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|00000510| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00000570| 75 61 72 65 73 20 61 6e | 64 20 63 75 62 65 73 2e |uares an|d cubes.|
|00000580| 20 49 6e 20 66 61 63 74 | 20 74 68 65 79 20 61 72 | In fact| they ar|
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|000005a0| 20 0a 20 20 20 20 20 20 | 20 20 58 27 20 3d 20 61 | .      |  X' = a|
|000005b0| 58 20 2b 20 63 59 20 2b | 20 50 0a 20 20 20 20 20 |X + cY +| P.     |
|000005c0| 20 20 20 59 27 20 3d 20 | 62 58 20 2b 20 64 59 20 |   Y' = |bX + dY |
|000005d0| 2b 20 51 0a 20 20 20 20 | 20 20 20 20 0a 77 68 65 |+ Q.    |    .whe|
|000005e0| 72 65 20 61 2c 62 2c 63 | 2c 64 2c 50 20 61 6e 64 |re a,b,c|,d,P and|
|000005f0| 20 51 20 61 72 65 20 63 | 6f 6e 73 74 61 6e 74 73 | Q are c|onstants|
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|00000610| 20 61 70 70 6c 79 20 6f | 6e 65 20 6f 66 20 74 68 | apply o|ne of th|
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|00000630| 6c 70 00 00 00 00 00 00 | 6a 16 00 00 46 fd ff ff |lp......|j...F...|
|00000640| eb fa 8f 04 03 00 10 61 | 0a 20 20 50 72 6f 67 72 |.......a|.  Progr|
|00000650| 61 6d 3a 20 21 49 46 53 | 0a 0a 20 20 56 65 72 73 |am: !IFS|..  Vers|
|00000660| 69 6f 6e 3a 20 31 2e 30 | 30 20 28 31 36 20 41 70 |ion: 1.0|0 (16 Ap|
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|00000680| 72 3a 20 20 4a 2e 4f 2e | 4c 69 6e 74 6f 6e 0a 20 |r:  J.O.|Linton. |
|00000690| 20 20 20 20 20 20 20 20 | 20 20 47 72 65 65 6e 61 |        |  Greena|
|000006a0| 63 72 65 73 2c 20 51 75 | 61 74 66 6f 72 64 2c 20 |cres, Qu|atford, |
|000006b0| 42 72 69 64 67 6e 6f 72 | 74 68 2c 20 53 68 72 6f |Bridgnor|th, Shro|
|000006c0| 70 73 68 69 72 65 2c 20 | 57 56 31 35 20 36 51 47 |pshire, |WV15 6QG|
|000006d0| 0a 20 20 20 20 20 20 20 | 20 20 20 0a 20 20 50 75 |.       |   .  Pu|
|000006e0| 72 70 6f 73 65 3a 20 44 | 69 73 70 6c 61 79 73 20 |rpose: D|isplays |
|000006f0| 49 46 53 20 66 72 61 63 | 74 61 6c 73 0a 20 0a 20 |IFS frac|tals. . |
|00000700| 0a 20 20 57 68 61 74 20 | 69 73 20 61 6e 20 49 46 |.  What |is an IF|
|00000710| 53 3f 0a 20 20 7e 7e 7e | 7e 7e 7e 7e 7e 7e 7e 7e |S?.  ~~~|~~~~~~~~|
|00000720| 7e 7e 7e 7e 0a 0a 20 20 | 41 6e 20 49 74 65 72 61 |~~~~..  |An Itera|
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|00000740| 74 65 6d 20 6f 72 20 49 | 46 53 20 69 73 20 61 20 |tem or I|FS is a |
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|00000760| 41 4e 53 46 4f 52 4d 41 | 54 49 4f 4e 53 20 65 61 |ANSFORMA|TIONS ea|
|00000770| 63 68 20 6f 66 20 77 68 | 69 63 68 20 69 73 20 61 |ch of wh|ich is a|
|00000780| 20 73 65 74 20 6f 66 20 | 65 71 75 61 74 69 6f 6e | set of |equation|
