home *** CD-ROM | disk | FTP | other *** search
/ BBS in a Box 15 / BBS in a box XV-1.iso / Files / Educ / Higher Ed / A-F / Fractal Lab Kit 3.0.sit / Fractal Lab Kit 3.0 / Documentation / TeachText / Manual 3.0 (Part 1) next >
MacBinary  |  1994-09-09  |  50.4 KB  |  [TEXT/ttxt]

open in: MacOS 8.1     |     Win98     |     DOS

browse contents    |     view JSON data     |     view as text


This file was processed as: MacBinary (archive/macBinary).

ConfidenceProgramDetectionMatch TypeSupport
10% dexvert MacBinary (archive/macBinary) fallback Supported
1% dexvert Text File (text/txt) fallback Supported
100% file MacBinary II, inited, Fri Sep 9 11:12:10 1994, modified Fri Sep 9 11:12:10 1994, creator SimpleText, type ASCII, 15364 bytes "Manual 3.0 (Part 1)" , at 0x3c84 35866 bytes resource default (weak)
99% file data default
74% TrID Macintosh plain text (MacBinary) default
25% TrID MacBinary 2 default (weak)
100% siegfried fmt/1762 MacBinary (II) default
100% lsar MacBinary default


id metadata
keyvalue
macFileType[TEXT]
macFileCreator[ttxt]



hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 13 4d 61 6e 75 61 6c | 20 33 2e 30 20 28 50 61 |..Manual| 3.0 (Pa|
|00000010| 72 74 20 31 29 00 00 00 | 00 00 00 00 00 00 00 00 |rt 1)...|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 54 45 58 54 74 74 78 | 74 01 00 00 00 00 00 00 |.TEXTttx|t.......|
|00000050| 00 00 00 00 00 3c 04 00 | 00 8c 1a aa 96 2b ca aa |.....<..|.....+..|
|00000060| 96 2b ca 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.+......|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 df 82 00 00 |........|........|
|00000080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000090| 20 20 20 0d 0d 20 20 20 | 20 20 20 20 20 20 20 20 | .. | |
|000000a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000000b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000000c0| 46 52 41 43 54 41 4c 20 | 4c 41 42 20 4b 49 54 0d |FRACTAL |LAB KIT.|
|000000d0| 20 0d 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | . | |
|000000e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000000f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000100| 20 20 20 20 20 20 20 20 | 20 42 79 0d 0d 20 20 20 | | By.. |
|00000110| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000120| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000130| 20 20 20 20 20 52 6f 6e | 61 6c 64 20 54 68 6f 6d | Ron|ald Thom|
|00000140| 61 73 20 4b 6e 65 75 73 | 65 6c 0d 0d 20 20 20 20 |as Kneus|el.. |
|00000150| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000160| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000170| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 76 65 72 | | ver|
|00000180| 73 69 6f 6e 20 33 2e 30 | 0d 0d 20 20 20 20 20 20 |sion 3.0|.. |
|00000190| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000001a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000001b0| 20 20 20 20 20 53 65 70 | 74 65 6d 62 65 72 20 39 | Sep|tember 9|
|000001c0| 2c 20 31 39 39 34 0d 20 | 0d 0d 54 68 69 73 20 6d |, 1994. |..This m|
|000001d0| 61 6e 75 61 6c 20 61 6e | 64 20 74 68 65 20 73 6f |anual an|d the so|
|000001e0| 66 74 77 61 72 65 20 69 | 74 20 64 65 73 63 72 69 |ftware i|t descri|
|000001f0| 62 65 73 20 61 72 65 20 | 63 6f 70 79 72 69 67 68 |bes are |copyrigh|
|00000200| 74 a9 20 31 39 39 34 2c | 20 52 6f 6e 61 6c 64 20 |t. 1994,| Ronald |
|00000210| 4b 6e 65 75 73 65 6c 2e | 20 41 6c 6c 20 52 69 67 |Kneusel.| All Rig|
|00000220| 68 74 73 20 52 65 73 65 | 72 76 65 64 2e 20 20 4e |hts Rese|rved. N|
|00000230| 6f 20 70 61 72 74 20 6f | 66 20 74 68 69 73 20 6d |o part o|f this m|
|00000240| 61 6e 75 61 6c 20 6f 72 | 20 73 6f 66 74 77 61 72 |anual or| softwar|
|00000250| 65 20 6d 61 79 20 62 65 | 20 63 6f 70 69 65 64 20 |e may be| copied |
|00000260| 69 6e 20 61 6e 79 20 66 | 6f 72 6d 20 77 69 74 68 |in any f|orm with|
|00000270| 6f 75 74 20 74 68 65 20 | 65 78 70 72 65 73 73 65 |out the |expresse|
|00000280| 64 20 77 72 69 74 74 65 | 6e 20 63 6f 6e 73 65 6e |d writte|n consen|
|00000290| 74 20 6f 66 20 74 68 65 | 20 61 75 74 68 6f 72 2e |t of the| author.|
|000002a0| 0d 0d 54 48 45 20 41 55 | 54 48 4f 52 20 41 53 53 |..THE AU|THOR ASS|
|000002b0| 55 4d 45 53 20 4e 4f 20 | 52 45 53 50 4f 4e 53 49 |UMES NO |RESPONSI|
|000002c0| 42 49 4c 49 54 59 20 46 | 4f 52 20 41 4e 59 20 4c |BILITY F|OR ANY L|
|000002d0| 4f 53 53 20 4f 52 20 44 | 41 4d 41 47 45 20 53 55 |OSS OR D|AMAGE SU|
|000002e0| 53 54 41 49 4e 45 44 20 | 42 59 20 54 48 45 20 55 |STAINED |BY THE U|
|000002f0| 53 45 20 4f 52 20 4d 49 | 53 55 53 45 20 4f 46 20 |SE OR MI|SUSE OF |
|00000300| 54 48 49 53 20 53 4f 46 | 54 57 41 52 45 20 41 4e |THIS SOF|TWARE AN|
|00000310| 44 20 4d 41 4e 55 41 4c | 2e 20 43 41 56 45 41 54 |D MANUAL|. CAVEAT|
|00000320| 20 45 4d 50 54 4f 52 2e | 0d 0d a5 49 6e 74 72 6f | EMPTOR.|...Intro|
|00000330| 64 75 63 74 69 6f 6e 0d | 0d a5 a5 57 68 61 74 20 |duction.|...What |
|00000340| 69 73 20 74 68 69 73 20 | 61 6c 6c 20 61 62 6f 75 |is this |all abou|
|00000350| 74 3f 0d 0d 54 68 65 20 | 66 72 61 63 74 61 6c 20 |t?..The |fractal |
|00000360| 6c 61 62 20 6b 69 74 20 | 69 73 20 61 20 63 6f 6d |lab kit |is a com|
|00000370| 6d 61 6e 64 20 64 72 69 | 76 65 6e 20 73 79 73 74 |mand dri|ven syst|
|00000380| 65 6d 20 66 6f 72 20 67 | 65 6e 65 72 61 74 69 6e |em for g|eneratin|
|00000390| 67 20 61 6e 64 20 69 6e | 76 65 73 74 69 67 61 74 |g and in|vestigat|
|000003a0| 69 6e 67 20 66 72 61 63 | 74 61 6c 20 69 6d 61 67 |ing frac|tal imag|
|000003b0| 65 73 2e 20 20 49 74 20 | 69 73 20 77 72 69 74 74 |es. It |is writt|
|000003c0| 65 6e 20 75 73 69 6e 67 | 20 43 68 72 69 73 20 48 |en using| Chris H|
|000003d0| 65 69 6c 6d 61 6e 27 73 | 20 50 6f 63 6b 65 74 20 |eilman's| Pocket |
|000003e0| 46 6f 72 74 68 20 20 2c | 20 61 20 73 6d 61 6c 6c |Forth ,| a small|
|000003f0| 20 46 6f 72 74 68 20 69 | 6e 74 65 72 70 72 65 74 | Forth i|nterpret|
|00000400| 65 72 20 66 6f 72 20 74 | 68 65 20 4d 61 63 69 6e |er for t|he Macin|
|00000410| 74 6f 73 68 2e 20 20 50 | 6f 63 6b 65 74 20 46 6f |tosh. P|ocket Fo|
|00000420| 72 74 68 20 20 69 73 20 | 61 76 61 69 6c 61 62 6c |rth is |availabl|
|00000430| 65 20 76 69 61 20 61 6e | 6f 6e 79 6d 6f 75 73 20 |e via an|onymous |
|00000440| 46 54 50 20 66 72 6f 6d | 20 5f 61 72 63 68 69 76 |FTP from| _archiv|
|00000450| 65 2e 75 6d 69 63 68 2e | 65 64 75 5f 20 69 6e 20 |e.umich.|edu_ in |
|00000460| 74 68 65 20 64 69 72 65 | 63 74 6f 72 79 20 2f 6d |the dire|ctory /m|
|00000470| 61 63 2f 64 65 76 65 6c | 6f 70 6d 65 6e 74 2f 6c |ac/devel|opment/l|
|00000480| 61 6e 67 75 61 67 65 73 | 2f 2e 0d 0d 54 68 65 20 |anguages|/...The |
|00000490| 6b 69 74 20 63 6f 6e 73 | 69 73 74 73 20 6f 66 20 |kit cons|ists of |
|000004a0| 61 20 73 65 74 20 6f 66 | 20 46 6f 72 74 68 20 77 |a set of| Forth w|
|000004b0| 6f 72 64 73 20 74 68 61 | 74 20 61 6c 6c 6f 77 20 |ords tha|t allow |
|000004c0| 74 68 65 20 75 73 65 72 | 20 74 6f 20 65 61 73 69 |the user| to easi|
|000004d0| 6c 79 20 63 72 65 61 74 | 65 20 66 72 61 63 74 61 |ly creat|e fracta|
|000004e0| 6c 73 20 62 61 73 65 64 | 20 6f 6e 20 49 46 53 20 |ls based| on IFS |
|000004f0| 6d 61 70 70 69 6e 67 73 | 2e 20 20 42 65 63 61 75 |mappings|. Becau|
|00000500| 73 65 20 6f 66 20 69 74 | 27 73 20 73 6d 61 6c 6c |se of it|'s small|
|00000510| 20 73 69 7a 65 20 61 6e | 64 20 67 65 6e 65 72 61 | size an|d genera|
|00000520| 6c 69 74 79 2c 20 20 69 | 74 20 73 68 6f 75 6c 64 |lity, i|t should|
|00000530| 20 72 75 6e 20 6f 6e 20 | 76 69 72 74 75 61 6c 6c | run on |virtuall|
|00000540| 79 20 61 6c 6c 20 4d 61 | 63 69 6e 74 6f 73 68 20 |y all Ma|cintosh |
|00000550| 63 6f 6d 70 75 74 65 72 | 73 2e 20 20 42 79 20 65 |computer|s. By e|
|00000560| 6e 74 65 72 69 6e 67 20 | 73 69 6d 70 6c 65 20 63 |ntering |simple c|
|00000570| 6f 6d 6d 61 6e 64 73 20 | 74 68 65 20 75 73 65 72 |ommands |the user|
|00000580| 20 63 61 6e 20 64 65 66 | 69 6e 65 20 6d 61 70 73 | can def|ine maps|
|00000590| 2c 20 64 72 61 77 20 74 | 68 65 20 72 65 73 75 6c |, draw t|he resul|
|000005a0| 74 61 6e 74 20 66 72 61 | 63 74 61 6c 73 20 69 6e |tant fra|ctals in|
|000005b0| 20 61 20 76 61 72 69 65 | 74 79 20 6f 66 20 63 6f | a varie|ty of co|
|000005c0| 6c 6f 72 73 2c 20 73 68 | 6f 77 20 74 68 65 20 6f |lors, sh|ow the o|
|000005d0| 72 69 65 6e 74 61 74 69 | 6f 6e 20 6f 66 20 74 68 |rientati|on of th|
|000005e0| 65 20 6d 61 70 70 69 6e | 67 73 2c 20 6d 65 61 73 |e mappin|gs, meas|
|000005f0| 75 72 65 20 70 6f 73 69 | 74 69 6f 6e 73 20 77 69 |ure posi|tions wi|
|00000600| 74 68 69 6e 20 74 68 65 | 20 69 6d 61 67 65 2c 20 |thin the| image, |
|00000610| 61 6e 64 20 7a 6f 6f 6d | 20 69 6e 20 74 6f 20 76 |and zoom| in to v|
|00000620| 69 65 77 20 64 65 74 61 | 69 6c 73 2e 20 20 46 72 |iew deta|ils. Fr|
|00000630| 61 63 74 61 6c 73 20 75 | 73 69 6e 67 20 75 70 20 |actals u|sing up |
|00000640| 74 6f 20 73 65 76 65 6e | 20 6d 61 70 73 20 6d 61 |to seven| maps ma|
|00000650| 79 20 62 65 20 67 65 6e | 65 72 61 74 65 64 2e 20 |y be gen|erated. |
|00000660| 0d 0d a5 a5 57 68 79 20 | 6e 6f 74 20 63 72 65 61 |....Why |not crea|
|00000670| 74 65 20 61 20 73 74 61 | 6e 64 61 72 64 20 4d 61 |te a sta|ndard Ma|
|00000680| 63 69 6e 74 6f 73 68 20 | 61 70 70 6c 69 63 61 74 |cintosh |applicat|
|00000690| 69 6f 6e 20 66 6f 72 20 | 61 6c 6c 20 6f 66 20 74 |ion for |all of t|
|000006a0| 68 69 73 3f 0d 0d 49 20 | 75 73 65 64 20 46 6f 72 |his?..I |used For|
