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mandel.docs

This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.

Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.

Tape/disk: Home » Personal collection » Commodore disks » disk40a_autostereo.d64
Filename: mandel.docs
Read OK:
File size: 101B bytes
Load address: 8000
Exec address: 0000
File contents
"���������� ��� ���� ��� ��������
"
"�ROGRAMMING AND TEXT BY �OMINIC �ORD.
"
"     �HE �ANDELBROT AND THE �ULIA
"SETS ARE MATHEMATICAL FRACTAL IMAGES,
"OR�IMAGES THAT CAN BE ZOOMED INTO
"INFINITELY MUCH WITHOUT DETAIL BEING
"LOST. �HEY ARE CALCULATED USING
"MATHEMATICAL FORMULAE INVOLVING
"COMPLEX NUMBERS. �OU DO NOT, HOWEVER,
"NEED TO UNDERSTAND THE MATHEMATICS
"INVOLVED WITH THESE FORMULAS, OR
"ABOUT COMPLEX NUMBERS TO APPRECIATE
"THE GRAPHICS PRODUCED. �HEN THEY WERE
"ORIGINALLY DISCOVERED THEY WERE
"THOUGHT OF ONLY AS OF MATHEMATICAL
"INTEREST, YET IN RECENT YEARS THEY
"HAVE BECOME POPULAR NOT JUST WITH
"MATHEMATICIANS, BUT ALSO WITH THE
"REST OF THE POPULATION. �HE STUNNING
"GRAPHICS WHICH ARE PRODUCED BY
"FRACTAL PLOTTERS HAS LEAD TO PLOTTERS
"BEING WRITTEN FOR ALMOST EVERY
"COMPUTER FORMAT THAT EXISTS. �N THE
"�64/128 FORMAT, HOWEVER, MOST OF THE
"PLOTTERS WERE SIMPLY PROGRAMS WRITTEN
"IN ����, AND WERE CONSEQUENTLY VERY
"SLOW, AND DIFFICULT TO USE.
"     �ANDELPLOT DIFFERS FROM MOST OF
"THESE PLOTTERS IN THAT IT IS WRITTEN
"IN 100% MACHINE LANGUAGE, AND IS
"THEREFORE FAR FASTER AND MORE
"EFFICIENT. �ESPITE THE FACT THAT IT
"IS WRITTEN IN FAST MACHINE LANGUAGE,
"AND IS MANY TIMES FASTER THAN ITS
"���� EQUIVELENTS, IT IS STILL A SLOW
"PROGRAM COMPARED TO MOST OF THOSE ON
"LARGER COMPUTERS, AND OFTEN TAKES
"OVER AN HOUR TO COMPLETE A PLOT. �
"HAVE TRIED TO OVERCOME THIS PROBLEM
"BY USING A PLOTTING SYSTEM WHICH
"PLOTS A VERY LOW RESOLUTION IMAGE
"FIRST OF ALL, AND THEN SLOWLY
"INCREASES THIS RESOLUTION. �SING THIS
"SYSTEM THE USER CAN BEGIN TO SEE THE
"ROUGH OUTLINE OF THE IMAGE VERY
"QUICKLY, AND THEN ZOOM IN FURTHER
"BEFORE THE PLOT HAS FINISHED.
"     � HAVE MADE THE SYSTEM AS
"USER-FRIENDLY AS POSSIBLE BY MAKING
"THE PROGRAM CONTROLLED ALMOST
"ENTIRELY BY A MOUSE POINTER WHICH MAY
"BE MOVED AROUND USING A
"MOUSE/JOYSTICK PLUGGED INTO PORT ��,
"OR USING THE FOLLOWING KEYS:
"
"      �   � - �EFT
"      �   � - �IGHT
"      �   ; - �P
"      �   / - �OWN
"     ������ - �LICK
"
"     �HE PROGRAM HAS BEEN DESIGNED SO
"THAT ZOOMS MAY BE PERFORMED NOT BY
"ENTERING THE CO-ORDINATES OF THE AREA
"TO ZOOM, BUT BY BOXING OUT THE AREA
"TO ZOOM ON THE SCREEN. �HIS MEANS
"THAT YOU CAN ACTUALLY SEE THE AREA
"THAT YOU ARE BLOWING UP TO FULL
"SCREEN SIZE, RATHER THAN GUESSING AT
"WHAT THE CO-ORDINATES ARE. �N ORDER
"TO MAINTAIN COMPATIBILITY WITH OTHER
"PLOTTERS, � HAVE ALLOWED THE USER TO
"ZOOM BY ENTERING CO-ORDINATES AS WELL
"AS BY BOXING OUT AN AREA ON SCREEN,
"AS THIS�ALLOWS YOU TO VIEW A SPECIFIC
"FRACTAL IMAGE�THAT YOU ONLY KNOW THE
"CO-ORDINATES FOR. � HAVE ALSO
"INCLUDED INSTRUCTIONS WITHIN THE
"PROGRAM SO THAT WHILE YOU ARE USING
"THE PROGRAM YOU CAN EASILY GET HELP
"WITHOUT HAVING TO FIND THESE
"INSTRUCTIONS. �O READ THESE HELP
"PAGES SIMPLY MOVE THE MOUSE POINTER
"DOWN TO THE BOTTOM LEFT CORNER OF THE
"SCREEN, AND CLICK ON THE '����'
"BUTTON.
