`p\B9L`"p^`#^6^:p]`a b6J9Lf 9ZLg 9[LgB9L(yL Ff(yLNuv eCֹ^" C/g y^:^6c> k `g& @gJf,Y^:`Jf aT` ^: ^:`fDJ(_B9LNu((@((?<NN.?<NNX LA HA HNua aa -Fga`Hp3da SN"X0 @e024EH$Jydk Bb5B5A6CC5CK5C8+:+AdB0000Dk~Ekz00Ad<:>:SFSGFn`Gn\DDk0BhDEk1EBh Fchh Gchh0hb&0hbpmrt#0#4`ϠNu _pNBaaaaa/a4>+<+:+8+&DbFEbGAdHP@dAdBD0ƞE03dAFC&000FF22N23BRG0@\@ _NB"2#`2a @0<}NB&IaNa @&XaH`az?<NNT @"K <}Nu @HPa^ _"X0 @Jg8zf:HPEJH LppJN$_4&bp$2Q"G HD&NuTpNup d@Tй^ @"X PfXLNupN z&"z2gB` zBp( g;j `` $&( "A2;N,PX2P,(r /` f"_#Hѩ` f@"_!I` f"_#Hѩ` g`/`j f"_#Hѩ` f"_!IE#J`: f&"_#Hѩ(g|`|` f"_2(if()g AdE#JE!J`  g  ft"_E#J`  fd"_E#J/ ` g g g f /`lHz`"Hz`Hz`Hz`Hz` Hz`Hz#]`tgB"#] g0 g0 g0 g0 g0 g0 +g0A`.X`zHz`"Hz`Hz`Hz`HzM` Hzp`HzAa" _aJf~NuH lHz``Hz`XJfHPr((( eA(ҁҁ"zpJf# Fgpѱ`T +fX`DHzM``8r(` r(A("zJf>"ёEXJg +fp`NqEXJg +f`Hz`Hz` +gJgHz`|Hz`trHPTgAGGCt"qpJf # _` _Hz`6 zFp( g -g g`~Nu (e`|vCgCֺ*"C&"CgijgHPbH~t( g(  g* +g .g±e _JgBHzc`R`S`Sj`vCgCֺа"C&"CgP~t) g,  g* +g .g g`JgBHz`*R`Sj`Division durch NullberlaufZahl nicht Integer|-2147483648 .. 2147483647Zahl nicht Byte|0 .. 255Zahl nicht Wort|0 .. 65535Quadratwurzel nur fr|positive ZahlenLogarithmen nur fr|Zahlen grer NullUnbekannter Fehler Speicher voll Funktion oder Befehl|noch nicht mglich String zu lang|max. 32767 Zeichen Kein GFA-BASIC V2.0 Programm Programm zu lang|Speicher voll|New Kein GFA-Basic Programm|File zu kurz|NewFeld zweimal dimensioniertFeld nicht dimensioniertFeld Index zu groDim Index zu groFalsche Anzahl IndizesProcedure nicht gefundenLabel nicht gefundenBei Open nur erlaubt:|"I"nput "O"utput "R"andom|"A"ppend "U"pdateFile schon geffnetFile # falschFile nicht geffnetFalsche Eingabe, keine ZahlFileende erreicht|EOFZu viele Punkte fr|Polyline/Polyfill|maximal 128Feld mu eindimensional seinAnzahl Punkte grer als FeldMerge - Kein ASCII-FileMerge - Zeile zu lang - Abbruch ==> Syntax nicht korrekt|Programmabbruch!Marke nicht definiert"Zuwenig Data#Data nicht numerisch$Syntaxfehler in Data|""paarweise verwenden%Diskette voll&Befehl im Direktmodus nicht mglich'Programmfehler|Kein Gosub mglich(Clear nicht mglich in|For-Next-Schleifen oder|Proceduren)Cont nicht mglich*Zuwenig Parameter+Ausdruck zu komplex,Funktion nicht definiert-Zuviele Parameter.Parameter falsch|mu Zahl sein/Parameter falsch|mu String sein0Open "R" - Satzlnge falsch1Zu viele "R"-Files (max. 10)2Kein "R"-File3Nur ein Field zu einem|Open "R" mglich4Fields grer als Satzlnge5Zu viele Fields (max. 19)6GET/PUT Field-String Lnge falsch7GET/PUT Satznummer falschFehlerhaftes Menu?Fehlerhaftes Reserve@Fehlerhafter PointerZFehler bei Local[Fehler bei For\Resume (next) nicht mglich |Fatal, For oder LocaldGFA-BASIC Version 2.0| Copyright 1986|GFA Systemtechnik GmbHf2 Bomben - Bus Error|Vielleicht Peek oder Poke falschg3 Bomben - Adress error|Ungerade Wort-Adresse!|Bei Dpoke, Dpeek, Lpoke|oder Lpeek?h4 Bomben - Illegal Instruktion|Ausfhrung eines ungltigen|68000-Maschinenbefehlsi5 Bomben - Divide by Zero|Division durch Null in|68000-Maschinensprachej6 Bomben - CHK-Exeption|68000-Interrupt durch CHK-Befehlk7 Bomben - TRAPV-Exeption|68000-Interrupt durch TRAPV-Befehll8 Bomben - Privilege Violation|68000-Interrupt durch Ausfhrung|eines priviligierten Befehlsm9 Bomben - Trace Exeption|68000-Trace-InterruptAllgemeiner FehlerDrive not Ready|ZeitberschreitungUnbekannter BefehlCRC Fehler|Disk-Prfsumme falschBad Request|Ungltiger BefehlSeek Error|Spur nicht gefundenUnknown Media|Falscher BootsektorSektor nicht gefundenKein PapierSchreibfehlerLesefehlerAllgemeiner Fehler 12Diskette schreibgeschtztDiskette wurde gewechseltUnbekanntes GertBad Sektor (Verify)Andere Diskette einlegenUngltige FunktionsnummerDatei nicht