|00000790| 73 20 77 68 69 63 68 20 | 6d 61 70 20 61 6e 79 0a |s which |map any.|
|000007a0| 67 69 76 65 6e 20 70 6f | 69 6e 74 20 6f 6e 20 74 |given po|int on t|
|000007b0| 68 65 20 70 6c 61 6e 65 | 20 6f 6e 74 6f 20 61 6e |he plane| onto an|
|000007c0| 6f 74 68 65 72 20 75 6e | 69 71 75 65 20 70 6f 69 |other un|ique poi|
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|00000840| 75 61 72 65 73 20 61 6e | 64 20 63 75 62 65 73 2e |uares an|d cubes.|
|00000850| 20 49 6e 20 66 61 63 74 | 20 74 68 65 79 20 61 72 | In fact| they ar|
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|00000870| 20 0a 20 20 20 20 20 20 | 20 20 58 27 20 3d 20 61 | .      |  X' = a|
|00000880| 58 20 2b 20 63 59 20 2b | 20 50 0a 20 20 20 20 20 |X + cY +| P.     |
|00000890| 20 20 20 59 27 20 3d 20 | 62 58 20 2b 20 64 59 20 |   Y' = |bX + dY |
|000008a0| 2b 20 51 0a 20 20 20 20 | 20 20 20 20 0a 77 68 65 |+ Q.    |    .whe|
|000008b0| 72 65 20 61 2c 62 2c 63 | 2c 64 2c 50 20 61 6e 64 |re a,b,c|,d,P and|
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|00000980| 29 20 4d 4f 56 45 20 74 | 68 65 20 73 71 75 61 72 |) MOVE t|he squar|
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|000009e0| 20 52 4f 54 41 54 45 20 | 74 68 65 20 73 71 75 61 | ROTATE |the squa|
|000009f0| 72 65 0a 20 20 0a 20 20 | 49 6e 20 73 70 69 74 65 |re.  .  |In spite|
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|00000a20| 6e 73 66 6f 72 6d 61 74 | 69 6f 6e 73 20 61 72 65 |nsformat|ions are|
|00000a30| 20 71 75 69 74 65 0a 70 | 6f 77 65 72 66 75 6c 21 | quite.p|owerful!|
|00000a40| 0a 0a 20 20 49 6e 20 6f | 72 64 65 72 20 74 6f 20 |..  In o|rder to |
|00000a50| 70 72 6f 64 75 63 65 20 | 61 6e 20 69 74 65 72 65 |produce |an itere|
|00000a60| 73 74 69 6e 67 20 49 46 | 53 20 66 72 61 63 74 61 |sting IF|S fracta|
|00000a70| 6c 20 79 6f 75 20 6e 65 | 65 64 20 61 74 20 6c 65 |l you ne|ed at le|
|00000a80| 61 73 74 0a 74 77 6f 20 | 63 61 72 65 66 75 6c 6c |ast.two |carefull|
|00000a90| 79 20 63 68 6f 73 65 6e | 20 74 72 61 6e 73 66 6f |y chosen| transfo|
|00000aa0| 72 6d 61 74 69 6f 6e 73 | 2e 20 41 74 20 65 61 63 |rmations|. At eac|
|00000ab0| 68 20 69 74 65 72 61 74 | 69 6f 6e 2c 20 6f 6e 65 |h iterat|ion, one|
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|00000ad0| 6d 61 74 69 6f 6e 73 20 | 69 73 20 63 68 6f 73 65 |mations |is chose|
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|00000af0| 61 20 70 6f 69 6e 74 20 | 69 73 20 70 6c 6f 74 74 |a point |is plott|
|00000b00| 65 64 2e 20 49 6e 0a 67 | 65 6e 65 72 61 6c 2c 20 |ed. In.g|eneral, |
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|00000b20| 6e 67 73 20 63 61 6e 20 | 68 61 70 70 65 6e 2e 20 |ngs can |happen. |