|000006b0| 74 68 20 66 6f 72 20 74 | 77 6f 20 72 65 61 73 6f |th for t|wo reaso|
|000006c0| 6e 73 2e 20 20 46 69 72 | 73 74 2c 20 49 20 61 6d |ns. Fir|st, I am|
|000006d0| 20 73 74 69 6c 6c 20 6c | 65 61 72 6e 69 6e 67 20 | still l|earning |
|000006e0| 74 68 65 20 6c 61 6e 67 | 75 61 67 65 20 61 6e 64 |the lang|uage and|
|000006f0| 20 74 68 6f 75 67 68 74 | 20 74 68 61 74 20 74 68 | thought| that th|
|00000700| 69 73 20 77 6f 75 6c 64 | 20 62 65 20 61 20 67 6f |is would| be a go|
|00000710| 6f 64 20 70 72 6f 6a 65 | 63 74 20 74 6f 77 61 72 |od proje|ct towar|
|00000720| 64 73 20 74 68 61 74 20 | 65 6e 64 2e 20 20 53 65 |ds that |end. Se|
|00000730| 63 6f 6e 64 6c 79 2c 20 | 20 49 20 68 61 76 65 20 |condly, | I have |
|00000740| 75 73 65 64 20 73 65 76 | 65 72 61 6c 20 66 72 61 |used sev|eral fra|
|00000750| 63 74 61 6c 20 70 72 6f | 67 72 61 6d 73 20 69 6e |ctal pro|grams in|
|00000760| 20 74 68 65 20 70 61 73 | 74 20 61 6e 64 20 77 68 | the pas|t and wh|
|00000770| 69 6c 65 20 74 68 65 79 | 20 61 72 65 20 65 78 63 |ile they| are exc|
|00000780| 65 6c 6c 65 6e 74 20 61 | 74 20 77 68 61 74 20 74 |ellent a|t what t|
|00000790| 68 65 79 20 64 6f 2c 20 | 74 68 65 79 20 61 72 65 |hey do, |they are|
|000007a0| 20 72 69 67 69 64 20 61 | 6e 64 20 69 6e 66 6c 65 | rigid a|nd infle|
|000007b0| 78 69 62 6c 65 2e 20 20 | 43 72 65 61 74 69 6e 67 |xible. |Creating|
|000007c0| 20 61 20 73 79 73 74 65 | 6d 20 6c 69 6b 65 20 74 | a syste|m like t|
|000007d0| 68 69 73 20 69 6e 20 46 | 6f 72 74 68 20 73 65 65 |his in F|orth see|
|000007e0| 6d 65 64 20 69 64 65 61 | 6c 2e 20 20 46 6f 72 74 |med idea|l. Fort|
|000007f0| 68 20 69 73 20 66 61 73 | 74 20 61 6e 64 20 68 69 |h is fas|t and hi|
|00000800| 67 68 6c 79 20 69 6e 74 | 65 72 61 63 74 69 76 65 |ghly int|eractive|
|00000810| 2e 20 20 49 74 20 69 73 | 20 61 6c 73 6f 20 73 6d |. It is| also sm|
|00000820| 61 6c 6c 20 61 6e 64 20 | 76 65 72 79 20 65 61 73 |all and |very eas|
|00000830| 69 6c 79 20 65 78 74 65 | 6e 64 65 64 2e 20 20 4e |ily exte|nded. N|
|00000840| 6f 74 20 6f 6e 6c 79 20 | 64 6f 65 73 20 74 68 65 |ot only |does the|
|00000850| 20 75 73 65 72 20 68 61 | 76 65 20 61 6c 6c 20 74 | user ha|ve all t|
|00000860| 68 65 20 66 72 61 63 74 | 61 6c 20 63 6f 6d 6d 61 |he fract|al comma|
|00000870| 6e 64 73 2c 20 62 75 74 | 20 74 68 65 79 20 61 6c |nds, but| they al|
|00000880| 73 6f 20 68 61 76 65 20 | 61 6c 6c 20 6f 66 20 46 |so have |all of F|
|00000890| 6f 72 74 68 20 73 74 69 | 6c 6c 20 61 74 20 74 68 |orth sti|ll at th|
|000008a0| 65 69 72 20 64 69 73 70 | 6f 73 61 6c 2e 20 20 41 |eir disp|osal. A|
|000008b0| 20 6c 69 74 74 6c 65 20 | 70 72 6f 67 72 61 6d 6d | little |programm|
|000008c0| 69 6e 67 20 63 61 6e 20 | 71 75 69 63 6b 6c 79 20 |ing can |quickly |
|000008d0| 65 78 74 65 6e 64 20 74 | 68 65 20 65 78 69 73 74 |extend t|he exist|
|000008e0| 69 6e 67 20 63 61 70 61 | 62 69 6c 69 74 69 65 73 |ing capa|bilities|
|000008f0| 2e 20 20 50 6f 63 6b 65 | 74 20 46 6f 72 74 68 20 |. Pocke|t Forth |
|00000900| 20 77 61 73 20 6d 79 20 | 63 68 6f 69 63 65 20 66 | was my |choice f|
|00000910| 6f 72 20 73 65 76 65 72 | 61 6c 20 72 65 61 73 6f |or sever|al reaso|
|00000920| 6e 73 2c 20 70 72 69 6d | 61 72 69 6c 79 2c 20 69 |ns, prim|arily, i|
|00000930| 74 20 69 73 20 66 72 65 | 65 20 61 6e 64 20 63 61 |t is fre|e and ca|
|00000940| 6e 20 62 65 20 66 72 65 | 65 6c 79 20 64 69 73 74 |n be fre|ely dist|
|00000950| 72 69 62 75 74 65 64 2c | 20 61 73 20 77 65 6c 6c |ributed,| as well|
|00000960| 20 61 73 20 73 75 70 70 | 6f 72 74 69 6e 67 20 66 | as supp|orting f|
|00000970| 6c 6f 61 74 69 6e 67 20 | 70 6f 69 6e 74 20 6e 75 |loating |point nu|
|00000980| 6d 62 65 72 73 20 74 6f | 20 6d 61 6b 65 20 6c 69 |mbers to| make li|
|00000990| 66 65 20 65 61 73 69 65 | 72 2e 0d 0d 4b 75 64 6f |fe easie|r...Kudo|
|000009a0| 73 20 74 6f 20 44 72 2e | 20 42 72 75 63 65 20 43 |s to Dr.| Bruce C|
|000009b0| 72 61 76 65 6e 2c 20 55 | 6e 69 76 65 72 73 69 74 |raven, U|niversit|
|000009c0| 79 20 6f 66 20 4d 65 6c | 62 6f 75 72 6e 65 2c 20 |y of Mel|bourne, |
|000009d0| 41 75 73 74 72 61 6c 69 | 61 2c 20 66 6f 72 20 61 |Australi|a, for a|
|000009e0| 6c 6c 20 68 69 73 20 68 | 65 6c 70 66 75 6c 20 63 |ll his h|elpful c|
|000009f0| 6f 6d 6d 65 6e 74 73 20 | 61 6e 64 20 73 75 67 67 |omments |and sugg|
|00000a00| 65 73 74 69 6f 6e 73 20 | 66 6f 72 20 69 6d 70 72 |estions |for impr|
|00000a10| 6f 76 69 6e 67 20 74 68 | 65 20 70 72 6f 67 72 61 |oving th|e progra|
|00000a20| 6d 2e 20 20 4b 75 64 6f | 73 20 61 6c 73 6f 0d 74 |m. Kudo|s also.t|
|00000a30| 6f 20 4d 72 2e 20 53 74 | 65 70 68 65 6e 20 47 61 |o Mr. St|ephen Ga|
|00000a40| 72 64 2c 20 41 75 73 74 | 72 61 6c 69 61 2c 20 66 |rd, Aust|ralia, f|
|00000a50| 6f 72 20 68 69 73 20 74 | 68 6f 72 6f 75 67 68 20 |or his t|horough |
|00000a60| 74 65 73 74 69 6e 67 20 | 6f 66 20 61 6e 64 20 65 |testing |of and e|
|00000a70| 6e 74 68 75 73 69 61 6d | 20 66 6f 72 20 74 68 65 |nthusiam| for the|
|00000a80| 20 70 72 6f 67 72 61 6d | 21 0d 0d 46 72 61 63 74 | program|!..Fract|
|00000a90| 61 6c 20 4c 61 62 20 4b | 69 74 20 69 73 20 66 72 |al Lab K|it is fr|
|00000aa0| 65 65 77 61 72 65 2c 20 | 20 69 66 20 79 6f 75 20 |eeware, | if you |
|00000ab0| 75 73 65 20 69 74 20 61 | 6e 64 20 68 61 76 65 20 |use it a|nd have |
|00000ac0| 61 6e 79 20 73 75 67 67 | 65 73 74 69 6f 6e 73 20 |any sugg|estions |
|00000ad0| 6f 72 20 63 6f 6d 6d 65 | 6e 74 73 20 70 6c 65 61 |or comme|nts plea|
|00000ae0| 73 65 20 6c 65 74 20 6d | 65 20 6b 6e 6f 77 20 61 |se let m|e know a|
|00000af0| 74 20 74 68 65 20 61 64 | 64 72 65 73 73 65 73 20 |t the ad|dresses |
|00000b00| 62 65 6c 6f 77 2e 20 20 | 49 20 68 61 76 65 20 70 |below. |I have p|
|00000b10| 6c 61 6e 73 20 66 6f 72 | 20 61 64 64 69 74 69 6f |lans for| additio|
|00000b20| 6e 61 6c 20 60 6d 6f 64 | 75 6c 65 73 27 20 66 6f |nal `mod|ules' fo|
|00000b30| 72 20 69 6e 76 65 73 74 | 69 67 61 74 69 6e 67 20 |r invest|igating |
|00000b40| 4d 61 6e 64 65 6c 62 72 | 6f 74 20 61 6e 64 20 4a |Mandelbr|ot and J|
|00000b50| 75 6c 69 61 20 73 65 74 | 73 2c 20 62 69 6f 6d 6f |ulia set|s, biomo|
|00000b60| 72 70 68 20 69 6d 61 67 | 65 73 2c 20 61 6e 64 20 |rph imag|es, and |
|00000b70| 63 68 61 6f 73 20 69 6e | 20 6f 6e 65 20 61 6e 64 |chaos in| one and|
|00000b80| 20 74 77 6f 20 64 69 6d | 65 6e 73 69 6f 6e 73 2e | two dim|ensions.|
|00000b90| 20 20 59 6f 75 72 20 66 | 65 65 64 62 61 63 6b 20 | Your f|eedback |
|00000ba0| 77 69 6c 6c 20 65 6e 63 | 6f 75 72 61 67 65 20 6d |will enc|ourage m|
|00000bb0| 65 20 74 6f 20 63 6f 6e | 74 69 6e 75 65 2e 20 20 |e to con|tinue. |
|00000bc0| 45 76 65 6e 20 69 66 20 | 79 6f 75 20 68 61 76 65 |Even if |you have|
|00000bd0| 20 6e 6f 20 73 70 65 63 | 69 66 69 63 20 63 6f 6d | no spec|ific com|
|00000be0| 6d 65 6e 74 2c 20 6c 65 | 74 20 6d 65 20 6b 6e 6f |ment, le|t me kno|
|00000bf0| 77 20 77 68 65 72 65 20 | 79 6f 75 20 61 72 65 20 |w where |you are |
|00000c00| 73 6f 20 49 20 63 61 6e | 20 66 6f 6c 6c 6f 77 20 |so I can| follow |
|00000c10| 74 68 65 20 70 72 6f 67 | 72 61 6d 2e 20 20 49 20 |the prog|ram. I |
|00000c20| 70 72 65 66 65 72 20 70 | 6f 73 74 63 61 72 64 73 |prefer p|ostcards|
|00000c30| 2c 20 62 75 74 20 65 6d | 61 69 6c 20 69 73 20 67 |, but em|ail is g|
|00000c40| 6f 6f 64 20 74 6f 6f 2e | 0d 0d 52 6f 6e 20 4b 6e |ood too.|..Ron Kn|
|00000c50| 65 75 73 65 6c 0d 38 37 | 32 35 20 57 65 73 74 20 |eusel.87|25 West |
|00000c60| 42 75 72 64 69 63 6b 20 | 41 76 65 0d 4d 69 6c 77 |Burdick |Ave.Milw|
|00000c70| 61 75 6b 65 65 2c 20 57 | 49 20 20 35 33 32 32 37 |aukee, W|I 53227|
|00000c80| 20 0d 55 53 41 0d 6b 6e | 65 75 73 65 6c 40 6d 73 | .USA.kn|eusel@ms|
|00000c90| 75 70 61 2e 70 61 2e 6d | 73 75 2e 65 64 75 0d 6f |upa.pa.m|su.edu.o|
|00000ca0| 72 0d 72 74 6b 40 68 65 | 72 6d 61 6e 2e 67 65 6d |r.rtk@he|rman.gem|
|00000cb0| 2e 76 61 6c 70 6f 2e 65 | 64 75 0d 0d 0d a5 46 72 |.valpo.e|du....Fr|
|00000cc0| 61 63 74 61 6c 73 20 61 | 6e 64 20 49 46 53 3a 20 |actals a|nd IFS: |
|00000cd0| 61 6e 20 6f 76 65 72 76 | 69 65 77 0d 0d 41 20 66 |an overv|iew..A f|
|00000ce0| 72 61 63 74 61 6c 20 69 | 73 20 61 20 67 65 6f 6d |ractal i|s a geom|
|00000cf0| 65 74 72 69 63 20 6f 62 | 6a 65 63 74 20 77 69 74 |etric ob|ject wit|
|00000d00| 68 20 61 20 6e 6f 6e 2d | 69 6e 74 65 67 65 72 20 |h a non-|integer |
|00000d10| 64 69 6d 65 6e 73 69 6f | 6e 2e 20 20 57 65 20 61 |dimensio|n. We a|
|00000d20| 72 65 20 75 73 65 64 20 | 74 6f 20 74 68 69 6e 6b |re used |to think|
|00000d30| 69 6e 67 20 69 6e 20 74 | 65 72 6d 73 20 6f 66 20 |ing in t|erms of |
|00000d40| 45 75 63 6c 69 64 65 61 | 6e 20 67 65 6f 6d 65 74 |Euclidea|n geomet|
|00000d50| 72 79 2c 20 74 68 61 74 | 20 69 73 2c 20 69 6e 20 |ry, that| is, in |
|00000d60| 74 65 72 6d 73 20 6f 66 | 20 70 6f 69 6e 74 73 2c |terms of| points,|
|00000d70| 20 6c 69 6e 65 73 2c 20 | 61 72 65 61 73 20 28 73 | lines, |areas (s|
|00000d80| 75 72 66 61 63 65 73 29 | 2c 20 61 6e 64 20 76 6f |urfaces)|, and vo|
|00000d90| 6c 75 6d 65 73 20 28 73 | 6f 6c 69 64 73 29 2e 20 |lumes (s|olids). |
|00000da0| 20 46 72 61 63 74 61 6c | 73 20 64 6f 20 6e 6f 74 | Fractal|s do not|
|00000db0| 20 65 61 73 69 6c 79 20 | 66 69 74 20 69 6e 20 73 | easily |fit in s|
|00000dc0| 75 63 68 20 61 20 66 72 | 61 6d 65 77 6f 72 6b 20 |uch a fr|amework |
|00000dd0| 61 6e 64 20 61 72 65 20 | 64 69 66 66 69 63 75 6c |and are |difficul|