gefundenPfadname nicht gefundenZuviele Dateien offenZugriff nicht mglichUngltiges HandleSpeicher vollUngltige SpeicherblockadresseUngltige LaufwerksbezeichnungKeine weiteren DateienGEMDOS-Bereichsfehler|Seek falsch?Interner GEMDOS FehlerKein BinrprogrammfileSpeicherblockfehler[1][Wollen Sie den Interpreter|wirklich verlassen?][Ja|Nein][1][Programmende][Return][2][Programmstop?][Stop|Cont][2][Druckerlisting?][Ja|Nein][2][NEW - Programm Lschen?][Ja|Nein]Mll - Editor FehlerWhile ohne WendRepeat ohne UntilDo ohne LoopFor ohne nextWend ohne WhileUntil ohne RepeatLoop ohne DoNext ohne ForIf ohne EndifEndif ohne IfElse ohne IfElse ohne EndifExit ohne SchleifeProcedure ohne ReturnProcedure in SchleifeProcedure doppelt definiertReturn ohne ProcedureMarke doppelt definiertLocal nur in ProcedureLocal nicht in SchleifeFunction doppelt definiertGoto in/aus For-Next oder ProcedureResume in For-Next-SchleifeResume ohne ProcedurejH lSyntax FehlerjH lZeile zu langVFb[3][\"& 6     B2p\ x~ 4*"t:< 2X00FB^  "  < T2&$"F"* &$ L&8@h24&"* &lJ"$,(:$P X>   x@& V4 j  @*JLr &:z$J( (.(F < Zt"N\"`  @*(<,8L*(j<,( @<    4^> 6 X:dH.( ZGfABASICp&TvVZ h$@j|BUTTONCLIMITPQ XREAL_MIN YREAL_MINSIDEOLD_XMINOLD_YMINTRUEFALSEDRIVENUMVALUENUMJXDELTYDELTQQ0Q0P0ZR2ZI2ZIZRYY0Y0X0XKYKMARKERSAVNUMPALETBACKGRNDFOREGRND LOWEST_ITER HIGHEST_ITER ARRAYBANDBARSTEP BARHEIGHTCOUNTERFILLKTRIMNUM FRONT_BIT BLANK_MOUSEMOUSBRO2SCREEN1VARTITLEFILETYPEFILENAMEDEFAULTTMPFILEOLDFILENEWPART1PART2REZMAX_SCRMAXITERZ_FRAMEBUTSPEEDOFFSETLEFT_XLEFT_YRIGHT_XCULFRAMEDROPOUT MAX_HEIGHTPNTR MAX_WIDTH ZOOM_WIDTHCOLNUMNYNXKKLROLD_K FILE_POINTERXXYYKKX1Y1X_SIDEY_SIDEIKEYMAX_WXCORNPOINTERMAXCOUNTMINCOUNTBANDPEAKJRBXBXW1BXW2LBXNUMREZMULST520PREVIEWMOVIEAUTOSAVEFRACTALJULIAMANDELCHAOS1CHAOS2RECONCHANGEREVIEWHISTORYSCREENSAVE_FLAGPQ XREAL_MIN YREAL_MINXDELTYDELTSIDESCREENZOOMAARRAYMAXITERBXWIDTHBXEXHISTORY CUL_ARRAYJULIAMANDELCHAOS1CHAOS2REVIEWPALET1PALET2PALET3PALET4BLANK_MMSFATPLTJPLTMPLTC1PLTC2LLBLPLTPLTREMAKE_MOUSEBROT WINDOW_NAMEDEFAULTSINFO GROWSHRINK SET_JULIA SET_MANDEL SET_CHAOS1 SET_CHAOS2ZOOM DRAW_FRACTAL GET_PARAMSMOVIESAVE LOAD_FILEHELP DELETE_FILE RENAME_FILE SET_AUTOSAVE SET_COLORSHISTORY SET_FRAME GET_SCREEN LOAD_MOVIE SAVE_MOVIE GET_MAX_MIN REDRAW_FRAME SET_CHECKS NEW_VALUE CHECK_VALUE GET_VALUES DRAW_JULIA DRAW_CHAOS1 DRAW_CHAOS2 DRAW_MANDELSHUFFLEAUTOSAVE EXIT_SCREEN NAME_FILE SAVE_DATA LOAD_DATA SHOW_SCREEN SET_CUL_ARRAY PLOT_GRAPH DO_COL_BLOCKSCUL_BAR R------------------------------------------------------------------------------  -J Fractal program for Mandelbrot, Julia and chaotic attractor curves -* V 1.6 Nov 1987 P----------------------------------------------------------------------------- E F F v)!\|Program designed for LOW or |HIGH resolution but will work |in MEDIUM if you insist. !! EXIT|GO ON!Fe FaqF F F NX t$F2^FLeave a bit of room for accessories iEF* @6 FEF F EFEF* @4 FEF FE * ! ! ! ! F&* ! ! ! !LL F * ! ! ! ! F2* ! !zz !zz@ FE +-.1234567890F EA:F2|FAD1638,1028,518,85,55,83,87,96,1120,1376,1616,1569,1601,1536,1584,0 |F,J1638,50,306,1074,562,1330,818,1586,1842,1858,1874,1636,1889,1637,1635,0 |F,H1638,529,802,1621,1075,1092,1348,819,546,274,547,1366,820,1075,1093,0 |F,H1638,307,308,836,324,852,580,1108,1380,1636,1892,1092,1620,820,1364,0 * F EDeskF, E About Fractals F8 E-------------------F  E1F E2F  E3F@ E4F` E5F E6F EF-  EOptionsF0 E Julia F0@ E Mandel F0P E Chaos(1) F0` E Chaos(2) F0p E -------------F E Zoom F, E Draw.. F, E -------------F E Preview F,  E Params F,( E Defaults F,0 E -------------F8 E min .01 F,@ E min .001 F,H E min .0001 F,P E min .00001 FX E -------------F` E Quit F,h EFup EExtrasF x E