T.EQUATIONS.64
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FILENAME(S): T.EQUATIONS.64
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FIRST SEEN: 2025-11-30 18:12:21
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|---|---|---|---|---|---|---|
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00000000: 00 80 5E 55 3A 43 42 4D 0D 0D 20 20 20 20 20 20 |..^U:CBM.. | 00000010: 20 20 20 20 20 20 20 C5 D1 D5 C1 D4 C9 CF CE D3 | .........| 00000020: 20 31 32 38 0D 0D 20 20 20 20 20 20 20 20 20 20 | 128.. | 00000030: 20 20 42 59 20 CA 4F 48 4E 20 C9 4F 56 49 4E 45 | BY .OHN .OVINE| 00000040: 0D 0D 20 20 20 20 CC 41 53 54 20 4D 4F 4E 54 48 |.. .AST MONTH| 00000050: 20 57 45 20 50 55 42 4C 49 53 48 45 44 20 41 20 | WE PUBLISHED A | 00000060: 50 52 4F 47 52 41 4D 0D 46 52 4F 4D 20 C3 4F 4D |PROGRAM.FROM .OM| 00000070: 4D 4F 44 4F 52 45 20 CD 41 47 41 5A 49 4E 45 20 |MODORE .AGAZINE | 00000080: 43 41 4C 4C 45 44 0D C6 D2 C1 C3 D4 C1 CC D3 2E |CALLED..........| 00000090: 20 20 C9 4E 20 54 48 45 20 54 45 58 54 20 C9 20 | .N THE TEXT . | 000000A0: 45 58 50 4C 41 49 4E 45 44 0D 45 56 45 52 59 54 |EXPLAINED.EVERYT| 000000B0: 48 49 4E 47 20 C9 20 4B 4E 4F 57 20 41 42 4F 55 |HING . KNOW ABOU| 000000C0: 54 20 54 48 45 53 45 0D 43 52 49 54 54 45 52 53 |T THESE.CRITTERS| 000000D0: 2C 20 53 4F 20 54 48 49 53 20 4D 4F 4E 54 48 20 |, SO THIS MONTH | 000000E0: C9 27 4C 4C 20 48 41 56 45 20 54 4F 0D 54 52 59 |.'LL HAVE TO.TRY| 000000F0: 20 41 20 44 49 46 46 45 52 45 4E 54 20 54 41 43 | A DIFFERENT TAC| 00000100: 4B 2E 20 20 C9 27 4C 4C 20 4C 45 54 20 54 48 45 |K. .'LL LET THE| 00000110: 0D 41 55 54 48 4F 52 20 45 58 50 4C 41 49 4E 2E |.AUTHOR EXPLAIN.| 00000120: 0D 0D 20 20 20 20 CA 4F 48 4E 20 C9 4F 56 49 4E |.. .OHN .OVIN| 00000130: 45 20 49 53 20 54 48 45 20 54 45 43 48 4E 49 43 |E IS THE TECHNIC| 00000140: 41 4C 0D 45 58 50 45 52 54 20 46 4F 52 20 C3 4F |AL.EXPERT FOR .O| 00000150: 4D 4D 4F 44 4F 52 45 20 CD 41 47 41 5A 49 4E 45 |MMODORE .AGAZINE| 00000160: 2E 20 20 C8 49 53 0D 4D 4F 4E 54 48 4C 59 20 41 |. .IS.MONTHLY A| 00000170: 52 54 49 43 4C 45 53 20 4F 4E 20 48 41 52 44 57 |RTICLES ON HARDW| 00000180: 41 52 45 20 28 41 4E 44 20 4E 4F 57 0D 4D 41 54 |ARE (AND NOW.MAT| 00000190: 48 45 4D 41 54 49 