|00000de0| 74 20 74 6f 20 63 6f 6d | 70 72 65 68 65 6e 64 20 |t to com|prehend |
|00000df0| 28 61 74 20 6c 65 61 73 | 74 20 66 6f 72 20 6d 65 |(at leas|t for me|
|00000e00| 29 2e 20 20 43 6f 6d 6d | 6f 6e 20 67 65 6f 6d 65 |). Comm|on geome|
|00000e10| 74 72 69 63 61 6c 20 6f | 62 6a 65 63 74 73 20 68 |trical o|bjects h|
|00000e20| 61 76 65 20 69 6e 74 65 | 67 65 72 20 64 69 6d 65 |ave inte|ger dime|
|00000e30| 6e 73 69 6f 6e 73 3a 0d | 0d 20 20 20 20 20 20 20 |nsions:.|. |
|00000e40| 20 20 20 20 20 20 20 20 | 20 20 20 20 4f 62 6a 65 | | Obje|
|00000e50| 63 74 20 20 20 20 20 20 | 20 20 44 69 6d 65 6e 73 |ct | Dimens|
|00000e60| 69 6f 6e 0d 20 20 20 20 | 20 20 20 20 20 20 20 20 |ion. | |
|00000e70| 20 20 20 20 20 20 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d | ==|========|
|00000e80| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 0d 20 20 20 20 |========|===. |
|00000e90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ea0| 70 6f 69 6e 74 20 20 20 | 20 20 20 20 20 20 20 20 |point | |
|00000eb0| 20 20 20 20 30 0d 20 20 | 20 20 20 20 20 20 20 20 | 0. | |
|00000ec0| 20 20 20 20 20 20 20 20 | 20 20 6c 69 6e 65 20 20 | | line |
|00000ed0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 31 | | 1|
|00000ee0| 0d 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00000ef0| 20 20 20 20 20 70 6c 61 | 6e 65 20 20 20 20 20 20 | pla|ne |
|00000f00| 20 20 20 20 20 20 20 20 | 20 32 0d 20 20 20 20 20 | | 2. |
|00000f10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 73 | | s|
|00000f20| 6f 6c 69 64 20 20 20 20 | 20 20 20 20 20 20 20 20 |olid | |
|00000f30| 20 20 20 33 0d 0d 0d 62 | 75 74 20 66 72 61 63 74 | 3...b|ut fract|
|00000f40| 61 6c 73 20 68 61 76 65 | 20 6e 6f 6e 2d 69 6e 74 |als have| non-int|
|00000f50| 65 67 65 72 20 64 69 6d | 65 6e 73 69 6f 6e 73 2c |eger dim|ensions,|
|00000f60| 20 6c 69 6b 65 20 30 2e | 36 33 2e 2e 2e 20 65 74 | like 0.|63... et|
|00000f70| 63 2e 20 20 20 48 6f 77 | 20 63 61 6e 20 74 68 69 |c. How| can thi|
|00000f80| 73 20 62 65 20 79 6f 75 | 20 73 61 79 3f 20 4c 65 |s be you| say? Le|
|00000f90| 74 27 73 20 6c 6f 6f 6b | 20 61 74 20 74 68 65 20 |t's look| at the |
|00000fa0| 73 69 6d 70 6c 65 73 74 | 20 66 72 61 63 74 61 6c |simplest| fractal|
|00000fb0| 20 6f 66 20 74 68 65 6d | 20 61 6c 6c 2c 20 74 68 | of them| all, th|
|00000fc0| 65 20 43 61 6e 74 6f 72 | 20 73 65 74 2e 0d 0d 54 |e Cantor| set...T|
|00000fd0| 6f 20 63 72 65 61 74 65 | 20 74 68 65 20 43 61 6e |o create| the Can|
|00000fe0| 74 6f 72 20 73 65 74 20 | 69 6d 61 67 69 6e 65 20 |tor set |imagine |
|00000ff0| 61 20 6c 69 6e 65 20 6f | 66 20 6c 65 6e 67 74 68 |a line o|f length|
|00001000| 20 31 2e 20 20 4e 6f 77 | 2c 20 72 65 6d 6f 76 65 | 1. Now|, remove|
|00001010| 20 74 68 65 20 6d 69 64 | 64 6c 65 20 74 68 69 72 | the mid|dle thir|
|00001020| 64 20 6f 66 20 74 68 61 | 74 20 6c 69 6e 65 2e 20 |d of tha|t line. |
|00001030| 20 52 65 6d 6f 76 65 20 | 74 68 65 20 6d 69 64 64 | Remove |the midd|
|00001040| 6c 65 20 74 68 69 72 64 | 20 6f 66 20 74 68 65 20 |le third| of the |
|00001050| 74 77 6f 20 72 65 6d 61 | 69 6e 69 6e 67 20 6c 69 |two rema|ining li|
|00001060| 6e 65 73 2e 20 20 43 6f | 6e 74 69 6e 75 65 20 72 |nes. Co|ntinue r|
|00001070| 65 6d 6f 76 69 6e 67 20 | 74 68 65 20 6d 69 64 64 |emoving |the midd|
|00001080| 6c 65 20 74 68 69 72 64 | 20 61 6e 20 69 6e 66 69 |le third| an infi|
|00001090| 6e 69 74 65 20 6e 75 6d | 62 65 72 20 6f 66 20 74 |nite num|ber of t|
|000010a0| 69 6d 65 73 2e 20 20 57 | 68 65 6e 20 79 6f 75 20 |imes. W|hen you |
|000010b0| 61 72 65 20 66 69 6e 69 | 73 68 65 64 20 74 68 65 |are fini|shed the|
|000010c0| 20 6f 62 6a 65 63 74 20 | 79 6f 75 20 77 69 6c 6c | object |you will|
|000010d0| 20 62 65 20 6c 65 66 74 | 20 77 69 74 68 20 69 73 | be left| with is|
|000010e0| 20 61 20 66 72 61 63 74 | 61 6c 20 77 69 74 68 20 | a fract|al with |
|000010f0| 61 20 64 69 6d 65 6e 73 | 69 6f 6e 20 74 68 61 74 |a dimens|ion that|
|00001100| 20 69 73 20 6e 6f 74 20 | 30 20 28 69 74 27 73 20 | is not |0 (it's |
|00001110| 6e 6f 74 20 61 20 70 6f | 69 6e 74 29 20 62 75 74 |not a po|int) but|
|00001120| 20 69 73 20 6c 65 73 73 | 20 74 68 61 6e 20 31 20 | is less| than 1 |
|00001130| 28 61 20 6c 69 6e 65 20 | 66 72 6f 6d 20 30 20 74 |(a line |from 0 t|
|00001140| 6f 20 31 20 77 6f 75 6c | 64 20 63 6f 6e 74 61 69 |o 1 woul|d contai|
|00001150| 6e 20 61 6c 6c 20 70 6f | 69 6e 74 73 2c 20 63 6c |n all po|ints, cl|
|00001160| 65 61 72 6c 79 20 61 20 | 63 61 6e 74 6f 72 20 73 |early a |cantor s|
|00001170| 65 74 20 64 6f 65 73 20 | 6e 6f 74 29 20 61 6e 64 |et does |not) and|
|00001180| 20 69 74 20 63 61 6e 20 | 62 65 20 73 68 6f 77 6e | it can |be shown|
|00001190| 20 74 68 61 74 20 74 68 | 65 20 66 69 6e 61 6c 20 | that th|e final |
|000011a0| 64 69 6d 65 6e 73 69 6f | 6e 20 69 73 20 6c 6e 32 |dimensio|n is ln2|
|000011b0| 2f 6c 6e 33 20 3d 20 30 | 2e 36 33 30 39 32 39 37 |/ln3 = 0|.6309297|
|000011c0| 35 33 36 2e 2e 2e 2e 2e | 0d 0d a5 a5 44 65 72 69 |536.....|....Deri|
|000011d0| 76 61 74 69 6f 6e 20 6f | 66 20 74 68 65 20 43 61 |vation o|f the Ca|
|000011e0| 6e 74 6f 72 20 53 65 74 | 20 64 69 6d 65 6e 73 69 |ntor Set| dimensi|
|000011f0| 6f 6e 0d 0d 4f 6e 65 20 | 70 6f 73 73 69 62 6c 65 |on..One |possible|
|00001200| 20 64 65 66 69 6e 69 74 | 69 6f 6e 20 6f 66 20 64 | definit|ion of d|
|00001210| 69 6d 65 6e 73 69 6f 6e | 2c 20 74 68 65 20 73 65 |imension|, the se|
|00001220| 6c 66 2d 73 69 6d 69 6c | 61 72 20 64 69 6d 65 6e |lf-simil|ar dimen|
|00001230| 73 69 6f 6e 2c 20 69 73 | 20 74 68 65 20 72 61 74 |sion, is| the rat|
|00001240| 69 6f 20 6f 66 20 74 68 | 65 20 6e 61 74 75 72 61 |io of th|e natura|
|00001250| 6c 20 6c 6f 67 20 6f 66 | 20 74 68 65 20 6e 75 6d |l log of| the num|
|00001260| 62 65 72 20 6f 66 20 69 | 6e 74 65 72 76 61 6c 73 |ber of i|ntervals|
|00001270| 20 4e 20 28 69 6e 20 31 | 2d 64 29 20 6f 66 20 6c | N (in 1|-d) of l|
|00001280| 65 6e 67 74 68 20 62 65 | 74 61 20 6e 65 65 64 65 |ength be|ta neede|
|00001290| 64 20 74 6f 20 63 6f 6d | 70 6c 65 74 65 6c 79 20 |d to com|pletely |
|000012a0| 63 6f 76 65 72 20 74 68 | 65 20 73 65 74 20 74 6f |cover th|e set to|
|000012b0| 20 74 68 65 20 6e 61 74 | 75 72 61 6c 20 6c 6f 67 | the nat|ural log|
|000012c0| 20 6f 66 20 74 68 65 20 | 72 65 63 69 70 72 6f 63 | of the |reciproc|
|000012d0| 61 6c 20 6f 66 20 62 65 | 74 61 2c 20 74 61 6b 65 |al of be|ta, take|
|000012e0| 6e 20 69 6e 20 74 68 65 | 20 6c 69 6d 69 74 20 74 |n in the| limit t|
|000012f0| 68 61 74 20 62 65 74 61 | 20 2d 2d 3e b0 2e 20 20 |hat beta| -->.. |
|00001300| 49 6e 20 74 68 65 20 63 | 61 73 65 20 6f 66 20 74 |In the c|ase of t|
|00001310| 68 65 20 43 61 6e 74 6f | 72 20 73 65 74 20 62 65 |he Canto|r set be|
|00001320| 74 61 3d 28 31 2f 33 29 | 5e 6e 20 77 68 65 72 65 |ta=(1/3)|^n where|
|00001330| 20 6e 20 69 73 20 74 68 | 65 20 60 6c 65 76 65 6c | n is th|e `level|
|00001340| 27 20 6f 66 20 74 68 65 | 20 73 65 74 2e 20 28 43 |' of the| set. (C|
|00001350| 68 65 63 6b 3a 20 74 68 | 65 20 73 65 63 6f 6e 64 |heck: th|e second|
|00001360| 20 6c 65 76 65 6c 20 68 | 61 73 20 74 77 6f 20 73 | level h|as two s|
|00001370| 65 63 74 69 6f 6e 73 20 | 6f 66 20 6c 65 6e 67 74 |ections |of lengt|
|00001380| 68 20 31 2f 33 20 77 68 | 69 6c 65 20 74 68 65 20 |h 1/3 wh|ile the |
|00001390| 6e 65 78 74 20 6c 65 76 | 65 6c 20 68 61 73 20 66 |next lev|el has f|
|000013a0| 6f 75 72 20 73 65 63 74 | 69 6f 6e 73 20 6f 66 20 |our sect|ions of |
|000013b0| 6c 65 6e 67 74 68 20 31 | 2f 39 20 3d 20 28 31 2f |length 1|/9 = (1/|
|000013c0| 33 29 5e 32 29 20 20 53 | 6f 20 74 68 65 20 63 6f |3)^2) S|o the co|
|000013d0| 6e 64 69 74 69 6f 6e 20 | 62 65 74 61 20 2d 2d 3e |ndition |beta -->|
|000013e0| b0 20 62 65 63 6f 6d 65 | 73 20 6e 20 2d 2d 3e b0 |. become|s n -->.|
|000013f0| 20 2e 20 20 41 6c 73 6f | 2c 20 66 6f 72 20 74 68 | . Also|, for th|
|00001400| 65 20 43 61 6e 74 6f 72 | 20 73 65 74 2c 20 74 68 |e Cantor| set, th|
|00001410| 65 20 6e 75 6d 62 65 72 | 20 6f 66 20 69 6e 74 65 |e number| of inte|
|00001420| 72 76 61 6c 73 20 74 6f | 20 63 6f 76 65 72 20 74 |rvals to| cover t|
|00001430| 68 65 20 73 65 74 20 61 | 74 20 74 68 65 20 6c 65 |he set a|t the le|
|00001440| 76 65 6c 20 6e 20 69 73 | 20 4e 3d 32 5e 6e 2e 20 |vel n is| N=2^n. |
|00001450| 20 28 43 68 65 63 6b 3a | 20 20 61 74 20 74 68 65 | (Check:| at the|
|00001460| 20 73 65 63 6f 6e 64 20 | 6c 65 76 65 6c 20 74 68 | second |level th|
|00001470| 65 72 65 20 61 72 65 20 | 32 5e 31 20 3d 20 32 20 |ere are |2^1 = 2 |
|00001480| 69 6e 74 65 72 76 61 6c | 73 2c 20 61 74 20 74 68 |interval|s, at th|
|00001490| 65 20 74 68 69 72 64 20 | 6c 65 76 65 6c 20 74 68 |e third |level th|
|000014a0| 65 72 65 20 61 72 65 20 | 32 5e 32 3d 34 20 69 6e |ere are |2^2=4 in|
|000014b0| 74 65 72 76 61 6c 73 20 | 61 6e 64 20 73 6f 20 6f |tervals |and so o|
|000014c0| 6e 2e 29 20 20 53 6f 20 | 77 65 20 77 72 69 74 65 |n.) So |we write|
|000014d0| 3a 0d ca 0d 0d 0d 0d 0d | 0d 0d 0d 54 68 65 20 43 |:.......|...The C|
|000014e0| 61 6e 74 6f 72 20 73 65 | 74 2c 20 6c 69 6b 65 20 |antor se|t, like |
|000014f0| 6f 74 68 65 72 20 70 75 | 72 65 6c 79 20 6d 61 74 |other pu|rely mat|
|00001500| 68 65 6d 61 74 69 63 61 | 6c 20 66 72 61 63 74 61 |hematica|l fracta|
|00001510| 6c 73 2c 20 69 73 20 63 | 6f 6d 70 6c 65 74 65 6c |ls, is c|ompletel|
|00001520| 79 20 73 65 6c 66 2d 73 | 69 6d 69 6c 61 72 2e 20 |y self-s|imilar. |