SAMPLE SCREENS F0  EF0 E Sample Julia F E Sample Mandel F  E Sample Chaos1 F E Sample Chaos2 F  E----------------F0  EIf preview on.. F0  E Make movie F0   E Play movie F0 $ E Movie speed F0 ( E----------------F0, E Screens F-0 E Re-contour F4 E Histogram F8 EFi< EFileFg@ E Load FFD E ------------FFH E Save FFL E Delete FFP E Rename FFT E AutoSave FFX E ------------FF\ E Load movie FF` E Save movie FFd E ------------FFh E Palette 1 FFl E Palette 2 FFp E Palette 3 FFt E Palette 4 FFx E ------------FF| E Help FF EFe EFeRF,FEFRFF,FF set the mouse shape eF&,F set window text to curve type  F activate menu ,FP---------------------------- Menu loop ------------------------------------- F-FvLF-F-@ -------------------------------------------- -+F F"   About Fractals F,F sF l)!X FRACTAL PROGRAMS | in | GFA BASIC | Version 1.6 Nov 1987 !! OK !FGz)!g By Ian Connor | MACE Melbourne. Australia | Based on a program | by Kevin Thomas. !! OK !Fv)!aReleased to the public |domain and may be freely |distributed. |NOT to be resold. !! OK !F sFI F *  Julia F,F F P  Mandel F,F F v  Chaos(1) F,F F   Chaos(2) F,F F   Zoom F, F F    Preview F,F sF PF,F@)!) | Preview mode is ON! !! OK !FEF F B)!* | Preview mode is OFF! !! OK !FmEF FE sF  F   Draw.. F, F F    Params F, F F  p  Defaults F,F,F sF 4)!| Default values now Reset. !! OK !F sFa F   min .01 FE## =qF FE   min .001 FEnF FE   min .0001 FEQQXF FE *  min .00001 FeE''ŬGF FE |  Quit FYF6!n F6!`F6p!FqF F   Sample Julia F.E# =qF E@F EFEF EppFEF ,F, F F b  Sample Mandel F.Eb ԲF E**F EN-F EHHF ,FH, FH F   Sample Chaos1 F.E## =qFE00 ěFEF E33홠F E$$7zF EF ,F, F F j  Sample Chaos2 F.ELLFELF EIIUIF EofF E**bF EHHF ,FH, FH F   Make movie F,F sF F>)!* | Make a movie is ON! !! OK !FEF F  Fx)!XADD frames to existing movie |Create a NEW movie |or turn movie mode OFF! !! ADD | NEW | OFF !F FaEF FE Fa>)!* | Make a movie's OFF! !! OK !FoEF FE FE FE sF  F   Play movie F,F bF*, F Play the movie resident in memory  F sFy\)!I Sorry, Make movie is | not ON or you have | not loaded a movie! !! OK !F sFy F FH   Movie speed F Length of time (delay) between frames ,F sF F)!%Set movie frame play speed. !!SLOW|MEDIUM|FAST!F sFo FvE@@FiEF F FFEFEF FE@@FiEF FE FE FE   Save F, F F  >  Load F,F F d  Help F,F F   Delete F,F F   Rename F,F F   AutoSave F,F F   Palette 1 FRF,Fzh !Fl F R  Palette 2 FRF,Fzl !Fl F   Palette 3 FRF,Fzp !Fl F   Palette 4 FRF,Fzt !Fl F    Histogram Fe,F F ,F F F @  Screens F,FEFEF FE f  Load movie F,F F   Save movie F,F F 2  Re-contour Fe*,F Max & min iteration for the frame $,F Replot with new color bands .Fp(,F Movie on? if so set the Z_frame  F F F,F .FP---------------------------- SET THE DEFAULT VALUES ------------------------- +F-  F-E00F- FEF- FERF,FE F-EF- E F- EF EFE@@F-EFEFEFEF,FEFEF,F,FE## =qF-E00 ěF-EppFEFEF-EHHF-EQQXF-*E&&fffiF EGpF-*E*&fffiF E *F  EF0! *F  F EFF EpF-.FP----------------------------------------------------------------------------- +F-EFEFEFEF,F-.F+F-EFEFEFEF,F-.F+F- .HF-0EGGF Optimum iter limit for chaos 1 - FEEFEFEFEF,F.F+FEFEFEFEF,F.FR------------------------------------------------------------------------------ !+F- F-&)! |Autosave On! !! OK !F-6)! |Which drive to save to? !! A | B |D ! F- V Fh EA:FF F: t Fh EB:FF F: ED:FF FE FEEF F:&)! |Autosave Off !! OK !FEF FE.FEP--------------------------- SET THE MENU TICKS ------------------------------ +F->x!F- de activate sample screen message in menu bar (!F- same for underline bar e60!F- first clear all curve types of ticks m@!F-P!F-`!F-.`!F- de activate save movie option !F- !F-0!F-4!F- fF!0!F- F F!@!F- F F!P!F- F F!