43 41 4C 20 44 49 56 45 52 53 |HEMATICAL DIVERS| 000001A0: 49 4F 4E 53 29 20 48 41 56 45 20 47 52 41 43 45 |IONS) HAVE GRACE| 000001B0: 44 0D 54 48 45 20 50 41 47 45 53 20 4F 46 20 54 |D.THE PAGES OF T| 000001C0: 48 45 20 4D 41 47 41 5A 49 4E 45 20 46 4F 52 20 |HE MAGAZINE FOR | 000001D0: 54 48 45 0D 4C 41 53 54 20 59 45 41 52 2E 0D 20 |THE.LAST YEAR.. | 000001E0: 20 20 20 D4 48 49 53 20 4D 4F 4E 54 48 20 48 45 | .HIS MONTH HE| 000001F0: 20 48 41 53 20 41 20 4C 4F 4E 47 2C 0D 44 45 54 | HAS A LONG,.DET| 00000200: 41 49 4C 45 44 20 41 52 54 49 43 4C 45 20 4F 4E |AILED ARTICLE ON| 00000210: 20 54 48 45 20 50 41 52 54 49 43 55 4C 41 52 0D | THE PARTICULAR.| 00000220: 52 45 43 55 52 53 49 56 45 20 46 4F 52 4D 55 4C |RECURSIVE FORMUL| 00000230: 41 20 54 48 41 54 20 54 48 49 53 20 50 52 4F 47 |A THAT THIS PROG| 00000240: 52 41 4D 0D 49 53 20 42 41 53 45 44 20 55 50 4F |RAM.IS BASED UPO| 00000250: 4E 2E 20 20 C6 4F 52 20 4D 4F 52 45 20 49 4E 46 |N. .OR MORE INF| 00000260: 4F 52 4D 41 54 49 4F 4E 0D 54 48 41 4E 20 C9 20 |ORMATION.THAN . | 00000270: 43 41 4E 20 47 49 56 45 20 59 4F 55 2C 20 59 4F |CAN GIVE YOU, YO| 00000280: 55 20 4D 41 59 20 57 41 4E 54 20 54 4F 0D 43 4F |U MAY WANT TO.CO| 00000290: 4E 53 55 4C 54 20 54 48 45 20 4D 41 47 41 5A 49 |NSULT THE MAGAZI| 000002A0: 4E 45 20 41 52 54 49 43 4C 45 2E 0D 0D 20 20 20 |NE ARTICLE... | 000002B0: 20 D4 48 45 20 46 4F 52 4D 55 4C 41 20 48 45 20 | .HE FORMULA HE | 000002C0: 55 53 45 53 20 49 53 20 41 20 27 47 52 4F 57 54 |USES IS A 'GROWT| 000002D0: 48 27 0D 41 4C 47 4F 52 49 54 48 4D 20 46 49 52 |H'.ALGORITHM FIR| 000002E0: 53 54 20 44 45 46 49 4E 45 44 20 42 59 20 D0 2E |ST DEFINED BY ..| 000002F0: C6 2E 0D D6 45 52 48 55 4C 53 54 20 49 4E 20 31 |....ERHULST IN 1| 00000300: 38 34 35 2E 20 20 C1 53 20 57 49 54 48 20 4D 4F |845. .S WITH MO| 00000310: 53 54 0D 46 52 41 43 54 41 4C 20 46 4F 52 4D 55 |ST.FRACTAL FORMU| 00000320: 4C 41 45 2C 20 49 54 27 53 20 51 55 49 54 45 20 |LAE, IT'S QUITE | 00000330: 53 49 4D 50 4C 45 0D 54 4F 20 4C 4F 4F 4B 20 41 |SIMPLE.TO LOOK A| 00000340: 54 2E 20 20 C9 54 20 4C 4F 4F 4B 53 20 4C 49 4B |T. .T LOOKS LIK| 00000350: 45 20 54 48 49 53 3A 0D 0D 20 20 20 20 20 20 D8 |E THIS:.. .| 00000360: 3D 28 31 2B D2 29 2A D8 2D 28 D2 2A D8 5E 32 29 |=(1+.)