T.EQUATIONS.128
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FILENAME(S): T.EQUATIONS.128
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FIRST SEEN: 2025-11-30 18:12:21
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| DISK TITLE | FILENAME | FILE TYPE | COLLECTION | TRACK | SECTOR | ACTIONS |
|---|---|---|---|---|---|---|
| LOADSTAR 47 S 2 | T.EQUATIONS.128 | PRG | Sailor, Ganheden | 29 | 2 | DOWNLOAD FILE |
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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 53 2C 20 49 54 27 53 20 51 55 49 54 45 20 |LAS, 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 4D 41 | ITSELF...HIS MA| 000003E0: 4B 45 53 20 54 48 45 20 45 51 55 41 54 49 4F 4E |KES THE EQUATION| 000003F0: 20 27 52 45 43 55 52 53 49 56 45 27 2E 0D 20 20 | 'RECURSIVE'.. | 00000400: 20 20 D4 48 45 20 46 41 43 54 4F 52 20 D2 20 49 | .HE FACTOR . I| 00000410: 53 20 43 41 4C 4C 45 44 20 54 48 45 0D 27 47 52 |S CALLED THE.'GR| 00000420: 4F 57 54 48 20 52 41 54 45 20 46 41 43 54 4F 52 |OWTH RATE FACTOR| 00000430: 27 20 41 4E 44 20 49 53 20 41 20 4E 55 4D 42 45 |' AND IS A NUMBE| 00000440: 52 0D 54 48 41 54 20 59 4F 55 20 43 41 4E 20 49 |R.THAT YOU CAN I| 00000450: 4E 50 55 54 2E 20 20 C9 54 20 44 45 53 43 52 49 |NPUT. .T DESCRI| 00000460: 42 45 53 20 48 4F 57 0D 46 41 53 54 20 41 20 50 |BES HOW.FAST A P| 00000470: 4F 50 55 4C 41 54 49 4F 4E 20 57 49 4C 4C 20 47 |OPULATION WILL G| 00000480: 52 4F 57 2E 20 20 C9 46 20 59 4F 55 0D 43 4F 4E |ROW. .F YOU.CON| 00000490: 53 49 44 45 52 20 D8 20 41 53 20 41 20 50 4F 50 |SIDER . AS A POP| 000004A0: 55 4C 41 54 49 4F 4E 20 4F 46 20 50 45 4F 50 4C |ULATION OF PEOPL| 000004B0: 45 2C 0D 59 4F 55 20 43 41 4E 20 49 4D 41 47 49 |E,.YOU CAN IMAGI| 000004C0: 4E 45 20 54 48 41 54 20 41 53 20 41 20 50 4F 50 |NE THAT AS A POP| 000004D0: 55 4C 41 54 49 4F 4E 0D 47 52 4F 57 53 2C 20 54 |ULATION.GROWS, T| 000004E0: 48 45 52 45 20 41 52 45 20 4D 4F 52 45 20 50 45 |HERE ARE MORE PE| 000004F0: 4F 50 4C 45 20 41 52 4F 55 4E 44 0D 54 4F 20 52 |OPLE AROUND.TO R| 00000500: 45 50 52 4F 44 55 43 45 2C 20 53 4F 20 54 48 45 |EPRODUCE, SO THE| 00000510: 20 50 4F 50 55 4C 41 54 49 4F 4E 20 47 52 4F 57 | POPULATION GROW| 00000520: 53 0D 45 56 45 4E 20 46 41 53 54 45 52 2E 20 20 |S.EVEN FASTER. | 00000530: D4 48 45 20 46 49 52 53 54 20 48 41 4C 46 20 4F |.HE FIRST HALF O| 00000540: 46 20 54 48 45 0D 46 4F 52 4D 55 4C 41 2C 20 28 |F THE.FORMULA, (| 00000550: 31 2B D2 29 2A D8 2C 20 44 45 53 43 52 49 42 45 |1+.)