|00000b30| 54 68 65 20 70 6f 69 6e | 74 20 63 61 6e 20 65 6e |The poin|t can en|
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|00000b50| 68 20 72 65 70 65 61 74 | 73 20 6f 76 65 72 20 61 |h repeat|s over a|
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|00000b70| 20 69 74 20 63 61 6e 20 | 73 68 6f 6f 74 20 6f 66 | it can |shoot of|
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|00000c20| 20 61 6e 64 20 77 68 69 | 63 68 20 63 61 6e 20 62 | and whi|ch can b|
|00000c30| 65 20 76 65 72 79 20 62 | 65 61 75 74 69 66 75 6c |e very b|eautiful|
|00000c40| 2e 20 49 6e 20 67 65 6e | 65 72 61 6c 2c 20 74 6f |. In gen|eral, to|
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|00000c90| 65 20 63 6f 6e 74 72 61 | 63 74 69 76 65 0a 28 69 |e contra|ctive.(i|
|00000ca0| 65 20 74 68 65 79 20 6d | 61 6b 65 20 74 68 65 20 |e they m|ake the |
|00000cb0| 70 69 63 74 75 72 65 20 | 73 6d 61 6c 6c 65 72 2e |picture |smaller.|
|00000cc0| 29 20 4f 6e 65 20 6f 66 | 20 74 68 65 20 6d 6f 73 |) One of| the mos|
|00000cd0| 74 20 73 75 72 70 72 69 | 73 69 6e 67 20 74 68 69 |t surpri|sing thi|
|00000ce0| 6e 67 73 0a 61 62 6f 75 | 74 20 61 6e 20 49 46 53 |ngs.abou|t an IFS|
|00000cf0| 20 69 73 20 74 68 61 74 | 20 74 68 65 20 73 74 61 | is that| the sta|
|00000d00| 72 74 69 6e 67 20 70 6f | 69 6e 74 20 75 73 65 64 |rting po|int used|
|00000d10| 20 74 6f 20 73 65 74 20 | 74 68 69 6e 67 73 20 67 | to set |things g|
|00000d20| 6f 69 6e 67 20 69 73 0a | 69 72 72 65 6c 65 76 61 |oing is.|irreleva|
|00000d30| 6e 74 2e 20 45 61 63 68 | 20 73 65 74 20 6f 66 20 |nt. Each| set of |
|00000d40| 74 72 61 6e 73 66 6f 72 | 6d 73 20 70 72 6f 64 75 |transfor|ms produ|
|00000d50| 63 65 73 20 69 74 73 20 | 6f 77 6e 20 75 6e 69 71 |ces its |own uniq|
|00000d60| 75 65 20 66 72 61 63 74 | 61 6c 2e 0a 0a 0a 20 20 |ue fract|al....  |
|00000d70| 48 6f 77 20 74 6f 20 75 | 73 65 20 74 68 65 20 70 |How to u|se the p|
|00000d80| 72 6f 67 72 61 6d 0a 20 | 20 7e 7e 7e 7e 7e 7e 7e |rogram. | ~~~~~~~|
|00000d90| 7e 7e 7e 7e 7e 7e 7e 7e | 7e 7e 7e 7e 7e 7e 7e 0a |~~~~~~~~|~~~~~~~.|
|00000da0| 20 20 0a 20 20 54 68 65 | 20 70 72 6f 67 72 61 6d |  .  The| program|
|00000db0| 20 69 73 20 52 49 53 43 | 2d 4f 53 20 63 6f 6d 70 | is RISC|-OS comp|
|00000dc0| 6c 69 61 6e 74 20 61 6e | 64 20 69 74 73 20 6d 65 |liant an|d its me|
|00000dd0| 6e 75 73 20 73 68 6f 75 | 6c 64 20 62 65 0a 73 65 |nus shou|ld be.se|
|00000de0| 6c 66 2d 65 78 70 6c 61 | 6e 61 74 6f 72 79 2e 20 |lf-expla|natory. |
|00000df0| 54 6f 20 6f 62 74 61 69 | 6e 20 69 6e 66 6f 72 6d |To obtai|n inform|
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