*.-(.*.^2)| 00000370: 0D 0D 20 20 20 20 C1 53 20 59 4F 55 20 43 41 4E |.. .S YOU CAN| 00000380: 20 53 45 45 2C 20 54 48 45 20 46 4F 52 4D 55 4C | SEE, THE FORMUL| 00000390: 41 20 48 41 53 0D 54 48 45 20 55 4E 55 53 55 41 |A HAS.THE UNUSUA| 000003A0: 4C 20 51 55 41 4C 49 54 59 20 4F 46 20 48 41 56 |L QUALITY OF HAV| 000003B0: 49 4E 47 20 D8 0D 4D 45 4E 54 49 4F 4E 45 44 20 |ING ..MENTIONED | 000003C0: 41 53 20 41 20 46 55 4E 43 54 49 4F 4E 20 4F 46 |AS A FUNCTION OF| 000003D0: 20 49 54 53 45 4C 46 2E 0D D4 48 49 53 20 49 53 | ITSELF...HIS IS| 000003E0: 20 4B 4E 4F 57 4E 20 41 53 20 52 45 43 55 52 53 | KNOWN AS RECURS| 000003F0: 49 4F 4E 2E 0D 20 20 20 20 D4 48 45 20 46 41 43 |ION.. .HE FAC| 00000400: 54 4F 52 20 D2 20 49 53 20 43 41 4C 4C 45 44 20 |TOR . IS CALLED | 00000410: 54 48 45 0D 27 47 52 4F 57 54 48 20 52 41 54 45 |THE.'GROWTH RATE| 00000420: 20 46 41 43 54 4F 52 27 20 41 4E 44 20 49 53 20 | FACTOR' AND IS | 00000430: 41 20 4E 55 4D 42 45 52 0D 54 48 41 54 20 59 4F |A NUMBER.THAT YO| 00000440: 55 20 43 41 4E 20 49 4E 50 55 54 2E 20 20 C9 54 |U CAN INPUT. .T| 00000450: 20 44 45 53 43 52 49 42 45 53 20 48 4F 57 0D 46 | DESCRIBES HOW.F| 00000460: 41 53 54 20 41 20 50 4F 50 55 4C 41 54 49 4F 4E |AST A POPULATION| 00000470: 20 57 49 4C 4C 20 47 52 4F 57 2E 20 20 C9 46 20 | WILL GROW. .F | 00000480: 59 4F 55 0D 43 4F 4E 53 49 44 45 52 20 D8 20 41 |YOU.CONSIDER . A| 00000490: 53 20 41 20 50 4F 50 55 4C 41 54 49 4F 4E 20 4F |S A POPULATION O| 000004A0: 46 20 50 45 4F 50 4C 45 2C 0D 59 4F 55 20 43 41 |F PEOPLE,.YOU CA| 000004B0: 4E 20 49 4D 41 47 49 4E 45 20 54 48 41 54 20 41 |N IMAGINE THAT A| 000004C0: 53 20 41 20 50 4F 50 55 4C 41 54 49 4F 4E 0D 47 |S A POPULATION.G| 000004D0: 52 4F 57 53 2C 20 54 48 45 52 45 20 41 52 45 20 |ROWS, THERE ARE | 000004E0: 4D 4F 52 45 20 50 45 4F 50 4C 45 20 41 52 4F 55 |MORE PEOPLE AROU| 000004F0: 4E 44 0D 54 4F 20 52 45 50 52 4F 44 55 43 45 2C |ND.TO REPRODUCE,| 00000500: 20 53 4F 20 54 48 45 20 50 4F 50 55 4C 41 54 49 | SO THE POPULATI| 00000510: 4F 4E 20 47 52 4F 57 53 0D 45 56 45 4E 20 46 41 |ON GROWS.EVEN FA| 00000520: 53 54 45 52 2E 20 20 D4 48 45 20 46 49 52 53 54 |STER. .HE FIRST| 00000530: 20 48 41 4C 46 20 4F 46 20 54 48 45 0D 46 4F 52 | HALF OF THE.FOR| 00000540: 4D 55 4C 41 2C 20 28 31 2B D2 29 2A D8 2C 20 44 |MULA, (1+.)