*., DESCRIBE| 00000560: 53 20 54 48 49 53 2E 0D 0D 20 20 20 20 C2 55 54 |S THIS... .UT| 00000570: 20 57 48 41 54 20 49 46 20 54 48 45 52 45 20 49 | WHAT IF THERE I| 00000580: 53 20 41 20 52 45 53 54 52 41 49 4E 54 0D 4F 4E |S A RESTRAINT.ON| 00000590: 20 47 52 4F 57 54 48 3F 20 20 D7 48 41 54 20 49 | GROWTH? .HAT I| 000005A0: 46 20 54 48 45 52 45 20 49 53 20 4E 4F 54 0D 45 |F THERE IS NOT.E| 000005B0: 4E 4F 55 47 48 20 46 4F 4F 44 20 54 4F 20 46 45 |NOUGH FOOD TO FE| 000005C0: 45 44 20 54 48 45 20 50 4F 50 55 4C 41 54 49 4F |ED THE POPULATIO| 000005D0: 4E 3F 0D D4 48 41 54 27 53 20 57 48 41 54 20 54 |N?..HAT'S WHAT T| 000005E0: 48 45 20 4C 41 53 54 20 48 41 4C 46 20 4F 46 20 |HE LAST HALF OF | 000005F0: 54 48 45 0D 45 51 55 41 54 49 4F 4E 20 49 53 20 |THE.EQUATION IS | 00000600: 41 4C 4C 20 41 42 4F 55 54 2E 20 20 D4 48 45 20 |ALL ABOUT. .HE | 00000610: 4D 49 4E 55 53 0D 53 49 47 4E 20 53 41 59 53 20 |MINUS.SIGN SAYS | 00000620: 54 48 41 54 20 41 53 20 50 4F 50 55 4C 41 54 49 |THAT AS POPULATI| 00000630: 4F 4E 20 47 4F 45 53 20 55 50 0D 28 41 46 54 45 |ON GOES UP.(AFTE| 00000640: 52 20 41 20 50 4F 49 4E 54 29 20 49 54 20 47 4F |R A POINT) IT GO| 00000650: 45 53 20 44 4F 57 4E 20 45 56 45 4E 0D 4D 4F 52 |ES DOWN EVEN.MOR| 00000660: 45 2E 0D 0D 20 20 20 20 D7 48 45 4E 20 59 4F 55 |E... .HEN YOU| 00000670: 20 52 55 4E 20 54 48 45 20 50 52 4F 47 52 41 4D | RUN THE PROGRAM| 00000680: 2C 20 43 48 4F 4F 53 45 0D 54 4F 20 53 45 45 20 |, CHOOSE.TO SEE | 00000690: C3 C8 C1 CF D3 20 23 31 2E 20 20 D9 4F 55 20 57 |..... #1. .OU W| 000006A0: 49 4C 4C 20 42 45 20 41 53 4B 45 44 0D 54 4F 20 |ILL BE ASKED.TO | 000006B0: 49 4E 50 55 54 20 41 20 47 52 4F 57 54 48 20 46 |INPUT A GROWTH F| 000006C0: 41 43 54 4F 52 2E 20 20 CA 4F 48 4E 0D 53 55 47 |ACTOR. .OHN.SUG| 000006D0: 47 45 53 54 53 20 31 2E 39 2C 20 32 2E 34 2C 20 |GESTS 1.9, 2.4, | 000006E0: 32 2E 35 20 41 4E 44 20 32 2E 39 36 20 41 53 0D |2.5 AND 2.96 AS.| 000006F0: 52 45 41 53 4F 4E 41 42 4C 45 20 56 41 4C 55 45 |REASONABLE VALUE| 00000700: 53 2E 20 20 D4 48 45 20 53 4D 41 4C 4C 45 52 0D |S. .HE SMALLER.| 00000710: 56 41 4C 55 45 53 20 43 52 45 41 54 45 20 50 52 |VALUES CREATE PR| 00000720: 45 44 49 43 54 41 42 4C 45 20 50 4C 4F 54 53 2E |EDICTABLE PLOTS.| 00000730: 20 20 D4 48 45 0D 32 2E 39 36 20 47 52 4F 57 54 | .HE.2.96 GROWT| 00000740: 48 20 46 41 43 54 4F 52 20 57 49 4C 4C 20 54 55 |H FACTOR WILL TU| 00000750: 52 4E 20 49 4E 54 4F 0D 43 48 41 4F 53 20 42 45 |RN INTO.CHAOS BE| 00000760: 46 4F 52 45 20 54 48 45 20 45 4E 44 20 4F 46 20 |FORE THE END OF | 00000770: 54 48 45 20 53 43 52 45 45 4E 2E 0D C1 20 47 52 |THE SCREEN... GR| 00000780: 4F 57 54 48 20 46 41 43 54 4F 52 20 4F 46 20 32 |OWTH FACTOR OF 2| 00000790: 2E 39 36 20 49 53 20 54 4F 4F 20 48 49 47 48 0D |.96 IS TOO HIGH.