`!F- F. F activate minimums if not chaos 8!F @!F H!F P!F  H# =qJF8!F= F pnJF@!F F QXFtH!FX FP!FX F F F F8!FX@!FXH!FXP!FX F *F! Set or clear tick T!Fe ,!F activate screens option if a screen complete  F0,!F otherwise de activate menu bar r F(}F Tell gem to use new mouse shape .FP------------------------ GET THE INPUT PARAMETERS --------------------------- + F-,F- get the screen save temp in string R\!Parameter Input ScreenFeYF!)!n Allows manual changes | to co-ordinates etc | Pressing Return accepts | each existing value. !! OK !F}F  bGFgEHHF FE0 FF P & Q not needed for Mandelbrots t EF$Y! "Real Const. Value = "Fa,F E F EF Imag. Const. Value = "F,FaE F  FE EF &Y!@ "Min. Fractal X = "F,F@E F EFFEMin. Fractal Y = "F,FnE FF EFFFESize of picture = "F ,FzE Fo EFoFEMax. Iterations = "F ,FxE FI z F Ezz F FE 4FF put the screen back  E#3  PFi Maximum window height in pixels &EF  Used in the zoom procedure JFEFd F JFEFd F1 !FiEF FE FE xF3!Fi3 !Fi !!! F!!! F#F!!! F\! PREVIEW of Fm tFV\!Frame A Fm F! F! EFE## =q  Fm.FEP--------------------------- DRAW THE JULIA CURVE --------------------------- -+F- |EG FEF- &EGFEFEF-EFFE EF EF ZF-EFEF4F  <F FEF-F FE# F  F FEF FE FE|F#F F@ EF F!F  FB r! RF ! If the mouse button pressed then exit ,%F F%  F .FP---------------------- DRAW THE MANDELBROT CURVE --------------------------- -+"F- >EG FEF- EGFEFEF-EFEFEFFE EF EF ZF-EFEF4F  0F FEF-F FE# F  F FEF FE FE|F#F F@ EF F!F  F 4! RF ,%F F%  F .FP---------------------------- NORMAL CHAOS ---------------------------------- -+ F- TEG FEF- 0EGFEFEF-EFFEE# # F- pZFEF pZF0!F4F pZ( ( FAEFEF  F FEF-F F E F  F FEF FE FE F4F F F5F FEF|FF#FF F@ EF( F!F  F J! RF ,%F F%  F .FP-------------------------- CHAOS VARIATION 2 ------------------------------- -+!F- <EG FEF- EGFEFEF-EFFEE# # FC ZFEF ZF0!F4F Z( F Z( FEFEF  F FEF- F F E F  F FEF FE FE |F#F F@ EF F!F  F 2! RF ,%F F%  F .FP------------------------- SAVE SCREEN -------------------------------------- -+ F- EF,F-F-,&F-EF-EF-f\*.frA !!F L zF DF\!Saving screen file FV 7O!M!F,'FMM!z !zzF 8MFz F F,FF sFzX)!DYou haven't got enough |room on the disk or|you have a save error !! ok !F sFa F,F EF.FE+$F EF,&FF 6 zFo 7O!M!F,'FMM!z !zzFo8MFz NF\! No free roomFo F! EF.FEP------------------------------ LOAD FILE ------------------------------------ +F-EF-EF- EA:\*.frA F-YFE,FA f !!FA v F- \!Loading screen file F 7I!M!F,(FMF(:M!F VZt#Ff 2F EtM F8MFM ! F FEF.FE+'F M!FM!FM!FM!FM!FM!FM!FM!FM!FM! FM!FM!FM!FM!FM!FM!FM!FM!FM!t#F.F+(F:M!F:M!F:M!F:M!F:M!F:M!F:M!F:M!F:M!F:M! F:M!F:M!F:M!F:M!F:M!F:M!F:M!F:M! F.FP------------------------------- DELETE FILE --------------------------------- +F-EF-fa:\*.*! !F-F tZF ^ FAF F tZ F 8F.FP----------------------------- RENAME THE FILE ------------------------------ +F-EF-fa:\*.*!Oldname! FF XZ Fl B Flfa:\*.*!Newname! F > F@ l F F  F  XZ F F.FP------------------------ NAME THE FILE ------------------------------------- +&F-EF EF-EF- F- EMANDELF- FE FE EJULIAF FE F ECHAOSF FEFE DF- EA F VF E0A F FE  FE .MVA F- FE .frA F- FE Z F4FZ F.FP--------------------------- EXIT FROM WORK ---------------------------------- +%F-,F- sF-|)!\ Had enough?:- Want to | Call it a screen?| or| Continue on... !! Enough|Continue !F sFe "*JF8 EF Needed to limit the array plot if early exit ?,E F  Force the for next loops to exit EF  FE.FEP------------------------------ ZOOM ----------------------------------------- + F- } F- { F-"\! Hold button & drag mouse FF! "ZRFl  "FR!F "!!FtEFEF  # Ft "!!Ft EF #B pFaE pF FEE\(F#F!!!Fa#F!!!Fa "F!