|00001530| 20 54 68 61 74 20 69 73 | 2c 20 69 74 20 6c 6f 6f | That is|, it loo|
|00001540| 6b 73 20 69 64 65 6e 74 | 69 63 61 6c 20 6f 6e 20 |ks ident|ical on |
|00001550| 64 69 66 66 65 72 65 6e | 74 20 73 63 61 6c 65 73 |differen|t scales|
|00001560| 20 28 61 63 74 75 61 6c | 6c 79 20 69 74 20 69 73 | (actual|ly it is|
|00001570| 20 69 6e 64 65 70 65 6e | 64 65 6e 74 20 6f 66 20 | indepen|dent of |
|00001580| 73 63 61 6c 65 29 2e 20 | 20 54 61 6b 65 20 61 20 |scale). | Take a |
|00001590| 70 69 65 63 65 20 6f 66 | 20 70 61 70 65 72 20 28 |piece of| paper (|
|000015a0| 79 6f 75 20 64 6f 20 68 | 61 76 65 20 73 63 72 61 |you do h|ave scra|
|000015b0| 70 20 70 61 70 65 72 20 | 6e 65 61 72 20 74 68 65 |p paper |near the|
|000015c0| 20 63 6f 6d 70 75 74 65 | 72 2c 20 64 6f 6e 27 74 | compute|r, don't|
|000015d0| 20 79 6f 75 3f 29 20 61 | 6e 64 20 64 72 61 77 20 | you?) a|nd draw |
|000015e0| 74 68 65 20 66 69 72 73 | 74 20 66 65 77 20 6c 69 |the firs|t few li|
|000015f0| 6e 65 73 20 6f 66 20 74 | 68 65 20 43 61 6e 74 6f |nes of t|he Canto|
|00001600| 72 20 73 65 74 2c 20 6f | 6e 65 20 62 65 6c 6f 77 |r set, o|ne below|
|00001610| 20 74 68 65 20 6f 74 68 | 65 72 3a 0d 0d ca 0d 0d | the oth|er:.....|
|00001620| 0d 0d 0d 0d 0d 0d 0d 0d | 0d 0d 0d 0d 49 66 20 79 |........|....If y|
|00001630| 6f 75 20 6c 6f 6f 6b 20 | 61 74 20 77 68 61 74 20 |ou look |at what |
|00001640| 79 6f 75 20 68 61 76 65 | 20 6a 75 73 74 20 64 72 |you have| just dr|
|00001650| 61 77 6e 20 79 6f 75 20 | 77 69 6c 6c 20 6e 6f 74 |awn you |will not|
|00001660| 69 63 65 20 74 68 61 74 | 20 69 66 20 79 6f 75 20 |ice that| if you |
|00001670| 6d 61 67 6e 69 66 79 20 | 61 20 6c 6f 77 65 72 20 |magnify |a lower |
|00001680| 6c 65 76 65 6c 20 69 74 | 20 77 69 6c 6c 20 6c 6f |level it| will lo|
|00001690| 6f 6b 20 6c 69 6b 65 20 | 6f 6e 65 20 61 62 6f 76 |ok like |one abov|
|000016a0| 65 20 69 74 2c 20 20 74 | 68 65 20 65 6e 74 69 72 |e it, t|he entir|
|000016b0| 65 20 73 65 74 20 69 73 | 20 6d 61 64 65 20 75 70 |e set is| made up|
|000016c0| 20 6f 66 20 61 6e 20 69 | 6e 66 69 6e 69 74 65 20 | of an i|nfinite |
|000016d0| 6e 75 6d 62 65 72 20 6f | 66 20 63 6f 70 69 65 73 |number o|f copies|
|000016e0| 20 6f 66 20 69 74 73 65 | 6c 66 2e 20 20 28 49 6e | of itse|lf. (In|
|000016f0| 66 69 6e 69 74 79 20 73 | 68 6f 77 73 20 75 70 20 |finity s|hows up |
|00001700| 66 72 65 71 75 65 6e 74 | 6c 79 20 77 68 65 6e 20 |frequent|ly when |
|00001710| 74 61 6c 6b 69 6e 67 20 | 61 62 6f 75 74 20 66 72 |talking |about fr|
|00001720| 61 63 74 61 6c 73 2e 29 | 20 20 41 73 20 74 68 69 |actals.)| As thi|
|00001730| 73 20 69 73 20 61 20 73 | 69 6d 70 6c 65 20 66 72 |s is a s|imple fr|
|00001740| 61 63 74 61 6c 20 69 74 | 20 69 73 20 6e 6f 74 20 |actal it| is not |
|00001750| 74 65 72 72 69 62 6c 79 | 20 69 6e 74 65 72 65 73 |terribly| interes|
|00001760| 74 69 6e 67 3b 20 74 68 | 65 20 70 72 6f 67 72 61 |ting; th|e progra|
|00001770| 6d 20 64 72 61 77 73 20 | 6d 6f 72 65 20 63 6f 6d |m draws |more com|
|00001780| 70 6c 65 78 20 66 72 61 | 63 74 61 6c 73 20 77 68 |plex fra|ctals wh|
|00001790| 65 72 65 20 6c 69 66 65 | 20 69 73 20 61 20 6c 69 |ere life| is a li|
|000017a0| 74 74 6c 65 20 6d 6f 72 | 65 20 65 78 63 69 74 69 |ttle mor|e exciti|
|000017b0| 6e 67 2e 20 20 0d 0d 54 | 68 65 79 20 61 72 65 20 |ng. ..T|hey are |
|000017c0| 64 65 66 69 6e 69 74 65 | 6c 79 20 6f 64 64 2c 20 |definite|ly odd, |
|000017d0| 62 75 74 20 66 72 61 63 | 74 61 6c 73 20 64 6f 20 |but frac|tals do |
|000017e0| 74 75 72 6e 20 75 70 20 | 69 6e 20 6d 61 6e 79 20 |turn up |in many |
|000017f0| 70 6c 61 63 65 73 20 69 | 6e 20 6e 61 74 75 72 65 |places i|n nature|
|00001800| 2c 20 74 68 65 20 6e 61 | 75 74 69 6c 75 73 20 73 |, the na|utilus s|
|00001810| 68 65 6c 6c 20 28 73 65 | 65 20 74 68 65 20 53 50 |hell (se|e the SP|
|00001820| 49 52 41 4c 29 2c 20 79 | 6f 75 72 20 6c 75 6e 67 |IRAL), y|our lung|
|00001830| 73 20 61 6e 64 20 63 69 | 72 63 75 6c 61 74 6f 72 |s and ci|rculator|
|00001840| 79 20 73 79 73 74 65 6d | 20 28 73 65 65 20 74 68 |y system| (see th|
|00001850| 65 20 54 52 45 45 29 2c | 20 65 74 63 2e 20 20 53 |e TREE),| etc. S|
|00001860| 6f 6d 65 20 70 65 6f 70 | 6c 65 20 65 76 65 6e 20 |ome peop|le even |
|00001870| 74 68 69 6e 6b 20 74 68 | 61 74 20 74 68 65 20 64 |think th|at the d|
|00001880| 69 73 74 72 69 62 75 74 | 69 6f 6e 20 6f 66 20 6d |istribut|ion of m|
|00001890| 61 74 74 65 72 20 69 6e | 20 74 68 65 20 75 6e 69 |atter in| the uni|
|000018a0| 76 65 72 73 65 20 69 73 | 20 61 20 66 72 61 63 74 |verse is| a fract|
|000018b0| 61 6c 2e 0d 0d a5 a5 57 | 68 61 74 20 61 62 6f 75 |al.....W|hat abou|
|000018c0| 74 20 66 72 61 63 74 61 | 6c 73 20 61 6e 64 20 63 |t fracta|ls and c|
|000018d0| 68 61 6f 73 3f 0d 0d 46 | 72 61 63 74 61 6c 73 20 |haos?..F|ractals |
|000018e0| 61 72 65 20 6f 66 74 65 | 6e 20 6d 65 6e 74 69 6f |are ofte|n mentio|
|000018f0| 6e 65 64 20 69 6e 20 63 | 6f 6e 6e 65 63 74 69 6f |ned in c|onnectio|
|00001900| 6e 20 77 69 74 68 20 63 | 68 61 6f 74 69 63 20 62 |n with c|haotic b|
|00001910| 65 68 61 76 69 6f 72 20 | 6f 66 20 64 79 6e 61 6d |ehavior |of dynam|
|00001920| 69 63 61 6c 20 73 79 73 | 74 65 6d 73 2e 20 20 54 |ical sys|tems. T|
|00001930| 68 65 20 6c 69 6e 6b 20 | 63 6f 6d 65 73 20 66 72 |he link |comes fr|
|00001940| 6f 6d 20 74 68 65 20 66 | 61 63 74 20 74 68 61 74 |om the f|act that|
|00001950| 20 74 68 65 20 66 69 6e | 61 6c 20 61 74 74 72 61 | the fin|al attra|
|00001960| 63 74 6f 72 20 20 20 20 | 28 61 20 73 74 72 61 6e |ctor |(a stran|
|00001970| 67 65 20 61 74 74 72 61 | 63 74 6f 72 29 20 6f 66 |ge attra|ctor) of|
|00001980| 20 61 20 64 69 73 73 69 | 70 61 74 69 76 65 20 64 | a dissi|pative d|
|00001990| 79 6e 61 6d 69 63 61 6c | 20 73 79 73 74 65 6d 20 |ynamical| system |
|000019a0| 69 73 20 61 20 66 72 61 | 63 74 61 6c 20 6f 62 6a |is a fra|ctal obj|
|000019b0| 65 63 74 20 28 73 6f 6d | 65 74 69 6d 65 73 29 2e |ect (som|etimes).|
|000019c0| 20 20 49 66 20 79 6f 75 | 20 77 61 6e 74 20 74 6f | If you| want to|
|000019d0| 20 74 61 6c 6b 20 6d 6f | 72 65 20 61 62 6f 75 74 | talk mo|re about|
|000019e0| 20 74 68 69 73 2c 20 63 | 6f 6e 74 61 63 74 20 6d | this, c|ontact m|
|000019f0| 65 20 61 74 20 74 68 65 | 20 61 62 6f 76 65 20 61 |e at the| above a|
|00001a00| 64 64 72 65 73 73 2e 0d | 0d a5 57 68 61 74 20 69 |ddress..|..What i|
|00001a10| 73 20 49 46 53 3f 0d 0d | 49 46 53 20 28 49 74 65 |s IFS?..|IFS (Ite|
|00001a20| 72 61 74 65 64 20 46 75 | 6e 63 74 69 6f 6e 20 53 |rated Fu|nction S|
|00001a30| 79 73 74 65 6d 29 20 69 | 73 20 74 68 65 20 6d 65 |ystem) i|s the me|
|00001a40| 61 6e 73 20 62 79 20 77 | 68 69 63 68 20 74 68 65 |ans by w|hich the|
|00001a50| 20 70 72 6f 67 72 61 6d | 20 67 65 6e 65 72 61 74 | program| generat|
|00001a60| 65 73 20 69 6d 61 67 65 | 73 2e 20 20 49 74 20 77 |es image|s. It w|
|00001a70| 61 73 20 64 65 76 65 6c | 6f 70 65 64 20 62 79 20 |as devel|oped by |
|00001a80| 4d 69 63 68 61 65 6c 20 | 42 61 72 6e 73 6c 65 79 |Michael |Barnsley|
|00001a90| 2e 20 20 49 46 53 20 69 | 6e 76 6f 6c 76 65 73 20 |. IFS i|nvolves |
|00001aa0| 64 65 66 69 6e 69 6e 67 | 20 61 20 6e 75 6d 62 65 |defining| a numbe|
|00001ab0| 72 20 6f 66 20 6d 61 70 | 73 20 74 68 61 74 20 69 |r of map|s that i|
|00001ac0| 6e 20 73 6f 6d 65 20 77 | 61 79 20 64 65 74 65 72 |n some w|ay deter|
|00001ad0| 6d 69 6e 65 20 77 68 61 | 74 20 74 68 65 20 66 69 |mine wha|t the fi|
|00001ae0| 6e 61 6c 20 70 72 6f 64 | 75 63 74 20 77 69 6c 6c |nal prod|uct will|
|00001af0| 20 6c 6f 6f 6b 20 6c 69 | 6b 65 20 28 6d 6f 72 65 | look li|ke (more|
|00001b00| 20 6f 6e 20 74 68 61 74 | 20 6c 61 74 65 72 29 2e | on that| later).|
|00001b10| 20 20 41 6e 20 69 6e 69 | 74 69 61 6c 20 70 6f 69 | An ini|tial poi|
|00001b20| 6e 74 20 69 73 20 63 68 | 6f 73 65 6e 20 28 74 68 |nt is ch|osen (th|
|00001b30| 65 20 6f 72 69 67 69 6e | 20 69 73 20 6e 69 63 65 |e origin| is nice|
|00001b40| 29 20 61 6e 64 20 69 74 | 65 72 61 74 65 64 20 28 |) and it|erated (|
|00001b50| 69 2e 65 2e 20 70 75 74 | 20 69 74 20 69 6e 20 2d |i.e. put| it in -|
|00001b60| 20 67 65 74 20 73 6f 6d | 65 74 68 69 6e 67 20 6f | get som|ething o|
|00001b70| 75 74 20 2d 20 70 75 74 | 20 74 68 61 74 20 73 6f |ut - put| that so|
|00001b80| 6d 65 74 68 69 6e 67 20 | 62 61 63 6b 20 69 6e 2c |mething |back in,|
|00001b90| 20 65 74 63 2e 29 20 2e | 20 20 54 68 65 73 65 20 | etc.) .| These |
|00001ba0| 61 72 65 20 6d 61 70 73 | 20 69 6e 20 74 68 65 20 |are maps| in the |
|00001bb0| 6d 61 74 68 65 6d 61 74 | 69 63 61 6c 20 73 65 6e |mathemat|ical sen|
|00001bc0| 73 65 20 2d 20 72 6f 75 | 67 68 6c 79 2c 20 61 20 |se - rou|ghly, a |
|00001bd0| 77 61 79 20 6f 66 20 74 | 72 61 6e 73 66 6f 72 6d |way of t|ransform|
|00001be0| 69 6e 67 20 61 20 63 6f | 6c 6c 65 63 74 69 6f 6e |ing a co|llection|
|00001bf0| 20 6f 66 20 70 6f 69 6e | 74 73 20 69 6e 74 6f 20 | of poin|ts into |
|00001c00| 61 6e 6f 74 68 65 72 20 | 73 70 61 63 65 20 6f 72 |another |space or|
|00001c10| 20 62 61 63 6b 20 69 6e | 74 6f 20 69 74 73 20 6f | back in|to its o|
|00001c20| 77 6e 20 73 70 61 63 65 | 20 61 73 20 69 73 20 74 |wn space| as is t|
|00001c30| 68 65 20 63 61 73 65 20 | 68 65 72 65 2e 20 20 54 |he case |here. T|
|00001c40| 68 65 20 6d 61 70 20 75 | 73 65 64 20 66 6f 72 20 |he map u|sed for |
|00001c50| 65 61 63 68 20 69 74 65 | 72 61 74 69 6f 6e 20 69 |each ite|ration i|
|00001c60| 73 20 63 68 6f 73 65 6e | 20 61 74 20 72 61 6e 64 |s chosen| at rand|