"
"���� ����
"
"     �HE �ANDELBROT SET IS ONE SINGLE
"FRACTAL IMAGE, WHICH IS THE IMAGE YOU
"SEE WHEN YOU FIRST RUN �ANDELPLOT.
"�ULIA SETS DIFFER FROM �ANDELBROT
"SETS IN THAT THERE ARE INFINITELY
"MANY OF THEM, AS THERE IS ONE �ULIA
"SET FOR EVERY POINT IN THE �ANDELBROT
"SET. �HE APPEARENCE OF THIS �ULIA SET
"DEPENDS UPON WHERE THE CORRESPONDING
"POINT IN THE �ANDELBROT SET IS. �ULIA
"SETS WHICH CORRESPOND TO POINTS
"AROUND THE OUTSIDE OF THE �ANDELBROT
"SET, FOR EXAMPLE, ARE SIMPLE, WHEREAS
"�ULIA SETS WHICH CORRESPOND TO POINTS
"AROUND THE EDGE OF THE �ANDELBROT
"LAKE (CENTRAL AREA) ARE FAR MARE
"COMPLICATED AND INTERESTING.
"     �ULIA SETS MAY BE PLOTTED BY
"�ANDELPLOT IF AN AREA OF THE
"�ANDELBROT SET IS BOXED OUT, AND THEN
"THE '�ULIA �ET' BUTTON IS SELECTED.
"�HE �ULIA SET WHICH CORRESPONDS TO
"THE POINT AT THE TOP-LEFT OF THE BOX
"WILL THEN BE PLOTTED, AND MAY BE
"ZOOMED INTO JUST LIKE THE �ANDELBROT
"SET ITSELF. �F '�ULIA �ET' IS
"SELECTED AGAIN, YOU RETURN TO THE
"�ANDELBROT SET WHERE YOU LEFT IT, AND
"MAY ZOOM IN, OR PLOT ANOTHER �ULIA
"�ET.
"     �OR MORE DETAILED INSTRUCTIONS
"ON HOW TO USE �ANDELPLOT, AND HOW TO
"USE MANY OF THE FUNCTIONS, SEE THE
"HELP PAGES WITHIN THE PROGRAM.
"
"........... ... ..... ... ..........M"M".rogramming and text by .ominic .ord.M"M"     .he .andelbrot and the .uliaM"sets are mathematical fractal images,M"or.images that can be zoomed intoM"infinitely much without detail beingM"lost. .hey are calculated usingM"mathematical formulae involvingM"complex numbers. .ou do not, however,M"need to understand the mathematicsM"involved with these formulas, orM"about complex numbers to appreciateM"the graphics produced. .hen they wereM"originally discovered they wereM"thought of only as of mathematicalM"interest, yet in recent years theyM"have become popular not just withM"mathematicians, but also with theM"rest of the population. .he stunningM"graphics which are produced byM"fractal plotters has lead to plottersM"being written for almost everyM"computer format that exists. .n theM".64/128 format, however, most of theM"plotters were simply programs writtenM"in ....., and were consequently veryM"slow, and difficult to use.M"     .andelplot differs from most ofM"these plotters in that it is writtenM"in 100% machine language, and isM"therefore far faster and moreM"efficient. .espite the fact that itM"is written in fast machine language,M"and is many times faster than itsM"..... equivelents, it is still a slowM"program compared to most of those onM"larger computers, and often takesM"over an hour to complete a plot. .M"have tried to overcome this problemM"by using a plotting system whichM"plots a very low resolution imageM"first of all, and then slowlyM"increases this resolution. .sing thisM"system the user can begin to see theM"rough outline of the image veryM"quickly, and then zoom in furtherM"before the plot has finished.M"     . have made the system asM"user-friendly as possible by makingM"the program controlled almostM"entirely by a mouse pointer which mayM"be moved around using aM"mouse/joystick plugged into port ..,M"or using the following keys:M"M"      .   . - .eftM"      .   . - .ightM"      .   ; - .pM"      .   / - .ownM"     ...... - .lickM"M"     .he program has been designed soM"that zooms may be performed not byM"entering the co-ordinates of the areaM"to zoom, but by boxing out the areaM"to zoom on the screen. .his meansM"that you can actually see the areaM"that you are blowing up to fullM"screen size, rather than guessing atM"what the co-ordinates are. .n orderM"to maintain compatibility with otherM"plotters, . have allowed the user toM"zoom by entering co-ordinates as wellM"as by boxing out an area on screen,M"as this.allows you to view a specificM"fractal image.that you only know theM"co-ordinates for. . have alsoM"included instructions within theM"program so that while you are usingM"the program you can easily get helpM"without having to find theseM"instructions. .o read these helpM"pages simply move the mouse pointerM"down to the bottom left corner of theM"screen, and click on the '....'M"button.M"M"..... ....M"M"     .he .andelbrot set is one singleM"fractal image, which is the image youM"see when you first run .andelplot.M".ulia sets differ from .andelbrotM"sets in that there are infinitelyM"many of them, as there is one .uliaM"set for every point in the .andelbrotM"set. .he appearence of this .ulia setM"depends upon where the correspondingM"point in the .andelbrot set is. .uliaM"sets which correspond to pointsM"around the outside of the .andelbrotM"set, for example, are simple, whereasM".ulia sets which correspond to pointsM"around the edge of the .andelbrotM"lake (central area) are far mareM"complicated and interesting.M"     .ulia sets may be plotted byM".andelplot if an area of theM".andelbrot set is boxed out, and thenM"the '.ulia .et' button is selected.M".he .ulia set which corresponds toM"the point at the top-left of the boxM"will then be plotted, and may beM"zoomed into just like the .andelbrotM"set itself. .f '.ulia .et' isM"selected again, you return to theM".andelbrot set where you left it, andM"may zoom in, or plot another .uliaM".et.M"     .or more detailed instructionsM"on how to use .andelplot, and how toM"use many of the functions, see theM"help pages within the program.M"M
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00000020  cc c1 d4 cf d2 0d 22 0d  22 d0 52 4f 47 52 41 4d  |......".".ROGRAM|
00000030  4d 49 4e 47 20 41 4e 44  20 54 45 58 54 20 42 59  |MING AND TEXT BY|
00000040  20 c4 4f 4d 49 4e 49 43  20 c6 4f 52 44 2e 0d 22  | .OMINIC .ORD.."|
00000050  0d 22 20 20 20 20 20 d4  48 45 20 cd 41 4e 44 45  |."     .HE .ANDE|
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00000070  4c 49 41 0d 22 53 45 54  53 20 41 52 45 20 4d 41  |LIA."SETS ARE MA|
00000080  54 48 45 4d 41 54 49 43  41 4c 20 46 52 41 43 54  |THEMATICAL FRACT|
00000090  41 4c 20 49 4d 41 47 45  53 2c 0d 22 4f 52 a0 49  |AL IMAGES,."OR.I|
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000000c0  4e 46 49 4e 49 54 45 4c  59 20 4d 55 43 48 20 57  |NFINITELY MUCH W|
000000d0  49 54 48 4f 55 54 20 44  45 54 41 49 4c 20 42 45  |ITHOUT DETAIL BE|
000000e0  49 4e 47 0d 22 4c 4f 53  54 2e 20 d4 48 45 59 20  |ING."LOST. .HEY |
000000f0  41 52 45 20 43 41 4c 43  55 4c 41 54 45 44 20 55  |ARE CALCULATED U|