$\!Press button when in positionF}F$!!!FnF "!!F! $ZF#F!!! Fi!!!Fi!!! F!!!F!!!F#F!!! F !!!F !!! F!!!F!!!F #F! $!!!F!!!FE# FE# F EF$\! When all set - Select Draw!FF!F.FFP--------------------------- SET THE SCREEN COLORS -------------------------- +F-zh !F-zl !F-zp !F-zt !F- %EGpFQF6!F  %FG & Fp6!F F!.F!P------------------------ SET THE WINDOW NAME ------------------------------- +F- &F-E Julia Curve F- 'F &Fl"E Chaotic Attractors type 1F  'FC &Fo"E Chaotic Attractors type 2F  'FCE Mandelbrot Curve F FE FE FE\!FM.F!R------------------------ BROT MOUSE SHAPE ------------------------------------ +F- Eb b F Eb F- Eb F- Eb F- 'EGF-Q F Eb F  'F  (EGF-Q!F Eb! F  'F |F"0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 "0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 |F0b32256,57856,41472,33791,33289,61441,8195,24577,16385,16385,16385,16385,16398,32776,36880,61408 \32768,31744,31744,31744,32246,4094,8188,8190,16382,16382,16382,16382,16368,32752,28640,0 6.F2P------------------------- HELP SCREEN --------------------------------------- +F-&F- Grab the crrent screen first EYFF"\! Help & Information screen F(!!!@Fo,Y`! "Fractals! - in GfA BasicF-(!!!@F4F!,& Based on a program by Kevin ThomasF-,& Re-written and enhanced by Ian ConnorF-,& ,M.A.C.E Melbourne. Ver 1.6 Nov 1987F-F&,& A quote from an article by A. DewdneyF-,& in the August 85 Scientific AmericanF-,& best describes what fractals are :-F-,& The various fractal curves brood inF-,& silent complexity at the centre ofF-,& a vast two dimensional sheet ofF-(# numbers called the complex plane.F,& When a certain operation is appliedF-,& repeatedly to the numbers, the onesF-(" outside the set flee to infinity.Fn,& The numbers inside remain to driftF- or dance about.FsF  M=MORE Q=RETURN"F Ea F AZ "" bbFiYF4Y! "# Close to the boundary minutelyF,& choreographed wanderings mark theFm,& onset of the instablilty. Here is anFm,& infinite regress of detail thatFm,& astonishes us with its variety, itsFm,& complexity and its strange beauty.Fm,& Note: Infinite is no exagerationFm,& here. We are only limited by theFm*$ maths precision of the computer.FeF$,& Further information is available fromFm,& the book 'The Beauty of Fractals.' byFm,& H.Peitgen and P.Richter. published byFm,& Springer Verlag. Another fine public-Fm,& ation 'The Fractal Geometry of NatureFm,& by Benoit B. Mandelbrot is publishedFm" by W.H.Freeman and Company.FpF  M=MORE Q=RETURN"F Ea F AZ "" bbF.YF"Y0! "ABOUT THE PROGRAMFF*% If you have a Half megabyte machineF*% some options are reduced in power.F These limitations are:-Fe*% 1) Two screen buffers instead of 4.F*% 2) RECONTOUR not available in fullF screen modeFo*% 3) HISTOGRAM not available in fullF screen modeFo*% The program will set itself to useF the memory available.F *% Designed for LOW rez,although usableF in Hi rez.F*% The Mouse is checked at the end ofF*% each scan line. Press and hold MouseF*% or press a key to end calculations.F*% PARAMS allows you to manually enterF,' the Real and Imaginary co-ordinatesF,' and alter the Maximum Iteration level.FF'  M=MORE Q=RETURN"F Ea F AZ "" bbFaYF2Y! "& The values for P & Q are not used inFl the MANDELbrot set.F ,& In the JULIA, and both CHAOS curvesFe,& the value of P & Q remain fixed forFe,& the complete set. They vary for eachFe" point in the MANDELbrot set.F,& The MIN options, e.g ( min .0001) areFe& used for the Chaos curves only.F),& Points are calculated only betweenFe,& 'min' and 2; For example .0001 to 2Fe,' is a wider band than .01 to 2 and someF,& numbers will iterate for longer usingFF(# the former value. Experiment here!F,& You have a choice of 4 'curves'; allFF,& use a slightly different iterationFF,& formula and give a wide variety ofFFF&  M=MORE Q=RETURN"F Ea F AZ "" bbFvYF2Y! "& results. The most famous being theFf,& Mandelbrot