| 000007A0: 54 4F 20 52 45 4D 41 49 4E 20 50 52 45 44 49 43 |TO REMAIN PREDIC| 000007B0: 54 41 42 4C 45 2E 20 20 C8 4F 50 45 46 55 4C 4C |TABLE. .OPEFULL| 000007C0: 59 20 54 48 45 0D 47 52 4F 57 54 48 20 46 41 43 |Y THE.GROWTH FAC| 000007D0: 54 4F 52 20 46 4F 52 20 48 55 4D 41 4E 49 54 59 |TOR FOR HUMANITY| 000007E0: 20 4F 4E 20 45 41 52 54 48 0D 49 53 20 4C 45 53 | ON EARTH.IS LES| 000007F0: 53 20 54 48 41 4E 20 32 2E 39 36 2E 0D 0D 20 20 |S THAN 2.96... | 00000800: 20 20 C9 46 20 59 4F 55 20 43 48 4F 4F 53 45 20 | .F YOU CHOOSE | 00000810: C3 C8 C1 CF D3 20 23 32 2C 20 59 4F 55 20 43 41 |..... #2, YOU CA| 00000820: 4E 0D 53 45 45 20 54 48 45 20 52 45 53 55 4C 54 |N.SEE THE RESULT| 00000830: 53 20 4F 46 20 41 4C 4C 20 4F 46 20 54 48 45 20 |S OF ALL OF THE | 00000840: 46 41 43 54 4F 52 53 0D 4D 45 4E 54 49 4F 4E 45 |FACTORS.MENTIONE| 00000850: 44 20 41 42 4F 56 45 2E 20 20 C9 54 20 49 53 20 |D ABOVE. .T IS | 00000860: 56 45 52 59 20 53 4C 4F 57 20 41 4E 44 0D 57 49 |VERY SLOW AND.WI| 00000870: 4C 4C 20 54 41 4B 45 20 41 42 4F 55 54 20 41 4E |LL TAKE ABOUT AN| 00000880: 20 48 4F 55 52 20 46 4F 52 20 49 54 20 54 4F 0D | HOUR FOR IT TO.| 00000890: 46 49 4E 49 53 48 2E 0D 20 20 20 20 D4 48 45 20 |FINISH.. .HE | 000008A0: 46 49 52 53 54 20 50 41 52 54 20 4F 46 20 54 48 |FIRST PART OF TH| 000008B0: 45 20 4C 49 4E 45 20 57 49 4C 4C 0D 52 45 50 52 |E LINE WILL.REPR| 000008C0: 45 53 45 4E 54 20 41 20 47 52 4F 57 54 48 20 46 |ESENT A GROWTH F| 000008D0: 41 43 54 4F 52 20 4F 46 20 31 2E 39 2C 20 54 48 |ACTOR OF 1.9, TH| 000008E0: 45 0D 4E 45 58 54 20 50 41 52 54 20 57 49 4C 4C |E.NEXT PART WILL| 000008F0: 20 52 45 50 52 45 53 45 4E 54 20 32 2E 34 2E 20 | REPRESENT 2.4. | 00000900: 20 C1 46 54 45 52 0D 54 48 41 54 20 59 4F 55 20 | .FTER.THAT YOU | 00000910: 57 49 4C 4C 20 53 45 45 20 54 48 45 20 50 4C 4F |WILL SEE THE PLO| 00000920: 54 54 49 4E 47 20 46 4F 52 0D 32 2E 35 20 41 4E |TTING FOR.2.5 AN| 00000930: 44 20 32 2E 39 36 2C 20 57 48 49 43 48 20 4C 45 |D 2.96, WHICH LE| 00000940: 41 44 53 20 41 47 41 49 4E 20 54 4F 0D 43 48 41 |ADS AGAIN TO.CHA| 00000950: 4F 53 2E 0D 0D 20 20 20 20 C6 4F 52 20 4D 4F 52 |OS... .OR MOR| 00000960: 45 20 49 4E 46 4F 52 4D 41 54 49 4F 4E 20 4F 4E |E INFORMATION ON| 00000970: 20 48 4F 57 20 54 4F 0D 43 48 41 4E 47 45 20 54 | HOW TO.CHANGE T| 00000980: 48 45 20 50 52 4F 47 52 41 4D 20 4C 49 53 54 49 |HE PROGRAM LISTI| 00000990: 4E 47 20 54 4F 20 46 55 52 54 48 45 52 0D 49 4C |NG TO FURTHER.IL| 000009A0: 4C 55 53 54 52 41 54 45 20 46 52 41 43 54 41 4C |LUSTRATE FRACTAL| 000009B0: 53 2C 20 53 45 45 20 54 48 45 20 C1 50 52 49 4C |S, SEE THE .PRIL| 000009C0: 0D 49 53 53 55 45 20 4F 46 20 C3 4F 4D 4D 4F 44 |.ISSUE OF .OMMOD| 000009D0: 4F 52 45 20 CD 41 47 41 5A 49 4E 45 2E 0D 0D C4 |ORE .AGAZINE....