00000100  53 49 4e 47 0d 22 4d 41  54 48 45 4d 41 54 49 43  |SING."MATHEMATIC|
00000110  41 4c 20 46 4f 52 4d 55  4c 41 45 20 49 4e 56 4f  |AL FORMULAE INVO|
00000120  4c 56 49 4e 47 0d 22 43  4f 4d 50 4c 45 58 20 4e  |LVING."COMPLEX N|
00000130  55 4d 42 45 52 53 2e 20  d9 4f 55 20 44 4f 20 4e  |UMBERS. .OU DO N|
00000140  4f 54 2c 20 48 4f 57 45  56 45 52 2c 0d 22 4e 45  |OT, HOWEVER,."NE|
00000150  45 44 20 54 4f 20 55 4e  44 45 52 53 54 41 4e 44  |ED TO UNDERSTAND|
00000160  20 54 48 45 20 4d 41 54  48 45 4d 41 54 49 43 53  | THE MATHEMATICS|
00000170  0d 22 49 4e 56 4f 4c 56  45 44 20 57 49 54 48 20  |."INVOLVED WITH |
00000180  54 48 45 53 45 20 46 4f  52 4d 55 4c 41 53 2c 20  |THESE FORMULAS, |
00000190  4f 52 0d 22 41 42 4f 55  54 20 43 4f 4d 50 4c 45  |OR."ABOUT COMPLE|
000001a0  58 20 4e 55 4d 42 45 52  53 20 54 4f 20 41 50 50  |X NUMBERS TO APP|
000001b0  52 45 43 49 41 54 45 0d  22 54 48 45 20 47 52 41  |RECIATE."THE GRA|
000001c0  50 48 49 43 53 20 50 52  4f 44 55 43 45 44 2e 20  |PHICS PRODUCED. |
000001d0  d7 48 45 4e 20 54 48 45  59 20 57 45 52 45 0d 22  |.HEN THEY WERE."|
000001e0  4f 52 49 47 49 4e 41 4c  4c 59 20 44 49 53 43 4f  |ORIGINALLY DISCO|
000001f0  56 45 52 45 44 20 54 48  45 59 20 57 45 52 45 0d  |VERED THEY WERE.|
00000200  22 54 48 4f 55 47 48 54  20 4f 46 20 4f 4e 4c 59  |"THOUGHT OF ONLY|
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00000220  43 41 4c 0d 22 49 4e 54  45 52 45 53 54 2c 20 59  |CAL."INTEREST, Y|
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00000260  20 4a 55 53 54 20 57 49  54 48 0d 22 4d 41 54 48  | JUST WITH."MATH|
00000270  45 4d 41 54 49 43 49 41  4e 53 2c 20 42 55 54 20  |EMATICIANS, BUT |
00000280  41 4c 53 4f 20 57 49 54  48 20 54 48 45 0d 22 52  |ALSO WITH THE."R|
00000290  45 53 54 20 4f 46 20 54  48 45 20 50 4f 50 55 4c  |EST OF THE POPUL|
000002a0  41 54 49 4f 4e 2e 20 d4  48 45 20 53 54 55 4e 4e  |ATION. .HE STUNN|
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000002c0  49 43 48 20 41 52 45 20  50 52 4f 44 55 43 45 44  |ICH ARE PRODUCED|
000002d0  20 42 59 0d 22 46 52 41  43 54 41 4c 20 50 4c 4f  | BY."FRACTAL PLO|
000002e0  54 54 45 52 53 20 48 41  53 20 4c 45 41 44 20 54  |TTERS HAS LEAD T|
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00000390  20 c2 c1 d3 c9 c3 2c 20  41 4e 44 20 57 45 52 45  | ....., AND WERE|
000003a0  20 43 4f 4e 53 45 51 55  45 4e 54 4c 59 20 56 45  | CONSEQUENTLY VE|
000003b0  52 59 0d 22 53 4c 4f 57  2c 20 41 4e 44 20 44 49  |RY."SLOW, AND DI|
000003c0  46 46 49 43 55 4c 54 20  54 4f 20 55 53 45 2e 0d  |FFICULT TO USE..|
000003d0  22 20 20 20 20 20 cd 41  4e 44 45 4c 50 4c 4f 54  |"     .ANDELPLOT|
000003e0  20 44 49 46 46 45 52 53  20 46 52 4f 4d 20 4d 4f  | DIFFERS FROM MO|
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00000400  54 54 45 52 53 20 49 4e  20 54 48 41 54 20 49 54  |TTERS IN THAT IT|
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00000420  31 30 30 25 20 4d 41 43  48 49 4e 45 20 4c 41 4e  |100% MACHINE LAN|
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00000520  43 4f 4d 50 55 54 45 52  53 2c 20 41 4e 44 20 4f  |COMPUTERS, AND O|