Set. DRAW.. begins theF ,& calculations and you may useF ,& PREVIEW to quickly plot a smallF ,& version in the left corner of theF ,& screen. Turn this option off for aF ,& full screen. You can ZOOM in & outF &! on screens for a magnified view.F,& To ZOOM out use PREVIEW mode and sizeF ,& the ZOOM window to be larger than theF ,& Preview frame size. Position newF $ frame over the Preview frame.Fo,& ZOOM may also be used to re-positionF ,& your view window. Set the Zoom frameF ,& to the same size as the PreviewF *$ screen and position where required.FwF$  M=MORE Q=RETURN"F Ea F AZ "" bbFrYF0Y! "% ZOOM is available once all or partF,& of a set is calculated. Select ZOOMFp,& from the menu then size your newFp,& screen box by holding a Mouse buttonFp,& and dragging the Mouse to the rightFp,& and down until you have the desiredFp,& size. Release the Mouse button thenFp,& press it again when your window is inFp,& position. Try again if necessary thenFp,& select DRAW.. from the menu to begin.Fp,& EXAMPLES has sample coordinate paramsFp,& (one for each curve type). If youFp,& select one of these the program willFp,& calculate and display an interestingFp,& area for you. FILE contains all theFp,& commands needed to Load and Save yourFp own pictures.FdF  M=MORE Q=RETURN"F Ea F AZ "" bbFdYF0Y! "$ MAKE MOVIE and PLAY MOVIE allow youFF,& to store up to 50 PREVIEW modeFy,& frames in memory or on disk. SelectFy,& Make movie to begin and Draw.. aFy,& screen as normal. As each frame isFy,& completed, Zoom in or out as you wishFy,& by a small amount and draw.. the nextFy,& frame. Select Play movie at any timeFy,& to check your work. A movie may beFy,& saved to disk from the File menu.Fy,& A full 50 frames will take approxFy 92K of disk space.F,& Saved movies can be loaded from theFy,& File menu as you please but you canFy,& only have one movie in memory at aFy  time.FhF  M=MORE Q=RETURN"F Ea F AZ "" bbFeYF2Y! "'Note: All the parameter and co-ordinateF,'information is saved with your picture.F,'If you later re-load a picture, the co-F,'ordinate information is also loaded.FF','PALETTE 1 to 4 are a variety of colorF*%sets you can use to suit your taste.FF%,'SCREENS Up to the last 4 screens calcF,'-ulated. Both the picture and theF,'co-ordinates are saved in the buffers.FF' HELP is where you are now!FtF,'DEFAULT resets the program parametersF(#and values to the default settings.F,'Handy to display the full curve forFeach set type.FlF Q=RETURN"F  Ea F AZ F )FYFFF.FP------------------------ shuffle the screens -------------------------------- +#F- EF- BEGF E F- E F- E F- E F- E F- E F- E F- E F- E F- E F- E F- E F- E F- E F-  BF.FP--------------------------- Get a screen ------------------------------------ +F-EF C FL)!5There's only one screen |in the buffers. !!SHOW IT!F-,)FT- FT F F  D6 FnJ)!/ Get a screen from | the screen buffers. !! FOWARD|EXIT!FF D2F 4F,)F F) F) EZF D FH)!0 Get a screen from | the screen buffers. !! BACK|EXIT!F DF 5F DF EF FE FE,)F F) EZF EFs Ep FP)!0 Get a screen from | the screen buffers. !!BACK|EXIT|FOWARD!F5 ElF 5F EhF EF FE FE FE EF 4F E FE F FE FE,)FF F) EZF CF |FF.F|P--------------------------- Show screen ------------------------------------ 5+)F- E F E F E F E F E F E F E F E F E F E F E F E F E F F,F .FP--------------------------- play the movie ---------------------------------- + F-F-YFF\!Playing movie F!E#3 F"E#! #! F"'"@!``!Frame F}F@FF HEGFF"!`! FF"'"`!