|00001c70| 6f 6d 20 62 61 73 65 64 | 20 6f 6e 20 74 68 65 20 |om based| on the |
|00001c80| 61 73 73 69 67 6e 65 64 | 20 70 72 6f 62 61 62 69 |assigned| probabi|
|00001c90| 6c 69 74 79 2c 20 74 68 | 65 20 68 69 67 68 65 72 |lity, th|e higher|
|00001ca0| 20 74 68 65 20 70 72 6f | 62 61 62 69 6c 69 74 79 | the pro|bability|
|00001cb0| 20 74 68 65 20 6d 6f 72 | 65 20 6c 69 6b 65 6c 79 | the mor|e likely|
|00001cc0| 20 74 68 61 74 20 6d 61 | 70 20 69 73 20 74 6f 20 | that ma|p is to |
|00001cd0| 62 65 20 63 68 6f 73 65 | 6e 2e 20 20 41 66 74 65 |be chose|n. Afte|
|00001ce0| 72 20 65 61 63 68 20 69 | 74 65 72 61 74 69 6f 6e |r each i|teration|
|00001cf0| 20 74 68 65 20 72 65 73 | 75 6c 74 69 6e 67 20 70 | the res|ulting p|
|00001d00| 6f 69 6e 74 20 69 73 20 | 70 6c 6f 74 74 65 64 2e |oint is |plotted.|
|00001d10| 20 20 41 73 20 74 68 69 | 73 20 70 72 6f 63 65 73 | As thi|s proces|
|00001d20| 73 20 69 73 20 63 6f 6e | 74 69 6e 75 65 64 20 74 |s is con|tinued t|
|00001d30| 68 65 20 66 72 61 63 74 | 61 6c 20 69 6d 61 67 65 |he fract|al image|
|00001d40| 20 69 73 20 62 75 69 6c | 74 2e 20 20 43 68 61 6e | is buil|t. Chan|
|00001d50| 67 69 6e 67 20 74 68 65 | 20 70 72 6f 62 61 62 69 |ging the| probabi|
|00001d60| 6c 69 74 79 20 6f 66 20 | 61 20 6d 61 70 20 63 61 |lity of |a map ca|
|00001d70| 6e 20 64 72 61 6d 61 74 | 69 63 61 6c 6c 79 20 61 |n dramat|ically a|
|00001d80| 66 66 65 63 74 20 74 68 | 65 20 72 65 73 75 6c 74 |ffect th|e result|
|00001d90| 69 6e 67 20 69 6d 61 67 | 65 2c 20 73 6f 20 69 74 |ing imag|e, so it|
|00001da0| 20 6d 69 67 68 74 20 74 | 61 6b 65 20 61 20 62 69 | might t|ake a bi|
|00001db0| 74 20 74 6f 20 67 65 74 | 20 74 68 65 20 70 69 63 |t to get| the pic|
|00001dc0| 74 75 72 65 20 60 6a 75 | 73 74 20 72 69 67 68 74 |ture `ju|st right|
|00001dd0| 27 2e 0d 0d 49 6e 20 6d | 61 74 68 65 6d 61 74 69 |'...In m|athemati|
|00001de0| 63 61 6c 20 74 65 72 6d | 73 20 61 20 32 20 64 69 |cal term|s a 2 di|
|00001df0| 6d 65 6e 73 69 6f 6e 61 | 6c 20 6d 61 70 20 69 73 |mensiona|l map is|
|00001e00| 20 6d 6f 73 74 20 65 61 | 73 69 6c 79 20 72 65 70 | most ea|sily rep|
|00001e10| 72 65 73 65 6e 74 65 64 | 20 69 6e 20 6d 61 74 72 |resented| in matr|
|00001e20| 69 78 20 66 6f 72 6d 2e | 20 20 41 20 6d 61 74 72 |ix form.| A matr|
|00001e30| 69 78 20 69 73 20 73 69 | 6d 69 6c 61 72 20 74 6f |ix is si|milar to|
|00001e40| 20 74 68 65 20 74 77 6f | 20 64 69 6d 65 6e 73 69 | the two| dimensi|
|00001e50| 6f 6e 61 6c 20 61 72 72 | 61 79 73 20 75 73 65 64 |onal arr|ays used|
|00001e60| 20 69 6e 20 6d 61 6e 79 | 20 70 72 6f 67 72 61 6d | in many| program|
|00001e70| 6d 69 6e 67 20 6c 61 6e | 67 75 61 67 65 73 2e 20 |ming lan|guages. |
|00001e80| 20 49 66 20 77 65 20 68 | 61 76 65 20 61 20 73 74 | If we h|ave a st|
|00001e90| 61 72 74 69 6e 67 20 70 | 6f 69 6e 74 20 28 78 2c |arting p|oint (x,|
|00001ea0| 79 29 20 61 6e 64 20 77 | 65 20 77 61 6e 74 20 74 |y) and w|e want t|
|00001eb0| 6f 20 66 69 6e 64 20 74 | 68 65 20 74 72 61 6e 73 |o find t|he trans|
|00001ec0| 66 6f 72 6d 65 64 20 63 | 6f 6f 72 64 69 6e 61 74 |formed c|oordinat|
|00001ed0| 65 73 2c 20 28 78 27 2c | 79 27 29 2c 20 77 65 20 |es, (x',|y'), we |
|00001ee0| 63 61 6e 20 77 72 69 74 | 65 20 74 68 65 20 74 72 |can writ|e the tr|
|00001ef0| 61 6e 73 66 6f 72 6d 61 | 74 69 6f 6e 20 69 6e 20 |ansforma|tion in |
|00001f00| 74 68 69 73 20 77 61 79 | 3a 0d ca 0d 0d 0d 0d 0d |this way|:.......|
|00001f10| 0d 54 68 69 73 20 69 73 | 20 65 71 75 69 76 61 6c |.This is| equival|
|00001f20| 65 6e 74 20 74 6f 20 77 | 72 69 74 69 6e 67 20 74 |ent to w|riting t|
|00001f30| 77 6f 20 65 71 75 61 74 | 69 6f 6e 73 3a 0d ca 0d |wo equat|ions:...|
|00001f40| 0d 0d 0d 0d 0d 54 68 65 | 20 32 78 32 20 6d 61 74 |.....The| 2x2 mat|
|00001f50| 72 69 78 20 63 6f 6e 74 | 72 6f 6c 73 20 74 68 65 |rix cont|rols the|
|00001f60| 20 72 65 6f 72 69 65 6e | 74 61 74 69 6f 6e 20 6f | reorien|tation o|
|00001f70| 66 20 74 68 65 20 69 6e | 69 74 69 61 6c 20 63 6f |f the in|itial co|
|00001f80| 6f 72 64 69 6e 61 74 65 | 20 73 79 73 74 65 6d 20 |ordinate| system |
|00001f90| 77 68 69 6c 65 20 74 68 | 65 20 76 65 63 74 6f 72 |while th|e vector|
|00001fa0| 20 28 65 20 66 29 20 69 | 73 20 61 6e 20 6f 66 66 | (e f) i|s an off|
|00001fb0| 73 65 74 20 74 6f 20 61 | 20 6e 65 77 20 6f 72 69 |set to a| new ori|
|00001fc0| 67 69 6e 20 70 6f 69 6e | 74 20 66 6f 72 20 74 68 |gin poin|t for th|
|00001fd0| 65 20 6d 61 70 2e 20 0d | 0d a5 a5 46 69 6e 64 69 |e map. .|...Findi|
|00001fe0| 6e 67 20 74 68 65 20 60 | 6d 61 67 69 63 27 20 6e |ng the `|magic' n|
|00001ff0| 75 6d 62 65 72 73 20 66 | 6f 72 20 61 6e 20 49 46 |umbers f|or an IF|
|00002000| 53 20 74 72 61 6e 73 66 | 6f 72 6d 61 74 69 6f 6e |S transf|ormation|
|00002010| 0d 0d 42 79 20 77 61 79 | 20 6f 66 20 65 78 61 6d |..By way| of exam|
|00002020| 70 6c 65 2c 20 49 20 77 | 69 6c 6c 20 73 68 6f 77 |ple, I w|ill show|
|00002030| 20 68 6f 77 20 74 6f 20 | 66 69 6e 64 20 74 68 65 | how to |find the|
|00002040| 20 6d 61 74 72 69 78 20 | 76 61 6c 75 65 73 20 74 | matrix |values t|
|00002050| 68 61 74 20 67 65 6e 65 | 72 61 74 65 20 77 68 61 |hat gene|rate wha|
|00002060| 74 20 68 61 73 20 62 65 | 63 6f 6d 65 20 6b 6e 6f |t has be|come kno|
|00002070| 77 6e 20 61 73 20 74 68 | 65 20 4d 61 6e 64 65 6c |wn as th|e Mandel|
|00002080| 62 72 6f 74 20 44 72 61 | 67 6f 6e 2e 20 20 57 68 |brot Dra|gon. Wh|
|00002090| 69 6c 65 20 74 68 65 20 | 64 72 61 67 6f 6e 20 69 |ile the |dragon i|
|000020a0| 73 20 75 73 75 61 6c 6c | 79 20 67 65 6e 65 72 61 |s usuall|y genera|
|000020b0| 74 65 64 20 61 63 63 6f | 72 64 69 6e 67 20 74 6f |ted acco|rding to|
|000020c0| 20 61 20 70 72 65 73 63 | 72 69 70 74 69 6f 6e 20 | a presc|ription |
|000020d0| 28 6c 69 6b 65 20 74 68 | 65 20 43 61 6e 74 6f 72 |(like th|e Cantor|
|000020e0| 20 73 65 74 20 61 62 6f | 76 65 29 20 69 74 20 63 | set abo|ve) it c|
|000020f0| 61 6e 20 61 6c 73 6f 20 | 62 65 20 66 6f 75 6e 64 |an also |be found|
|00002100| 20 75 73 69 6e 67 20 74 | 77 6f 20 6d 61 70 70 69 | using t|wo mappi|
|00002110| 6e 67 73 20 28 69 2e 65 | 2e 20 74 77 6f 20 6d 61 |ngs (i.e|. two ma|
|00002120| 74 72 69 63 65 73 29 2e | 20 20 0d 09 0d 52 65 63 |trices).| ...Rec|
|00002130| 61 6c 6c 69 6e 67 20 74 | 68 61 74 20 61 20 66 72 |alling t|hat a fr|
|00002140| 61 63 74 61 6c 20 69 73 | 20 6d 61 64 65 20 75 70 |actal is| made up|
|00002150| 20 6f 66 20 61 6e 20 69 | 6e 66 69 6e 69 74 65 20 | of an i|nfinite |
|00002160| 6e 75 6d 62 65 72 20 6f | 66 20 63 6f 70 69 65 73 |number o|f copies|
|00002170| 20 6f 66 20 69 74 73 65 | 6c 66 2c 20 77 65 20 6e | of itse|lf, we n|
|00002180| 65 65 64 20 6f 6e 6c 79 | 20 73 70 65 63 69 66 79 |eed only| specify|
|00002190| 20 74 68 65 20 60 66 69 | 72 73 74 27 20 63 6f 70 | the `fi|rst' cop|
|000021a0| 79 20 61 6e 64 20 74 68 | 65 20 49 46 53 20 61 6c |y and th|e IFS al|
|000021b0| 67 6f 72 69 74 68 6d 20 | 77 69 6c 6c 20 66 69 6c |gorithm |will fil|
|000021c0| 6c 20 69 6e 20 74 68 65 | 20 72 65 73 74 2e 20 20 |l in the| rest. |
|000021d0| 54 68 65 72 65 66 6f 72 | 65 2c 20 69 6d 61 67 69 |Therefor|e, imagi|
|000021e0| 6e 65 20 61 20 73 71 75 | 61 72 65 20 66 72 6f 6d |ne a squ|are from|
|000021f0| 20 30 20 74 6f 20 31 2c | 20 74 68 69 73 20 69 73 | 0 to 1,| this is|
|00002200| 20 74 68 65 20 73 74 61 | 72 74 69 6e 67 20 70 6f | the sta|rting po|
|00002210| 69 6e 74 20 61 73 20 69 | 74 20 77 65 72 65 2e 20 |int as i|t were. |
|00002220| 20 57 65 20 6d 75 73 74 | 20 74 72 61 6e 73 66 6f | We must| transfo|
|00002230| 72 6d 20 74 68 65 20 70 | 6f 69 6e 74 73 20 66 72 |rm the p|oints fr|
|00002240| 6f 6d 20 74 68 69 73 20 | 73 71 75 61 72 65 20 69 |om this |square i|
|00002250| 6e 74 6f 20 61 20 64 69 | 66 66 65 72 65 6e 74 20 |nto a di|fferent |
|00002260| 73 71 75 61 72 65 20 28 | 6f 72 20 73 71 75 61 72 |square (|or squar|
|00002270| 65 73 29 2c 20 77 68 65 | 72 65 20 74 68 65 20 6e |es), whe|re the n|
|00002280| 75 6d 62 65 72 20 6f 66 | 20 74 72 61 6e 73 66 6f |umber of| transfo|
|00002290| 72 6d 61 74 69 6f 6e 73 | 20 65 71 75 61 6c 73 20 |rmations| equals |
|000022a0| 74 68 65 20 6e 75 6d 62 | 65 72 20 6f 66 20 60 70 |the numb|er of `p|
|000022b0| 61 72 74 73 27 20 74 68 | 61 74 20 6d 61 6b 65 20 |arts' th|at make |
|000022c0| 75 70 20 74 68 65 20 66 | 72 61 63 74 61 6c 2e 20 |up the f|ractal. |
|000022d0| 20 54 68 65 20 64 72 61 | 67 6f 6e 20 63 6f 6e 73 | The dra|gon cons|
|000022e0| 69 73 74 73 20 6f 66 20 | 74 77 6f 20 70 61 72 74 |ists of |two part|
|000022f0| 73 3a 20 61 20 63 6f 6e | 74 72 61 63 74 65 64 20 |s: a con|tracted |
|00002300| 34 35 20 64 65 67 72 65 | 65 20 72 6f 74 61 74 69 |45 degre|e rotati|
|00002310| 6f 6e 20 6f 66 20 74 68 | 65 20 63 6f 6f 72 64 69 |on of th|e coordi|
|00002320| 6e 61 74 65 20 61 78 65 | 73 20 61 6e 64 20 61 20 |nate axe|s and a |
|00002330| 63 6f 6e 74 72 61 63 74 | 65 64 20 2d 34 35 20 64 |contract|ed -45 d|
|00002340| 65 67 72 65 65 20 72 6f | 74 61 74 69 6f 6e 20 28 |egree ro|tation (|
|00002350| 77 69 74 68 20 61 20 66 | 6c 69 70 29 2e 20 20 50 |with a f|lip). P|
|00002360| 65 72 68 61 70 73 20 74 | 68 65 20 62 65 73 74 20 |erhaps t|he best |
|00002370| 77 61 79 20 74 6f 20 69 | 6d 61 67 69 6e 65 20 74 |way to i|magine t|
|00002380| 68 69 73 20 69 73 20 74 | 6f 20 70 69 63 74 75 72 |his is t|o pictur|
|00002390| 65 20 61 6e 20 61 72 72 | 6f 77 3a 20 2d 2d 2d 2d |e an arr|ow: ----|