*., D| 00000550: 45 53 43 52 49 42 45 53 20 54 48 49 53 2E 0D 0D |ESCRIBES THIS...| 00000560: 20 20 20 20 C2 55 54 20 57 48 41 54 20 49 46 20 | .UT WHAT IF | 00000570: 54 48 45 52 45 20 49 53 20 41 20 52 45 53 54 52 |THERE IS A RESTR| 00000580: 41 49 4E 54 0D 4F 4E 20 47 52 4F 57 54 48 3F 20 |AINT.ON GROWTH? | 00000590: 20 D7 48 41 54 20 49 46 20 54 48 45 52 45 20 49 | .HAT IF THERE I| 000005A0: 53 20 4E 4F 54 0D 45 4E 4F 55 47 48 20 46 4F 4F |S NOT.ENOUGH FOO| 000005B0: 44 20 54 4F 20 46 45 45 44 20 54 48 45 20 50 4F |D TO FEED THE PO| 000005C0: 50 55 4C 41 54 49 4F 4E 3F 0D D4 48 41 54 53 20 |PULATION?..HATS | 000005D0: 57 48 41 54 20 54 48 45 20 4C 41 53 54 20 48 41 |WHAT THE LAST HA| 000005E0: 4C 46 20 4F 46 20 54 48 45 0D 45 51 55 41 54 49 |LF OF THE.EQUATI| 000005F0: 4F 4E 20 49 53 20 41 4C 4C 20 41 42 4F 55 54 2E |ON IS ALL ABOUT.| 00000600: 20 20 D4 48 45 20 4D 49 4E 55 53 0D 53 49 47 4E | .HE MINUS.SIGN| 00000610: 20 53 41 59 53 20 54 48 41 54 20 41 53 20 50 4F | SAYS THAT AS PO| 00000620: 50 55 4C 41 54 49 4F 4E 20 47 4F 45 53 20 55 50 |PULATION GOES UP| 00000630: 0D 28 41 46 54 45 52 20 41 20 50 4F 49 4E 54 29 |.(AFTER A POINT)| 00000640: 20 49 54 20 47 4F 45 53 20 44 4F 57 4E 20 45 56 | IT GOES DOWN EV| 00000650: 45 4E 0D 4D 4F 52 45 2E 0D 0D 20 20 20 20 D7 48 |EN.MORE... .H| 00000660: 45 4E 20 59 4F 55 20 52 55 4E 20 54 48 45 20 50 |EN YOU RUN THE P| 00000670: 52 4F 47 52 41 4D 2C 20 43 48 4F 4F 53 45 0D 54 |ROGRAM, CHOOSE.T| 00000680: 4F 20 53 45 45 20 C3 C8 C1 CF D3 20 23 31 2E 20 |O SEE ..... #1. | 00000690: 20 D9 4F 55 20 57 49 4C 4C 20 42 45 20 41 53 4B | .OU WILL BE ASK| 000006A0: 45 44 0D 54 4F 20 49 4E 50 55 54 20 41 20 47 52 |ED.TO INPUT A GR| 000006B0: 4F 57 54 48 20 46 41 43 54 4F 52 2E 20 20 CA 4F |OWTH FACTOR. .O| 000006C0: 48 4E 0D 53 55 47 47 45 53 54 53 20 31 2E 39 2C |HN.SUGGESTS 1.9,| 000006D0: 20 32 2E 34 2C 20 32 2E 35 20 41 4E 44 20 32 2E | 2.4, 2.5 AND 2.