``!A  F{F` G! RF EF FE  GF  H*Z! RF {`F  GFF,FFFYFFF}FF.FR-------------------------- load movie ---------------------------------------- 2+F-EF-EF-YFEf\*.MVA !!F I F\! Loading Movie file F 7I!M!F:M!F#EFFE# Ed@ ! F IrZrM F# E_d@ !M Fl4#FE IrZ#F  I F8MF\!Movie has loaded!FEFEFEF FE.FER-------------------------- save movie ---------------------------------------- 2+F-#EF,F-,&F-EF-EF-f\*.MVA !!F K2 d@ FF JF\! Saving Movie file Fa 7O!M!FuM!F J#EGFM!z# !d@ Fe  J#F 8MF K(F#X)!DYou haven't got enough |room on the disk or|you have a save error !! ok !F, F!,FY F.FP---------------- Get the maximum and minimum iteration counts---------------- +F-F*\!"Calculating max and min iterationsF$EF%EF- LFEG F L<EGFE@ F- LF L$F$EF FE FE L2%F%EF FE  KF%  KF%.FJ---------------------------------------------------------------------- -+F-&\!Re-drawing Fractal Please WaitF&E##$% ` F MXEG F MNEGFE@ F M$FEF- F F E#% &F |F#F!F  LF  LF ,FRF.FP---------------------- Capture the movie frame ------------------------------ +F- NHF-"\!This is MOVIE frame A F,FT sFiz)!\| Keep this movie frame? | or recontour, do histogram | or re-calculate the frame? !! Keep it|Re-do !F sFp NF 4F!!! ! F F! O0F,FF sF R)!>| You have 50 frames stored. | No more can be saved. !! OK !Fe sF  F.FR------------------ Graph the fractal and adjust color bands------------------- e+F-}FF-YF(\! Fractal history & Color contoursFa RT Fl(!!!Ft '4!4! Thinking.FoJ !F'EF PEG F PEGFE@ F PF4 F6 P 'F! no of points with highest iteration 'E F FE FE  P*F'  PF'0(EF find the start of the lowest iteration rFE in the history array h E( F Q,ZF Q,Z(yy Fy4(FZ PF8"E(F history array position with lowest iteration (Ezz FtFE<E( F find the array position with highest iteration d QZF QZ(F5(FZ QvF8#E(F history array position with highest iteration  E $E#"F E%E$RF E&E\\'F EFYFE FE#F0p!!!Ft GRAPH box $p!"!!-Ft#F4\!H!!@@FR Text box t !H!X!F$ !!X!&F(!!!@F"'`!! INFORMATIONF(!!!F'}!!GRAPHFA'!*!EXITF.' !!NUMBER OF SCREEN POINTSFt*' !`!FOR EACH ITERATION.FN$'\!PP! ITERATIONFT"'^!``!MAXIMUMFN8' !@@!ITERATIONS   F :' !,!# MOUSE  TO ALTER THE COLOR BANDSFn$'b!! THE NUMBER OFFA$'b!! SCREEN POINTSFA$'b!4! AT EACH ITER-FA"'b!L! ATION LEVEL F"'b!d! ARE GRAPHED.F"'b!! YOU MAY ALSOF 'b!! ALTER THEF$'b!! COLOR BANDINGFA"'b!&! TO GET THEF$'b!2!BEST RECONTOURF'b!>!RESULTS.F(!!!F$' !0! PEAK POINTS =FF 'i!P! ITERATIONSF(p!!!FE'.!0!'F'!^!"F'!j!#F'^!!FF(!!!F'b!^!LOW =FI'b!j!HIGH=FI WEGpFH$! !!F#F " ! ! ! FT $!!!F#F$ !! !$FR  !! !$FR  WNF ,*FSet colors  *,+FPlot histogram  +F+ "!!Fs: Xl RR%%RFn ,,F F,. YNp RF% ,*F(!!!F'}!! F%!!F&x!F,+F%!!F&x!F(!!!F'}!!GRAPHF F0 YZpp##--RF  XF,*FFYF*FF%!!F(!!!@F$! !!F !! ! F $!!!FF!.\!&Re-plotting Fractal to new color bandsF" ZEG F Redraw the fractal  ZEGFE@ Fd ZvF#F- F F # F |F !F  ZNF  Z@FF,FR.FP-------------------- Adjust the color block sizes--------------------------- -+-F- \)VF-$! !!F-#F [F! [*F!05*Fdecrement the size of selected col block 5)F4+F,! !)! Fs#F)! !)+! Fc F) F) \F! \+F!4*F4)F5+F,! !)! 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Probably the best of these is GST FRACALS, however, all fail in various areas because the programmers do not have a sound understanding of Fractal curves and what is needed in a program to fully study and appreciate them. I have written many fractal programs over the years ranging from 8 bit basic programs to pascal, to Machine language. Speed was always the main driving force and with the 8 bit Atari we ended up with what we think is probably the fastest Mandelbrot around for those machines. With the arrival of the ST we have been going through the same process with versions in ST Basic, Megamax C , Alcyon C and now GfA basic. Dbasic also looks worthy of investigation. We Have found that compiled GfA is almost as fast as C but allows faster development and is easier to use. Back to the