|000023a0| 2d 2d 2d 2d 2d 2d 2d 2d | 5c 66 72 6f 6d 20 30 20 |--------|\from 0 |
|000023b0| 74 6f 20 31 2c 20 74 68 | 65 20 68 65 61 64 20 6f |to 1, th|e head o|
|000023c0| 66 20 74 68 65 20 61 72 | 72 6f 77 20 69 73 20 6f |f the ar|row is o|
|000023d0| 6e 6c 79 20 61 20 68 61 | 6c 66 20 68 65 61 64 20 |nly a ha|lf head |
|000023e0| 73 6f 20 77 65 20 63 61 | 6e 20 73 65 65 20 69 66 |so we ca|n see if|
|000023f0| 20 74 68 65 72 65 20 69 | 73 20 61 20 66 6c 69 70 | there i|s a flip|
|00002400| 20 61 73 20 77 65 6c 6c | 20 61 73 20 61 20 72 6f | as well| as a ro|
|00002410| 74 61 74 69 6f 6e 20 61 | 6e 64 20 74 72 61 6e 73 |tation a|nd trans|
|00002420| 6c 61 74 69 6f 6e 2e 20 | 20 41 66 74 65 72 20 73 |lation. | After s|
|00002430| 6f 6d 65 20 74 68 6f 75 | 67 68 74 20 77 65 20 72 |ome thou|ght we r|
|00002440| 65 61 6c 69 7a 65 20 74 | 68 61 74 20 77 65 20 6e |ealize t|hat we n|
|00002450| 65 65 64 20 73 6f 6d 65 | 74 68 69 6e 67 20 6c 69 |eed some|thing li|
|00002460| 6b 65 20 74 68 65 20 66 | 6f 6c 6c 6f 77 69 6e 67 |ke the f|ollowing|
|00002470| 20 74 6f 20 67 65 6e 65 | 72 61 74 65 20 74 68 65 | to gene|rate the|
|00002480| 20 64 72 61 67 6f 6e 3a | 0d 0d 41 67 61 69 6e 20 | dragon:|..Again |
|00002490| 74 61 6b 65 20 61 20 70 | 69 65 63 65 20 6f 66 20 |take a p|iece of |
|000024a0| 70 61 70 65 72 20 61 6e | 64 20 64 72 61 77 20 61 |paper an|d draw a|
|000024b0| 20 32 20 69 6e 63 68 20 | 61 72 72 6f 77 20 61 73 | 2 inch |arrow as|
|000024c0| 20 61 62 6f 76 65 2c 20 | 74 68 65 20 68 65 61 64 | above, |the head|
|000024d0| 20 6f 66 74 68 65 20 61 | 72 72 6f 77 20 69 73 20 | ofthe a|rrow is |
|000024e0| 6f 6e 20 74 68 65 20 72 | 69 67 68 74 20 61 6e 64 |on the r|ight and|
|000024f0| 20 74 68 65 20 62 61 72 | 62 20 69 73 20 70 6f 69 | the bar|b is poi|
|00002500| 6e 74 69 6e 67 20 6e 6f | 72 74 68 2e 20 20 4e 6f |nting no|rth. No|
|00002510| 77 2c 20 64 72 61 77 20 | 61 6e 6f 74 68 65 72 20 |w, draw |another |
|00002520| 61 72 72 6f 77 20 66 72 | 6f 6d 20 74 68 65 20 6c |arrow fr|om the l|
|00002530| 65 66 74 20 65 64 67 65 | 20 6f 66 20 74 68 65 20 |eft edge| of the |
|00002540| 66 69 72 73 74 20 67 6f | 69 6e 67 20 61 74 20 61 |first go|ing at a|
|00002550| 20 34 35 20 64 65 67 72 | 65 65 20 61 6e 67 6c 65 | 45 degr|ee angle|
|00002560| 20 75 6e 74 69 6c 20 69 | 74 20 69 6e 74 65 72 73 | until i|t inters|
|00002570| 65 63 74 73 20 61 6e 20 | 69 6d 61 67 69 6e 61 72 |ects an |imaginar|
|00002580| 79 20 6c 69 6e 65 20 72 | 75 6e 6e 69 6e 67 20 6e |y line r|unning n|
|00002590| 6f 72 74 68 20 74 6f 20 | 73 6f 75 74 68 20 74 68 |orth to |south th|
|000025a0| 61 74 20 70 61 73 73 65 | 73 20 74 68 72 6f 75 67 |at passe|s throug|
|000025b0| 68 20 74 68 65 20 6d 69 | 64 70 6f 69 6e 74 20 6f |h the mi|dpoint o|
|000025c0| 66 20 74 68 65 20 66 69 | 72 73 74 20 6c 69 6e 65 |f the fi|rst line|
|000025d0| 2e 20 20 20 44 72 61 77 | 20 74 68 65 20 62 61 72 |. Draw| the bar|
|000025e0| 62 20 6f 66 20 74 68 69 | 73 20 61 72 72 6f 77 20 |b of thi|s arrow |
|000025f0| 6f 6e 20 74 68 65 20 6c | 65 66 74 20 73 69 64 65 |on the l|eft side|
|00002600| 20 6f 66 20 74 68 65 20 | 72 69 67 68 74 20 65 6e | of the |right en|
|00002610| 64 70 6f 69 6e 74 20 6f | 66 20 74 68 69 73 20 6c |dpoint o|f this l|
|00002620| 69 6e 65 2e 20 20 46 69 | 6e 61 6c 6c 79 2c 20 63 |ine. Fi|nally, c|
|00002630| 6f 6d 70 6c 65 74 65 20 | 74 68 65 20 74 72 69 61 |omplete |the tria|
|00002640| 6e 67 6c 65 20 61 6e 64 | 20 64 72 61 77 20 74 68 |ngle and| draw th|
|00002650| 65 20 62 61 72 62 20 6f | 66 20 74 68 69 73 20 61 |e barb o|f this a|
|00002660| 72 72 6f 77 20 6f 6e 20 | 74 68 65 20 6c 65 66 74 |rrow on |the left|
|00002670| 20 73 69 64 65 20 61 6e | 64 20 74 6f 75 63 68 69 | side an|d touchi|
|00002680| 6e 67 20 74 68 65 20 68 | 65 61 64 20 6f 66 20 74 |ng the h|ead of t|
|00002690| 68 65 20 73 65 63 6f 6e | 64 20 61 72 72 6f 77 2e |he secon|d arrow.|
|000026a0| 20 57 68 65 6e 20 79 6f | 75 20 61 72 65 20 66 69 | When yo|u are fi|
|000026b0| 6e 69 73 68 65 64 20 79 | 6f 75 20 77 69 6c 6c 20 |nished y|ou will |
|000026c0| 68 61 76 65 20 73 6f 6d | 65 74 68 69 6e 67 20 6c |have som|ething l|
|000026d0| 69 6b 65 20 74 68 69 73 | 3a 20 0d ca 0d 0d 0d 0d |ike this|: ......|
|000026e0| 0d 0d 0d 0d 0d 0d 0d 0d | 0d 0d 0d 0d 0d 0d 0d 77 |........|.......w|
|000026f0| 68 65 72 65 20 74 68 65 | 20 64 69 72 65 63 74 69 |here the| directi|
|00002700| 6f 6e 73 20 6f 66 20 74 | 68 65 20 61 72 72 6f 77 |ons of t|he arrow|
|00002710| 20 68 65 61 64 73 20 61 | 72 65 20 69 6e 64 69 63 | heads a|re indic|
|00002720| 61 74 65 64 2e 20 20 46 | 69 6e 61 6c 6c 79 2c 20 |ated. F|inally, |
|00002730| 63 6f 6d 70 6c 65 74 65 | 20 65 61 63 68 20 6f 66 |complete| each of|
|00002740| 20 74 68 65 20 74 68 72 | 65 65 20 73 71 75 61 72 | the thr|ee squar|
|00002750| 65 73 20 64 65 66 69 6e | 65 64 20 62 79 20 74 68 |es defin|ed by th|
|00002760| 65 20 61 72 72 6f 77 73 | 20 61 73 20 6f 6e 65 20 |e arrows| as one |
|00002770| 65 64 67 65 2e 20 20 0d | 0d 4e 6f 77 20 63 6f 6d |edge. .|.Now com|
|00002780| 65 73 20 74 68 65 20 66 | 75 6e 20 70 61 72 74 2c |es the f|un part,|
|00002790| 20 20 68 6f 77 20 64 6f | 20 77 65 20 63 68 61 6e | how do| we chan|
|000027a0| 67 65 20 74 68 65 20 64 | 72 61 77 69 6e 67 20 69 |ge the d|rawing i|
|000027b0| 6e 74 6f 20 74 68 65 20 | 6e 75 6d 62 65 72 73 20 |nto the |numbers |
|000027c0| 20 66 6f 72 20 74 68 65 | 20 6d 61 70 73 3f 20 20 | for the| maps? |
|000027d0| 54 6f 20 66 69 6e 64 20 | 74 68 65 20 6d 61 70 73 |To find |the maps|
|000027e0| 20 77 65 20 6e 65 65 64 | 20 74 6f 20 73 6f 6c 76 | we need| to solv|
|000027f0| 65 2c 20 66 6f 72 20 65 | 61 63 68 20 6d 61 70 2c |e, for e|ach map,|
|00002800| 20 74 77 6f 20 73 79 73 | 74 65 6d 73 20 6f 66 20 | two sys|tems of |
|00002810| 74 68 72 65 65 20 6c 69 | 6e 65 61 72 20 65 71 75 |three li|near equ|
|00002820| 61 74 69 6f 6e 73 20 73 | 69 6e 63 65 20 74 68 65 |ations s|ince the|
|00002830| 72 65 20 61 72 65 20 73 | 69 78 20 6e 75 6d 62 65 |re are s|ix numbe|
|00002840| 72 73 20 74 6f 20 66 69 | 6e 64 2e 20 20 54 6f 20 |rs to fi|nd. To |
|00002850| 77 72 69 74 65 20 74 68 | 65 20 73 69 78 20 65 71 |write th|e six eq|
|00002860| 75 61 74 69 6f 6e 73 20 | 77 65 20 6d 75 73 74 20 |uations |we must |
|00002870| 6b 6e 6f 77 20 77 68 65 | 72 65 20 61 74 20 6c 65 |know whe|re at le|
|00002880| 61 73 74 20 74 68 72 65 | 65 20 70 6f 69 6e 74 73 |ast thre|e points|
|00002890| 20 6f 66 20 74 68 65 20 | 6f 72 69 67 69 6e 61 6c | of the |original|
|000028a0| 20 73 71 75 61 72 65 20 | 28 74 68 65 20 6f 6e 65 | square |(the one|
|000028b0| 20 66 72 6f 6d 20 30 20 | 74 6f 20 31 29 20 6d 61 | from 0 |to 1) ma|
|000028c0| 70 20 74 6f 20 69 6e 20 | 74 68 65 20 6e 65 77 20 |p to in |the new |
|000028d0| 6d 61 70 73 2e 20 20 54 | 68 69 73 20 69 73 20 77 |maps. T|his is w|
|000028e0| 68 65 72 65 20 74 68 65 | 20 61 72 72 6f 77 20 68 |here the| arrow h|
|000028f0| 65 61 64 20 64 69 72 65 | 63 74 69 6f 6e 73 20 62 |ead dire|ctions b|
|00002900| 65 63 6f 6d 65 20 69 6d | 70 6f 72 74 61 6e 74 2e |ecome im|portant.|
|00002910| 20 20 54 68 65 20 61 72 | 72 6f 77 20 64 65 74 65 | The ar|row dete|
|00002920| 72 6d 69 6e 65 73 20 74 | 77 6f 20 70 6f 69 6e 74 |rmines t|wo point|
|00002930| 73 20 66 6f 72 20 75 73 | 2c 20 74 68 65 20 68 65 |s for us|, the he|
|00002940| 61 64 20 61 6e 64 20 74 | 68 65 20 74 61 69 6c 2c |ad and t|he tail,|
|00002950| 20 77 68 69 6c 65 20 74 | 68 65 20 6c 61 73 74 20 | while t|he last |
|00002960| 70 6f 69 6e 74 20 63 61 | 6e 20 62 65 20 65 69 74 |point ca|n be eit|
|00002970| 68 65 72 20 6f 66 20 74 | 68 65 20 74 77 6f 20 63 |her of t|he two c|
|00002980| 6f 72 6e 65 72 73 20 6f | 66 20 74 68 65 20 6f 72 |orners o|f the or|
|00002990| 69 67 69 6e 61 6c 20 73 | 71 75 61 72 65 20 61 6e |iginal s|quare an|
|000029a0| 64 20 77 68 65 72 65 20 | 74 68 65 79 20 6d 61 70 |d where |they map|
|000029b0| 20 74 6f 20 69 6e 20 74 | 68 65 20 66 69 6e 61 6c | to in t|he final|
|000029c0| 20 73 71 75 61 72 65 2e | 20 53 6f 2c 20 74 6f 20 | square.| So, to |
|000029d0| 74 68 69 73 20 65 6e 64 | 2c 20 6c 61 62 65 6c 20 |this end|, label |
|000029e0| 74 68 65 20 74 61 69 6c | 20 61 6e 64 20 68 65 61 |the tail| and hea|
|000029f0| 64 20 6f 66 20 74 68 65 | 20 66 69 72 73 74 20 61 |d of the| first a|
|00002a00| 72 72 6f 77 20 64 72 61 | 77 6e 20 28 61 31 2c 61 |rrow dra|wn (a1,a|
|00002a10| 32 29 20 61 6e 64 20 28 | 62 31 2c 62 32 29 20 72 |2) and (|b1,b2) r|
|00002a20| 65 73 70 65 63 74 69 76 | 65 6c 79 2c 20 61 6e 64 |espectiv|ely, and|
|00002a30| 20 6c 61 62 65 6c 20 74 | 68 65 20 63 6f 72 6e 65 | label t|he corne|
|00002a40| 72 20 6f 66 20 74 68 65 | 20 73 71 75 61 72 65 20 |r of the| square |
|00002a50| 61 62 6f 76 65 20 28 61 | 31 2c 61 32 29 20 61 73 |above (a|1,a2) as|
|00002a60| 20 28 63 31 2c 63 32 29 | 2e 20 20 54 68 65 73 65 | (c1,c2)|. These|
|00002a70| 20 61 72 65 20 74 68 65 | 20 6f 72 69 67 69 6e 61 | are the| origina|
|00002a80| 6c 20 74 68 72 65 65 20 | 70 6f 69 6e 74 73 2c 20 |l three |points, |
|00002a90| 6e 6f 77 20 6c 61 62 65 | 6c 20 74 68 65 20 63 6f |now labe|l the co|
|00002aa0| 72 72 65 73 70 6f 6e 64 | 69 6e 67 20 70 6f 69 6e |rrespond|ing poin|
|00002ab0| 74 73 20 69 6e 20 74 68 | 65 20 73 65 63 6f 6e 64 |ts in th|e second|
|00002ac0| 20 73 71 75 61 72 65 20 | 28 74 68 65 20 6f 6e 65 | square |(the one|
|00002ad0| 20 61 74 20 61 20 70 6f | 73 69 74 69 76 65 20 34 | at a po|sitive 4|