| 000009E0: C9 D3 CB 20 C6 C9 CC C5 D3 20 D4 C8 C9 D3 20 D0 |... ..... .... .| 000009F0: D2 CF C7 D2 C1 CD 20 D5 D3 C5 D3 0D 0D C5 D1 D5 |...... .........| 00000A00: C1 D4 C9 CF CE D3 2E 31 32 38 20 20 20 20 20 20 |.......128 | 00000A10: D4 2E C5 D1 D5 C1 D4 C9 CF CE D3 2E 31 32 38 0D |............128.| 00000A20: 0D 20 20 20 20 20 20 20 20 2A 2A 2A 2A 20 C5 4E |. **** .N| 00000A30: 44 20 4F 46 20 D4 45 58 54 20 2A 2A 2A 2A 0D |D OF .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
LAS, 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 MAKES THE
EQUATION 'RECURSIVE'.. THE FACTOR R I
S CALLED THE.'GROWTH RATE FACTOR' AND IS
A NUMBER.THAT YOU CAN INPUT. IT DESCRI
BES HOW.FAST A POPULATION WILL GROW. IF
YOU.CONSIDER X AS A POPULATION OF PEOPL
E,.YOU CAN IMAGINE THAT AS A POPULATION.
GROWS, THERE ARE MORE PEOPLE AROUND.TO R
EPRODUCE, SO THE POPULATION GROWS.EVEN F
ASTER. THE FIRST HALF OF THE.FORMULA, (
1+R)*X, DESCRIBES THIS... BUT WHAT IF
THERE IS A RESTRAINT.ON GROWTH? WHAT I
F THERE IS NOT.ENOUGH FOOD TO FEED THE P
OPULATION?.THAT'S WHAT THE LAST HALF OF
THE.EQUATION IS ALL ABOUT. THE MINUS.SI
GN SAYS THAT AS POPULATION GOES UP.(AFTE
R A POINT) IT GOES DOWN EVEN.MORE...
WHEN YOU RUN THE PROGRAM, CHOOSE.TO SEE
CHAOS #1. YOU WILL BE ASKED.TO INPUT A
GROWTH FACTOR. JOHN.SUGGESTS 1.9, 2.4,
2.5 AND 2.96 AS.REASONABLE VALUES. THE
SMALLER.VALUES CREATE PREDICTABLE PLOTS.
THE.2.96 GROWTH FACTOR WILL TURN INTO.
CHAOS BEFORE THE END OF THE SCREEN..A GR
OWTH FACTOR OF 2.96 IS TOO HIGH.TO REMAI
N PREDICTABLE. HOPEFULLY THE.GROWTH FAC
TOR FOR HUMANITY ON EARTH.IS LESS THAN 2
.96... IF YOU CHOOSE CHAOS #2, YOU CA
N.SEE THE RESULTS OF ALL OF THE FACTORS.
MENTIONED ABOVE. IT IS VERY SLOW AND.WI
LL TAKE ABOUT AN HOUR FOR IT TO.FINISH..
THE FIRST PART OF THE LINE WILL.REPR
ESENT A GROWTH FACTOR OF 1.9, THE.NEXT P
ART WILL REPRESENT 2.4. AFTER.THAT YOU
WILL SEE THE PLOTTING FOR.2.5 AND 2.96,
WHICH LEADS AGAIN TO.CHAOS... FOR MOR
E INFORMATION ON HOW TO.CHANGE THE PROGR
AM LISTING TO FURTHER.ILLUSTRATE FRACTAL
S, SEE THE APRIL.ISSUE OF COMMODORE MAGA
ZINE...DISK FILES THIS PROGRAM USES..EQU
ATIONS.128 T.EQUATIONS.128..
**** END OF TEXT ****.
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