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00000540  20 41 4e 20 48 4f 55 52  20 54 4f 20 43 4f 4d 50  | AN HOUR TO COMP|
00000550  4c 45 54 45 20 41 20 50  4c 4f 54 2e 20 c9 0d 22  |LETE A PLOT. .."|
00000560  48 41 56 45 20 54 52 49  45 44 20 54 4f 20 4f 56  |HAVE TRIED TO OV|
00000570  45 52 43 4f 4d 45 20 54  48 49 53 20 50 52 4f 42  |ERCOME THIS PROB|
00000580  4c 45 4d 0d 22 42 59 20  55 53 49 4e 47 20 41 20  |LEM."BY USING A |
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000005a0  57 48 49 43 48 0d 22 50  4c 4f 54 53 20 41 20 56  |WHICH."PLOTS A V|
000005b0  45 52 59 20 4c 4f 57 20  52 45 53 4f 4c 55 54 49  |ERY LOW RESOLUTI|
000005c0  4f 4e 20 49 4d 41 47 45  0d 22 46 49 52 53 54 20  |ON IMAGE."FIRST |
000005d0  4f 46 20 41 4c 4c 2c 20  41 4e 44 20 54 48 45 4e  |OF ALL, AND THEN|
000005e0  20 53 4c 4f 57 4c 59 0d  22 49 4e 43 52 45 41 53  | SLOWLY."INCREAS|
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00000660  41 4e 44 20 54 48 45 4e  20 5a 4f 4f 4d 20 49 4e  |AND THEN ZOOM IN|
00000670  20 46 55 52 54 48 45 52  0d 22 42 45 46 4f 52 45  | FURTHER."BEFORE|
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00000690  4e 49 53 48 45 44 2e 0d  22 20 20 20 20 20 c9 20  |NISHED.."     . |
000006a0  48 41 56 45 20 4d 41 44  45 20 54 48 45 20 53 59  |HAVE MADE THE SY|
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00000720  41 59 0d 22 42 45 20 4d  4f 56 45 44 20 41 52 4f  |AY."BE MOVED ARO|
00000730  55 4e 44 20 55 53 49 4e  47 20 41 0d 22 4d 4f 55  |UND USING A."MOU|
00000740  53 45 2f 4a 4f 59 53 54  49 43 4b 20 50 4c 55 47  |SE/JOYSTICK PLUG|
00000750  47 45 44 20 49 4e 54 4f  20 50 4f 52 54 20 c9 c9  |GED INTO PORT ..|
00000760  2c 0d 22 4f 52 20 55 53  49 4e 47 20 54 48 45 20  |,."OR USING THE |
00000770  46 4f 4c 4c 4f 57 49 4e  47 20 4b 45 59 53 3a 0d  |FOLLOWING KEYS:.|
00000780  22 0d 22 20 20 20 20 20  20 a0 20 20 20 da 20 2d  |"."      .   . -|
00000790  20 cc 45 46 54 0d 22 20  20 20 20 20 20 a0 20 20  | .EFT."      .  |
000007a0  20 d8 20 2d 20 d2 49 47  48 54 0d 22 20 20 20 20  | . - .IGHT."    |
000007b0  20 20 a0 20 20 20 3b 20  2d 20 d5 50 0d 22 20 20  |  .   ; - .P."  |
000007c0  20 20 20 20 a0 20 20 20  2f 20 2d 20 c4 4f 57 4e  |    .   / - .OWN|
000007d0  0d 22 20 20 20 20 20 d2  c5 d4 d5 d2 ce 20 2d 20  |."     ...... - |
000007e0  c3 4c 49 43 4b 0d 22 0d  22 20 20 20 20 20 d4 48  |.LICK."."     .H|
000007f0  45 20 50 52 4f 47 52 41  4d 20 48 41 53 20 42 45  |E PROGRAM HAS BE|
00000800  45 4e 20 44 45 53 49 47  4e 45 44 20 53 4f 0d 22  |EN DESIGNED SO."|
00000810  54 48 41 54 20 5a 4f 4f  4d 53 20 4d 41 59 20 42  |THAT ZOOMS MAY B|
00000820  45 20 50 45 52 46 4f 52  4d 45 44 20 4e 4f 54 20  |E PERFORMED NOT |
00000830  42 59 0d 22 45 4e 54 45  52 49 4e 47 20 54 48 45  |BY."ENTERING THE|
00000840  20 43 4f 2d 4f 52 44 49  4e 41 54 45 53 20 4f 46  | CO-ORDINATES OF|
00000850  20 54 48 45 20 41 52 45  41 0d 22 54 4f 20 5a 4f  | THE AREA."TO ZO|
00000860  4f 4d 2c 20 42 55 54 20  42 59 20 42 4f 58 49 4e  |OM, BUT BY BOXIN|
00000870  47 20 4f 55 54 20 54 48  45 20 41 52 45 41 0d 22  |G OUT THE AREA."|
00000880  54 4f 20 5a 4f 4f 4d 20  4f 4e 20 54 48 45 20 53  |TO ZOOM ON THE S|
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