|00002ae0| 35 20 64 65 67 72 65 65 | 20 61 6e 67 6c 65 20 74 |5 degree| angle t|
|00002af0| 6f 20 74 68 65 20 66 69 | 72 73 74 29 20 61 73 20 |o the fi|rst) as |
|00002b00| 28 41 31 2c 41 32 29 20 | 66 6f 72 20 74 68 65 20 |(A1,A2) |for the |
|00002b10| 74 61 69 6c 20 28 69 6e | 20 74 68 69 73 20 63 61 |tail (in| this ca|
|00002b20| 73 65 20 74 68 65 79 20 | 61 72 65 20 74 68 65 20 |se they |are the |
|00002b30| 73 61 6d 65 20 70 6f 69 | 6e 74 29 20 61 6e 64 20 |same poi|nt) and |
|00002b40| 28 42 31 2c 42 32 29 20 | 66 6f 72 20 74 68 65 20 |(B1,B2) |for the |
|00002b50| 68 65 61 64 2e 20 20 4c | 61 62 65 6c 20 74 68 65 |head. L|abel the|
|00002b60| 20 66 61 72 74 68 65 73 | 74 20 6c 65 66 74 20 63 | farthes|t left c|
|00002b70| 6f 72 6e 65 72 20 6f 66 | 20 74 68 65 20 73 71 75 |orner of| the squ|
|00002b80| 61 72 65 20 28 43 31 2c | 43 32 29 2e 20 20 0d 0d |are (C1,|C2). ..|
|00002b90| 4f 6e 63 65 20 74 68 69 | 73 20 69 73 20 64 6f 6e |Once thi|s is don|
|00002ba0| 65 2c 20 77 65 20 63 61 | 6e 20 77 72 69 74 65 20 |e, we ca|n write |
|00002bb0| 74 68 65 20 66 6f 6c 6c | 6f 77 69 6e 67 20 73 69 |the foll|owing si|
|00002bc0| 78 20 65 71 75 61 74 69 | 6f 6e 73 20 74 6f 20 64 |x equati|ons to d|
|00002bd0| 65 74 65 72 6d 69 6e 65 | 20 74 68 65 20 66 69 72 |etermine| the fir|
|00002be0| 73 74 20 6d 61 70 3a 0d | 0d 20 20 41 31 20 3d 20 |st map:.|. A1 = |
|00002bf0| 61 31 2a 61 20 2b 20 61 | 32 2a 62 20 2b 20 65 0d |a1*a + a|2*b + e.|
|00002c00| 20 20 42 31 20 3d 20 62 | 31 2a 61 20 2b 20 62 32 | B1 = b|1*a + b2|
|00002c10| 2a 62 20 2b 20 65 0d 20 | 20 43 31 20 3d 20 63 31 |*b + e. | C1 = c1|
|00002c20| 2a 61 20 2b 20 63 32 2a | 62 20 2b 20 65 0d 0d 61 |*a + c2*|b + e..a|
|00002c30| 6e 64 0d 0d 20 20 41 32 | 20 3d 20 61 31 2a 63 20 |nd.. A2| = a1*c |
|00002c40| 2b 20 61 32 2a 64 20 2b | 20 66 0d 20 20 42 32 20 |+ a2*d +| f. B2 |
|00002c50| 3d 20 62 31 2a 63 20 2b | 20 62 32 2a 64 20 2b 20 |= b1*c +| b2*d + |
|00002c60| 66 0d 20 20 43 32 20 3d | 20 63 31 2a 63 20 2b 20 |f. C2 =| c1*c + |
|00002c70| 63 32 2a 64 20 2b 20 66 | 0d 0d 49 6e 20 6f 72 64 |c2*d + f|..In ord|
|00002c80| 65 72 20 74 6f 20 67 65 | 74 20 61 63 74 75 61 6c |er to ge|t actual|
|00002c90| 20 6e 75 6d 62 65 72 73 | 20 77 65 20 6e 65 65 64 | numbers| we need|
|00002ca0| 20 74 6f 20 69 6d 70 6f | 73 65 20 61 20 63 6f 6f | to impo|se a coo|
|00002cb0| 72 64 69 6e 61 74 65 20 | 73 79 73 74 65 6d 2e 20 |rdinate |system. |
|00002cc0| 20 44 72 61 77 20 61 6e | 20 78 20 61 6e 64 20 79 | Draw an| x and y|
|00002cd0| 20 61 78 69 73 20 77 68 | 65 72 65 20 74 68 65 20 | axis wh|ere the |
|00002ce0| 66 69 72 73 74 20 61 72 | 72 6f 77 20 67 6f 65 73 |first ar|row goes|
|00002cf0| 20 66 72 6f 6d 20 30 20 | 74 6f 20 31 20 6f 6e 20 | from 0 |to 1 on |
|00002d00| 74 68 65 20 78 20 61 78 | 69 73 20 61 6e 64 20 6c |the x ax|is and l|
|00002d10| 65 66 74 20 65 64 67 65 | 20 6f 66 20 74 68 65 20 |eft edge| of the |
|00002d20| 66 69 72 73 74 20 73 71 | 75 61 72 65 20 67 6f 65 |first sq|uare goe|
|00002d30| 73 20 66 72 6f 6d 20 30 | 20 74 6f 20 31 20 6f 6e |s from 0| to 1 on|
|00002d40| 20 74 68 65 20 79 20 61 | 78 69 73 2e 20 20 49 6e | the y a|xis. In|
|00002d50| 20 74 68 69 73 20 63 6f | 6f 72 64 69 6e 61 74 65 | this co|ordinate|
|00002d60| 20 73 79 73 74 65 6d 2c | 20 28 61 31 2c 61 32 29 | system,| (a1,a2)|
|00002d70| 3d 28 30 2c 30 29 3b 20 | 28 62 31 2c 62 32 29 3d |=(0,0); |(b1,b2)=|
|00002d80| 28 31 2c 30 29 3b 20 28 | 63 31 2c 63 32 29 3d 28 |(1,0); (|c1,c2)=(|
|00002d90| 30 2c 31 29 20 61 6e 64 | 20 74 68 65 20 70 6f 69 |0,1) and| the poi|
|00002da0| 6e 74 73 20 66 6f 72 20 | 74 68 65 66 69 72 73 74 |nts for |thefirst|
|00002db0| 20 6d 61 70 20 61 72 65 | 20 28 41 31 2c 41 32 29 | map are| (A1,A2)|
|00002dc0| 3d 28 30 2c 30 29 3b 20 | 28 42 31 2c 42 32 29 3d |=(0,0); |(B1,B2)=|
|00002dd0| 28 30 2e 35 2c 30 2e 35 | 29 3b 20 28 43 31 2c 43 |(0.5,0.5|); (C1,C|
|00002de0| 32 29 3d 28 2d 30 2e 35 | 2c 30 2e 35 29 2e 20 20 |2)=(-0.5|,0.5). |
|00002df0| 54 68 65 20 76 61 6c 75 | 65 73 20 66 6f 72 20 74 |The valu|es for t|
|00002e00| 68 65 20 6d 61 74 72 69 | 78 20 61 6e 64 20 76 65 |he matri|x and ve|
|00002e10| 63 74 6f 72 20 61 72 65 | 20 66 6f 75 6e 64 20 62 |ctor are| found b|
|00002e20| 79 20 73 6f 6c 76 69 6e | 67 20 74 68 65 20 74 77 |y solvin|g the tw|
|00002e30| 6f 20 73 79 73 74 65 6d | 73 2e 20 20 43 72 61 6d |o system|s. Cram|
|00002e40| 65 72 27 73 20 72 75 6c | 65 20 61 6c 6c 6f 77 73 |er's rul|e allows|
|00002e50| 20 74 68 65 20 73 6f 6c | 75 74 69 6f 6e 73 20 74 | the sol|utions t|
|00002e60| 6f 20 62 65 20 77 72 69 | 74 74 65 6e 20 61 73 3a |o be wri|tten as:|
|00002e70| 0d ca 0d 0d 0d 0d 0d 0d | 0d 0d 0d 0d ca 0d 0d 0d |........|........|
|00002e80| 0d 0d 0d 0d 0d 0d 0d ca | 0d 0d 0d 0d 0d 0d 0d 0d |........|........|
|00002e90| 0d 0d 57 68 65 72 65 20 | 74 68 65 20 76 65 72 74 |..Where |the vert|
|00002ea0| 69 63 61 6c 20 6c 69 6e | 65 73 20 72 65 70 72 65 |ical lin|es repre|
|00002eb0| 73 65 6e 74 20 74 68 65 | 20 64 65 74 65 72 6d 69 |sent the| determi|
|00002ec0| 6e 61 6e 74 2e 20 20 54 | 68 65 72 65 20 65 78 69 |nant. T|here exi|
|00002ed0| 73 74 73 20 61 20 63 6f | 72 72 65 73 70 6f 6e 64 |sts a co|rrespond|
|00002ee0| 69 6e 67 20 73 65 74 20 | 66 6f 72 20 74 68 65 20 |ing set |for the |
|00002ef0| 63 2c 20 64 2c 20 61 6e | 64 20 66 20 76 61 6c 75 |c, d, an|d f valu|
|00002f00| 65 73 2e 20 20 57 69 74 | 68 20 74 68 65 73 65 20 |es. Wit|h these |
|00002f10| 77 65 20 66 69 6e 64 20 | 74 68 61 74 20 74 68 65 |we find |that the|
|00002f20| 20 74 72 61 6e 73 66 6f | 72 6d 61 74 69 6f 6e 73 | transfo|rmations|
|00002f30| 20 61 72 65 3a 0d ca 0d | 0d 0d 0d 0d 0d 0d 0d 0d | are:...|........|
|00002f40| 49 20 77 69 6c 6c 20 6c | 65 61 76 65 20 74 68 65 |I will l|eave the|
|00002f50| 20 61 63 74 75 61 6c 20 | 73 6f 6c 75 74 69 6f 6e | actual |solution|
|00002f60| 20 61 73 20 61 6e 20 65 | 78 65 72 63 69 73 65 20 | as an e|xercise |
|00002f70| 66 6f 72 20 74 68 65 20 | 72 65 61 64 65 72 2e 0d |for the |reader..|
|00002f80| 0d 54 68 65 20 6c 61 73 | 74 20 74 68 69 6e 67 20 |.The las|t thing |
|00002f90| 74 6f 20 63 6f 6e 73 69 | 64 65 72 20 69 73 20 77 |to consi|der is w|
|00002fa0| 68 61 74 20 73 6f 72 74 | 20 6f 66 20 70 72 6f 62 |hat sort| of prob|
|00002fb0| 61 62 69 6c 69 74 79 20 | 77 65 20 77 61 6e 74 20 |ability |we want |
|00002fc0| 74 6f 20 61 73 73 69 67 | 6e 20 74 6f 20 65 61 63 |to assig|n to eac|
|00002fd0| 68 20 6f 66 20 74 68 65 | 73 65 20 6d 61 70 73 2e |h of the|se maps.|
|00002fe0| 20 20 53 69 6e 63 65 20 | 74 68 65 72 65 20 69 73 | Since |there is|
|00002ff0| 20 6e 6f 20 72 65 61 73 | 6f 6e 20 74 6f 20 66 61 | no reas|on to fa|
|00003000| 76 6f 72 20 6f 6e 65 20 | 6d 61 70 20 74 6f 20 61 |vor one |map to a|
|00003010| 6e 6f 74 68 65 72 20 77 | 65 20 63 61 6e 20 69 6e |nother w|e can in|
|00003020| 20 74 68 69 73 20 63 61 | 73 65 20 67 65 74 20 61 | this ca|se get a|
|00003030| 77 61 79 20 77 69 74 68 | 20 61 20 70 72 6f 62 61 |way with| a proba|
|00003040| 62 69 6c 69 74 79 20 6f | 66 20 30 2e 35 20 66 6f |bility o|f 0.5 fo|
|00003050| 72 20 65 61 63 68 20 28 | 72 65 6d 65 6d 62 65 72 |r each (|remember|
|00003060| 2c 20 70 72 6f 62 61 62 | 69 6c 69 74 69 65 73 20 |, probab|ilities |
|00003070| 73 68 6f 75 6c 64 20 61 | 64 64 20 74 6f 20 31 29 |should a|dd to 1)|
|00003080| 2e 20 20 54 68 69 73 20 | 69 73 20 6e 6f 74 20 61 |. This |is not a|
|00003090| 6c 77 61 79 73 20 74 68 | 65 20 63 61 73 65 2c 20 |lways th|e case, |
|000030a0| 74 68 6f 75 67 68 2e 0d | 09 0d 54 68 65 72 65 20 |though..|..There |
|000030b0| 61 72 65 20 6d 61 6e 79 | 20 67 6f 6f 64 20 62 6f |are many| good bo|
|000030c0| 6f 6b 73 20 6f 6e 20 66 | 72 61 63 74 61 6c 73 20 |oks on f|ractals |
|000030d0| 61 6e 64 20 63 68 61 6f | 73 20 61 74 20 61 6c 6c |and chao|s at all|
|000030e0| 20 6c 65 76 65 6c 73 2c | 20 63 68 65 63 6b 20 74 | levels,| check t|
|000030f0| 68 65 20 6c 6f 63 61 6c | 20 62 6f 6f 6b 20 73 74 |he local| book st|
|00003100| 6f 72 65 20 6f 72 20 6c | 69 62 72 61 72 79 2e 20 |ore or l|ibrary. |
|00003110| 20 54 68 65 20 62 6f 6f | 6b 20 7b 5c 65 6d 20 43 | The boo|k {\em C|
|00003120| 68 61 6f 73 3a 20 54 68 | 65 20 4d 61 6b 69 6e 67 |haos: Th|e Making|
|00003130| 20 6f 66 20 61 20 4e 65 | 77 20 53 63 69 65 6e 63 | of a Ne|w Scienc|
|00003140| 65 7d 20 62 79 20 4a 6f | 68 6e 20 47 6c 65 69 6b |e} by Jo|hn Gleik|
|00003150| 20 69 73 20 61 20 67 6f | 6f 64 20 70 6c 61 63 65 | is a go|od place|
|00003160| 20 74 6f 20 73 74 61 72 | 74 2c 20 74 68 6f 75 67 | to star|t, thoug|
|00003170| 68 20 69 74 20 69 73 20 | 6c 65 61 6e 20 6f 6e 20 |h it is |lean on |
|00003180| 74 68 65 20 74 65 63 68 | 6e 69 63 61 6c 20 61 73 |the tech|nical as|
|00003190| 70 65 63 74 2e 0d 0d a5 | a5 47 65 74 74 69 6e 67 |pect....|.Getting|
|000031a0| 20 53 74 61 72 74 65 64 | 0d 0d 54 68 65 20 49 46 | Started|..The IF|
|000031b0| 53 20 6d 6f 64 75 6c 65 | 20 69 6e 63 6c 75 64 65 |S module| include|
|000031c0| 73 20 74 68 65 20 46 72 | 61 63 74 61 6c 20 4c 61 |s the Fr|actal La|
|000031d0| 62 20 4b 69 74 20 61 70 | 70 6c 69 63 61 74 69 6f |b Kit ap|plicatio|
|000031e0| 6e 20 61 6e 64 20 74 68 | 65 20 64 6f 63 75 6d 65 |n and th|e docume|
|000031f0| 6e 74 61 74 69 6f 6e 2c | 20 64 65 6d 6f 20 61 6e |ntation,| demo an|
|00003200| 64 20 6d 61 70 73 20 66 | 6f 6c 64 65 72 73 2e 20 |d maps f|olders. |