subject, One of the most needed features missing on most other programs was the ability to enter Real & Imaginary co- ordinates and to have these available for viewing in the program and saved as part of a file. Also most are only able to produce one type of curve or suffer from scaling problems and lack of versatility. With this program I have tried to produce a very versatile program capable of being used by both beginners as well as seasoned Fractalists (is that a word?). PROGRAM FEATURES * Optimum performance iteration loop for maximum speed. * A choice of 4 curves available for a wide variety of results. * The ability to Zoom in or out on any of the fractals. * Manual entry of parameters if required. * A Preview mode to quickly calculate and view a area. * All program features available in full screen OR preview mode. * Recontour and Histograms for optimum color banding. * Screen saves with parameters in Full screen or preview. * Calculations can be interupted before completion if required. * Recall of up to 4 previous screens complete with parameters. * Choice of 4 preset color palettes. * Movie mode to produce/play up to 50 preview sized frames. NOTE:- Recontour & Histogram not available in full screen mode without 1 Megabyte of memory. HINTS ON GENERAL PROGRAM OPERATION ================================== SCREEN SAVES All parameters are saved in the picture files including the fractal type, screen mode, maximum iteration level, Fractal co-ordinates and side value etc. This will enable you to re load a picture at any time and continue zooming etc. ZOOMING All curves can be zoomed including those interupted before completion. Zooming in is easy, select Zoom from the menu and size & position a new zoom window rectangle. You must be in preview mode to Zoom OUT. Size your Zoom rectangle to a size larger than the preview frame and position over the preview frame,then select Draw.. from the menu. MIN VALUES (eg: Min .001) These values are used in the Chaos curves only. Experiment to achieve different results. RE-CONTOUR During the calculation and plotting of a fractal, the program has no way of knowing the maximum and minimum iteration values it will encounter, and so a quick color routine is used to set the color of a screen point. This is set to use a new color roughly every third iteration. Once a Fractal is complete, re contour calculates the lowest and highest iteration and divides the available colors evenly into this band, then re plots the Fractal data. HISTOGRAM Provides you with a graph of the frequency of iterations calculated and allows you to adjust the allocation of colors. Position the mouse pointer on the color bar and press the left or right mouse buttons to change the size or position of each color block. When you select EXIT the Fractal will be replotted to your color bands. MAKE/PLAY MOVIE Available only in preview mode. Load and play one of the Fractal movies on the disk. Press and hold the mouse or press any key to interupt play. PARAMS HINT:- Try increasing the iteration limit as you zoom in , this will slow the program down but produce more interesting and accurate results. In the curves that use the P and Q values, try different values for interesting results. The program is designed to work best in low resolution but is useable in the other modes. NOTE:- Some of the program features may behave a little strangely in the other modes. Please write to me if any further information is required or if any bugs are located. write to Ian Connor 9 Waratah Drive Warragul 3820 Australia. ====================================================================