| 000006E0: 39 36 20 41 53 0D 52 45 41 53 4F 4E 41 42 4C 45 |96 AS.REASONABLE| 000006F0: 20 56 41 4C 55 45 53 2E 20 20 D4 48 45 20 53 4D | VALUES. .HE SM| 00000700: 41 4C 4C 45 52 0D 56 41 4C 55 45 53 20 43 52 45 |ALLER.VALUES CRE| 00000710: 41 54 45 20 50 52 45 44 49 43 54 41 42 4C 45 20 |ATE PREDICTABLE | 00000720: 50 4C 4F 54 53 2E 20 20 D4 48 45 0D 32 2E 39 36 |PLOTS. .HE.2.96| 00000730: 20 47 52 4F 57 54 48 20 46 41 43 54 4F 52 20 57 | GROWTH FACTOR W| 00000740: 49 4C 4C 20 54 55 52 4E 20 49 4E 54 4F 0D 43 48 |ILL TURN INTO.CH| 00000750: 41 4F 53 20 42 45 46 4F 52 45 20 54 48 45 20 45 |AOS BEFORE THE E| 00000760: 4E 44 20 4F 46 20 54 48 45 20 53 43 52 45 45 4E |ND OF THE SCREEN| 00000770: 2E 0D C1 20 47 52 4F 57 54 48 20 46 41 43 54 4F |... GROWTH FACTO| 00000780: 52 20 4F 46 20 32 2E 39 36 20 49 53 20 54 4F 4F |R OF 2.96 IS TOO| 00000790: 20 48 49 47 48 0D 54 4F 20 52 45 4D 41 49 4E 20 | HIGH.TO REMAIN | 000007A0: 50 52 45 44 49 43 54 41 42 4C 45 2E 20 20 C8 4F |PREDICTABLE. .O| 000007B0: 50 45 46 55 4C 4C 59 20 54 48 45 0D 47 52 4F 57 |PEFULLY THE.GROW| 000007C0: 54 48 20 46 41 43 54 4F 52 20 46 4F 52 20 48 55 |TH FACTOR FOR HU| 000007D0: 4D 41 4E 49 54 59 20 4F 4E 20 45 41 52 54 48 0D |MANITY ON EARTH.| 000007E0: 49 53 20 4C 45 53 53 20 54 48 41 54 20 32 2E 39 |IS LESS THAT 2.9| 000007F0: 36 2E 0D 0D 20 20 20 20 C9 46 20 59 4F 55 20 43 |6... .F YOU C| 00000800: 48 4F 4F 53 45 20 C3 C8 C1 CF D3 20 23 32 2C 20 |HOOSE ..... #2, | 00000810: 59 4F 55 20 43 41 4E 0D 53 45 45 20 54 48 45 20 |YOU CAN.SEE THE | 00000820: 52 45 53 55 4C 54 53 20 4F 46 20 41 4C 4C 20 4F |RESULTS OF ALL O| 00000830: 46 20 54 48 45 20 46 41 43 54 4F 52 53 0D 4D 45 |F THE FACTORS.ME| 00000840: 4E 54 49 4F 4E 45 44 20 41 42 4F 56 45 2E 20 20 |NTIONED ABOVE. | 00000850: C9 54 20 49 53 20 D6 C5 D2 D9 20 53 4C 4F 57 20 |.T IS .... SLOW | 00000860: 41 4E 44 0D 57 49 4C 4C 20 54 41 4B 45 20 41 42 |AND.WILL TAKE AB| 00000870: 4F 55 54 20 41 4E 20 48 4F 55 52 20 46 4F 52 20 |OUT AN HOUR FOR | 00000880: 49 54 20 54 4F 0D 46 49 4E 49 53 48 2E 0D 20 20 |IT TO.FINISH.. | 00000890: 20 20 D4 48 45 20 46 49 52 53 54 20 50 41 52 54 | .HE FIRST PART| 000008A0: 20 4F 46 20 54 48 45 20 4C 49 4E 45 20 57 49 4C | OF THE LINE WIL| 000008B0: 4C 0D 52 45 50 52 45 53 45 4E 54 20 41 20 47 52 |L.REPRESENT A GR| 000008C0: 4F 57 54 48 20 46 41 43 54 4F 52 20 4F 46 20 31 |OWTH FACTOR OF 1| 000008D0: 2E 39 2C 20 54 48 45 0D 4E 45 58 54 20 50 41 52 |.9, THE.NEXT PAR| 000008E0: 54 20 57 49 4C 4C 20 52 45 50 52 45 53 45 4E 54 |T WILL REPRESENT| 000008F0: 20 32 2E 34 2E 20 20 C1 46 54 45 52 0D 54 48 41 | 2.4. .FTER.THA| 00000900: 54 20 59 4F 55 20 57 49 4C 4C 20 53 45 45 20 54 |T YOU WILL SEE T| 00000910: 48 45 20 50 4C 4F 54 54 49 4E 47 20 46 4F 52 0D |HE PLOTTING FOR.| 00000920: 32 2E 35 20 41 4E 44 20 32 2E 39 36 2C 20 57 48 |2.5 AND 2.96, WH| 00000930: 49 43 48 20 4C 45 41 44 53 20 41 47 41 49 4E 20 |ICH LEADS AGAIN | 00000940: 54 4F 0D 43 48 41 4F 53 2E 0D 0D 20 20 20 20 C6 |TO.CHAOS... .| 00000950: 4F 52 20 4D 4F 52 45 20 49 4E 46 4F 52 4D 41 54 |OR MORE INFORMAT| 00000960: 49 4F 4E 20 4F 4E 20 48 4F 57 20 54 4F 0D 43 48 |ION ON HOW TO.CH| 00000970: 41 4E 47 45 20 54 48 45 20 50 52 4F 47 52 41 4D |ANGE THE PROGRAM| 00000980: 20 4C 49 53 54 49 4E 47 20 54 4F 20 46 55 52 54 | LISTING TO FURT| 00000990: 48 45 52 0D 49 4C 4C 55 53 54 52 41 54 45 20 46 |HER.ILLUSTRATE F| 000009A0: 52 41 43 54 41 4C 53 2C 20 53 45 45 20 54 48 45 |RACTALS, SEE THE| 000009B0: 20 C1 50 52 49 4C 0D 49 53 53 55 45 20 4F 46 20 | .PRIL.ISSUE OF | 000009C0: C3 4F 4D 4D 4F 44 4F 52 45 20 CD 41 47 41 5A 49 |.OMMODORE .AGAZI| 000009D0: 4E 45 2E 0D 0D C4 C9 D3 CB 20 C6 C9 CC C5 D3 20 |NE....... ..... | 000009E0: D4 C8 C9 D3 20 D0 D2 CF C7 D2 C1 CD 20 D5 D3 C5 |.... ....... ...| 000009F0: D3 0D 0D C5 D1 D5 C1 D4 C9 CF CE D3 2E 36 34 20 |.............64 | 00000A00: 20 20 20 20 20 20 36 34 C3 C8 C1 CF D3 31 2E CF | 64.....1..| 00000A10: CB 0D 36 34 C3 C8 C1 CF D3 32 2E CF CB 20 20 20 |..64.....2... | 00000A20: 20 20 20 20 20 D0 CC CF D4 2E CD CC 0D D4 2E C5 | ...........| 00000A30: D1 D5 C1 D4 C9 CF CE D3 2E 36 34 0D 0D 20 20 20 |.........64.. | 00000A40: 20 20 20 20 20 2A 2A 2A 2A 20 C5 4E 44 20 4F 46 | **** .ND OF| 00000A50: 20 D4 45 58 54 20 2A 2A 2A 2A 0D | .EXT ****. |
..^U:CBM.. EQUATIONS 128..
BY JOHN IOVINE.. LAST MONTH
WE PUBLISHED A PROGRAM.FROM COMMODORE M
AGAZINE CALLED.FRACTALS. IN THE TEXT I
EXPLAINED.EVERYTHING I KNOW ABOUT THESE.
CRITTERS, SO THIS MONTH I'LL HAVE TO.TRY
A DIFFERENT TACK. I'LL LET THE.AUTHOR
EXPLAIN... JOHN IOVINE IS THE TECHNIC
AL.EXPERT FOR COMMODORE MAGAZINE. HIS.M
ONTHLY ARTICLES ON HARDWARE (AND NOW.MAT
HEMATICAL DIVERSIONS) HAVE GRACED.THE PA
GES OF THE MAGAZINE FOR THE.LAST YEAR..
THIS MONTH HE HAS A LONG,.DETAILED AR
TICLE ON THE PARTICULAR.RECURSIVE FORMUL
A THAT THIS PROGRAM.IS BASED UPON. FOR
MORE INFORMATION.THAN I CAN GIVE YOU, YO
U MAY WANT TO.CONSULT THE MAGAZINE ARTIC
LE... THE FORMULA HE USES IS A 'GROWT
H'.ALGORITHM FIRST DEFINED BY P.F..VERHU
LST IN 1845. AS WITH MOST.FRACTAL FORMU
LAE, IT'S QUITE SIMPLE.TO LOOK AT. IT L
OOKS LIKE THIS:.. X=(1+R)*X-(R*X^2)
.. AS YOU CAN SEE, THE FORMULA HAS.TH
E UNUSUAL QUALITY OF HAVING X.MENTIONED
AS A FUNCTION OF ITSELF..THIS IS KNOWN A
S RECURSION.. THE FACTOR R IS CALLED
THE.'GROWTH RATE FACTOR' AND IS A NUMBER
.THAT YOU CAN INPUT. IT DESCRIBES HOW.F
AST A POPULATION WILL GROW. IF YOU.CONS
IDER X AS A POPULATION OF PEOPLE,.YOU CA
N IMAGINE THAT AS A POPULATION.GROWS, TH
ERE ARE MORE PEOPLE AROUND.TO REPRODUCE,
SO THE POPULATION GROWS.EVEN FASTER. T
HE FIRST HALF OF THE.FORMULA, (1+R)*X, D
ESCRIBES THIS... BUT WHAT IF THERE IS
A RESTRAINT.ON GROWTH? WHAT IF THERE I
S NOT.ENOUGH FOOD TO FEED THE POPULATION
?.THATS WHAT THE LAST HALF OF THE.EQUATI
ON IS ALL ABOUT. THE MINUS.SIGN SAYS TH
AT AS POPULATION GOES UP.(AFTER A POINT)
IT GOES DOWN EVEN.MORE... WHEN YOU R
UN THE PROGRAM, CHOOSE.TO SEE CHAOS #1.
YOU WILL BE ASKED.TO INPUT A GROWTH FAC
TOR. JOHN.SUGGESTS 1.9, 2.4, 2.5 AND 2.
96 AS.REASONABLE VALUES. THE SMALLER.VA
LUES CREATE PREDICTABLE PLOTS. THE.2.96
GROWTH FACTOR WILL TURN INTO.CHAOS BEFO
RE THE END OF THE SCREEN..A GROWTH FACTO
R OF 2.96 IS TOO HIGH.TO REMAIN PREDICTA
BLE. HOPEFULLY THE.GROWTH FACTOR FOR HU
MANITY ON EARTH.IS LESS THAT 2.96...
IF YOU CHOOSE CHAOS #2, YOU CAN.SEE THE
RESULTS OF ALL OF THE FACTORS.MENTIONED
ABOVE. IT IS VERY SLOW AND.WILL TAKE AB
OUT AN HOUR FOR IT TO.FINISH.. THE FI
RST PART OF THE LINE WILL.REPRESENT A GR
OWTH FACTOR OF 1.9, THE.NEXT PART WILL R
EPRESENT 2.4. AFTER.THAT YOU WILL SEE T
HE PLOTTING FOR.2.5 AND 2.96, WHICH LEAD
S AGAIN TO.CHAOS... FOR MORE INFORMAT
ION ON HOW TO.CHANGE THE PROGRAM LISTING
TO FURTHER.ILLUSTRATE FRACTALS, SEE THE
APRIL.ISSUE OF COMMODORE MAGAZINE...DIS
K FILES THIS PROGRAM USES..EQUATIONS.64
64CHAOS1.OK.64CHAOS2.OK PLO
T.ML.T.EQUATIONS.64.. **** END OF
TEXT ****.
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