|00003210| 20 54 68 65 20 70 72 6f | 67 72 61 6d 20 73 74 61 | The pro|gram sta|
|00003220| 72 74 73 20 69 6e 20 69 | 6e 74 65 72 61 63 74 69 |rts in i|nteracti|
|00003230| 76 65 20 6d 6f 64 65 20 | 28 69 2e 65 2e 20 69 6e |ve mode |(i.e. in|
|00003240| 20 46 6f 72 74 68 29 2e | 20 20 54 68 65 72 65 20 | Forth).| There |
|00003250| 69 73 20 61 20 6d 6f 75 | 73 65 20 64 72 69 76 65 |is a mou|se drive|
|00003260| 6e 20 73 68 65 6c 6c 20 | 74 68 61 74 20 79 6f 75 |n shell |that you|
|00003270| 20 6d 61 79 20 75 73 65 | 20 74 6f 20 61 64 6a 75 | may use| to adju|
|00003280| 73 74 20 74 68 65 20 73 | 65 74 74 69 6e 67 73 20 |st the s|ettings |
|00003290| 61 6e 64 20 64 72 61 77 | 69 6e 67 2c 20 74 6f 20 |and draw|ing, to |
|000032a0| 75 73 65 20 69 74 20 65 | 6e 74 65 72 20 73 68 65 |use it e|nter she|
|000032b0| 6c 6c 20 61 74 20 74 68 | 65 20 70 72 6f 6d 70 74 |ll at th|e prompt|
|000032c0| 2e 20 53 65 65 20 5f 55 | 73 69 6e 67 20 74 68 65 |. See _U|sing the|
|000032d0| 20 53 68 65 6c 6c 5f 20 | 66 6f 72 20 6d 6f 72 65 | Shell_ |for more|
|000032e0| 20 69 6e 66 6f 72 6d 61 | 74 69 6f 6e 2e 20 54 68 | informa|tion. Th|
|000032f0| 65 20 65 78 61 6d 70 6c | 65 73 20 69 6e 20 74 68 |e exampl|es in th|
|00003300| 65 20 5f 54 75 74 6f 72 | 69 61 6c 5f 20 64 6f 20 |e _Tutor|ial_ do |
|00003310| 6e 6f 74 20 75 73 65 20 | 74 68 65 20 73 68 65 6c |not use |the shel|
|00003320| 6c 2e 0d 0d 54 68 65 20 | 5f 4d 61 70 73 5f 20 66 |l...The |_Maps_ f|
|00003330| 6f 6c 64 65 72 20 63 6f | 6e 74 61 69 6e 73 20 64 |older co|ntains d|
|00003340| 65 66 69 6e 69 74 69 6f | 6e 73 20 66 6f 72 20 73 |efinitio|ns for s|
|00003350| 65 76 65 72 61 6c 20 66 | 72 61 63 74 61 6c 73 20 |everal f|ractals |
|00003360| 63 6f 75 72 74 65 73 79 | 20 6f 66 20 20 20 20 20 |courtesy| of |
|00003370| 44 72 2e 20 44 61 6c 65 | 20 53 6e 69 64 65 72 2c |Dr. Dale| Snider,|
|00003380| 20 55 57 2d 4d 69 6c 77 | 61 75 6b 65 65 20 44 65 | UW-Milw|aukee De|
|00003390| 70 61 72 74 6d 65 6e 74 | 20 6f 66 20 50 68 79 73 |partment| of Phys|
|000033a0| 69 63 73 2e 20 20 55 73 | 65 20 5f 4f 70 65 6e 5f |ics. Us|e _Open_|
|000033b0| 20 75 6e 64 65 72 20 74 | 68 65 20 5f 46 69 6c 65 | under t|he _File|
|000033c0| 5f 20 6d 65 6e 75 20 74 | 6f 20 6c 6f 61 64 20 74 |_ menu t|o load t|
|000033d0| 68 65 20 6d 61 70 73 2e | 20 20 54 6f 20 75 73 65 |he maps.| To use|
|000033e0| 2c 20 65 6e 74 65 72 20 | 74 68 65 20 6d 61 70 20 |, enter |the map |
|000033f0| 6e 61 6d 65 20 61 6e 64 | 20 74 68 65 20 77 6f 72 |name and| the wor|
|00003400| 64 20 27 64 72 61 77 27 | 2e 0d 54 68 65 20 5f 44 |d 'draw'|..The _D|
|00003410| 65 6d 6f 5f 20 66 6f 6c | 64 65 72 20 63 6f 6e 74 |emo_ fol|der cont|
|00003420| 61 69 6e 73 20 61 20 63 | 6f 6c 6f 72 20 61 6e 64 |ains a c|olor and|
|00003430| 20 62 6c 61 63 6b 20 26 | 20 77 68 69 74 65 20 76 | black &| white v|
|00003440| 65 72 73 69 6f 6e 20 6f | 66 20 27 43 61 74 68 65 |ersion o|f 'Cathe|
|00003450| 64 72 61 6c 27 20 77 68 | 69 63 68 20 64 72 61 77 |dral' wh|ich draw|
|00003460| 73 20 61 20 63 61 74 68 | 65 64 72 61 6c 20 75 73 |s a cath|edral us|
|00003470| 69 6e 67 20 66 72 61 63 | 74 61 6c 73 2e 20 20 45 |ing frac|tals. E|
|00003480| 78 61 6d 69 6e 65 20 74 | 68 65 20 73 6f 75 72 63 |xamine t|he sourc|
|00003490| 65 20 63 6f 64 65 20 28 | 69 6e 20 46 6f 72 74 68 |e code (|in Forth|
|000034a0| 29 20 74 6f 20 73 65 65 | 20 68 6f 77 20 69 74 20 |) to see| how it |
|000034b0| 77 6f 72 6b 73 2e 20 20 | 55 6e 66 6f 72 74 75 6e |works. |Unfortun|
|000034c0| 61 74 65 6c 79 2c 20 69 | 74 20 77 6f 72 6b 73 20 |ately, i|t works |
|000034d0| 62 65 73 74 20 6f 6e 20 | 6c 61 72 67 65 20 73 63 |best on |large sc|
|000034e0| 72 65 65 6e 73 2e 2e 2e | 20 73 6f 72 72 79 20 43 |reens...| sorry C|
|000034f0| 6c 61 73 73 69 63 20 61 | 6e 64 20 53 45 20 75 73 |lassic a|nd SE us|
|00003500| 65 72 73 21 0d 0d 54 68 | 65 20 63 6f 6d 6d 61 6e |ers!..Th|e comman|
|00003510| 64 73 20 79 6f 75 20 65 | 6e 74 65 72 20 61 72 65 |ds you e|nter are|
|00003520| 20 72 65 61 6c 6c 79 20 | 6a 75 73 74 20 46 6f 72 | really |just For|
|00003530| 74 68 20 77 6f 72 64 73 | 2e 20 20 49 6e 20 66 61 |th words|. In fa|
|00003540| 63 74 2c 20 79 6f 75 20 | 61 72 65 20 72 65 61 6c |ct, you |are real|
|00003550| 6c 79 20 75 73 69 6e 67 | 20 50 6f 63 6b 65 74 20 |ly using| Pocket |
|00003560| 46 6f 72 74 68 20 77 69 | 74 68 20 74 68 65 20 49 |Forth wi|th the I|
|00003570| 46 53 20 77 6f 72 64 73 | 20 70 72 65 64 65 66 69 |FS words| predefi|
|00003580| 6e 65 64 2c 20 68 6f 77 | 65 76 65 72 2c 20 79 6f |ned, how|ever, yo|
|00003590| 75 20 6e 65 65 64 20 6e | 6f 74 20 62 65 20 66 61 |u need n|ot be fa|
|000035a0| 6d 69 6c 69 61 72 20 77 | 69 74 68 20 46 6f 72 74 |miliar w|ith Fort|
|000035b0| 68 20 74 6f 20 75 73 65 | 20 74 68 65 20 70 72 6f |h to use| the pro|
|000035c0| 67 72 61 6d 2e 0d 0d a5 | a5 53 65 74 74 69 6e 67 |gram....|.Setting|
|000035d0| 20 75 70 20 66 6f 72 20 | 44 69 66 66 65 72 65 6e | up for |Differen|
|000035e0| 74 20 53 69 7a 65 64 20 | 4d 6f 6e 69 74 6f 72 73 |t Sized |Monitors|
|000035f0| 0d 0d 55 70 6f 6e 20 73 | 74 61 72 74 75 70 20 46 |..Upon s|tartup F|
|00003600| 72 61 63 74 61 6c 20 4c | 61 62 20 4b 69 74 20 77 |ractal L|ab Kit w|
|00003610| 69 6c 6c 20 67 65 74 20 | 74 68 65 20 73 69 7a 65 |ill get |the size|
|00003620| 20 6f 66 20 74 68 65 20 | 6d 61 69 6e 20 6d 6f 6e | of the |main mon|
|00003630| 69 74 6f 72 27 73 20 73 | 63 72 65 65 6e 20 61 6e |itor's s|creen an|
|00003640| 64 20 73 65 74 20 74 68 | 65 20 61 70 70 6c 69 63 |d set th|e applic|
|00003650| 61 74 69 6f 6e 20 77 69 | 6e 64 6f 77 20 61 63 63 |ation wi|ndow acc|
|00003660| 6f 72 64 69 6e 67 6c 79 | 2e 20 20 48 6f 77 65 76 |ordingly|. Howev|
|00003670| 65 72 2c 20 74 68 65 20 | 64 72 61 77 69 6e 67 20 |er, the |drawing |
|00003680| 70 61 72 61 6d 65 74 65 | 72 73 20 77 69 6c 6c 20 |paramete|rs will |
|00003690| 62 65 20 70 72 65 73 65 | 74 20 6f 6e 6c 79 20 69 |be prese|t only i|
|000036a0| 66 20 74 68 65 20 73 63 | 72 65 65 6e 20 69 73 20 |f the sc|reen is |
|000036b0| 35 31 32 20 78 20 33 34 | 32 2c 20 35 31 32 20 78 |512 x 34|2, 512 x|
|000036c0| 20 33 38 34 2c 20 6f 72 | 20 20 36 34 30 20 78 20 | 384, or| 640 x |
|000036d0| 34 38 30 20 70 69 78 65 | 6c 73 2e 20 20 49 66 20 |480 pixe|ls. If |
|000036e0| 79 6f 75 20 75 73 65 20 | 61 20 64 69 66 66 65 72 |you use |a differ|
|000036f0| 65 6e 74 20 73 69 7a 65 | 64 20 6d 6f 6e 69 74 6f |ent size|d monito|
|00003700| 72 20 79 6f 75 20 77 69 | 6c 6c 20 6e 65 65 64 20 |r you wi|ll need |
|00003710| 74 6f 20 61 64 6a 75 73 | 74 20 74 68 65 20 73 63 |to adjus|t the sc|
|00003720| 72 65 65 6e 20 6f 72 69 | 67 69 6e 20 74 6f 20 6d |reen ori|gin to m|
|00003730| 61 6b 65 20 74 68 65 20 | 6d 6f 73 74 20 75 73 65 |ake the |most use|
|00003740| 20 6f 66 20 69 74 20 61 | 73 20 46 72 61 63 74 61 | of it a|s Fracta|
|00003750| 6c 20 4c 61 62 20 4b 69 | 74 20 77 69 6c 6c 20 73 |l Lab Ki|t will s|
|00003760| 65 74 20 75 70 20 66 6f | 72 20 61 20 35 31 32 20 |et up fo|r a 512 |
|00003770| 78 20 33 38 34 20 70 69 | 78 65 6c 20 73 63 72 65 |x 384 pi|xel scre|
|00003780| 65 6e 20 69 66 20 69 74 | 20 64 6f 65 73 20 6e 6f |en if it| does no|
|00003790| 74 20 72 65 63 6f 67 6e | 69 7a 65 20 6f 6e 65 20 |t recogn|ize one |
|000037a0| 6f 66 20 74 68 65 20 61 | 62 6f 76 65 20 6d 6f 6e |of the a|bove mon|
|000037b0| 69 74 6f 72 20 73 69 7a | 65 73 2e 0d 0d 49 66 20 |itor siz|es...If |
|000037c0| 79 6f 75 20 61 72 65 20 | 75 73 69 6e 67 20 61 20 |you are |using a |
|000037d0| 6d 6f 6e 69 74 6f 72 20 | 6f 74 68 65 72 20 74 68 |monitor |other th|
|000037e0| 61 6e 20 74 68 65 20 6d | 61 69 6e 20 6d 6f 6e 69 |an the m|ain moni|
|000037f0| 74 6f 72 20 79 6f 75 20 | 77 69 6c 6c 20 61 6c 73 |tor you |will als|
|00003800| 6f 20 6e 65 65 64 20 74 | 6f 20 61 64 6a 75 73 74 |o need t|o adjust|
|00003810| 20 74 68 65 20 73 63 72 | 65 65 6e 20 6f 72 69 67 | the scr|een orig|
|00003820| 69 6e 20 77 69 74 68 20 | 74 68 65 20 77 6f 72 64 |in with |the word|
|00003830| 20 7b 5c 74 74 20 73 63 | 72 65 65 6e 7d 20 74 6f | {\tt sc|reen} to|
|00003840| 20 6d 6f 76 65 20 74 68 | 65 20 64 72 61 77 69 6e | move th|e drawin|
|00003850| 67 20 72 65 67 69 6f 6e | 20 6f 6e 74 6f 20 74 68 |g region| onto th|
|00003860| 65 20 73 65 63 6f 6e 64 | 61 72 79 20 6d 6f 6e 69 |e second|ary moni|
|00003870| 74 6f 72 2e 20 20 42 79 | 20 64 65 66 61 75 6c 74 |tor. By| default|
|00003880| 2c 20 74 68 65 20 6d 61 | 69 6e 20 6d 6f 6e 69 74 |, the ma|in monit|
|00003890| 6f 72 20 69 73 20 75 73 | 65 64 2e 0d 0d a5 54 75 |or is us|ed....Tu|
|000038a0| 74 6f 72 69 61 6c 0d 0d | a5 a5 41 20 53 61 6d 70 |torial..|..A Samp|
|000038b0| 6c 65 20 53 65 73 73 69 | 6f 6e 0d 0d 49 6e 20 74 |le Sessi|on..In t|
|000038c0| 68 69 73 20 73 61 6d 70 | 6c 65 20 73 65 73 73 69 |his samp|le sessi|
|000038d0| 6f 6e 2e 0d 0d c7 61 66 | 74 65 72 20 64 6f 75 62 |on....af|ter doub|
|000038e0| 6c 65 2d 63 6c 69 63 6b | 69 6e 67 20 74 68 65 20 |le-click|ing the |
|000038f0| 46 72 61 63 74 61 6c 20 | 4c 61 62 20 4b 69 74 20 |Fractal |Lab Kit |
|00003900| 69 63 6f 6e c8 0d 6f 6b | 5f 20 6f 70 65 6e 0d c7 |icon..ok|_ open..|
|00003910| 63 68 6f 6f 73 65 20 74 | 68 65 20 49 46 53 2d 4d |choose t|he IFS-M|
|00003920| 61 70 73 20 66 69 6c 65 | 20 66 72 6f 6d 20 74 68 |aps file| from th|
|00003930| 65 20 73 74 61 6e 64 61 | 72 64 20 4d 61 63 20 6f |e standa|rd Mac o|
|00003940| 70 65 6e 20 64 69 61 6c | 6f 67 c8 0d 6f 6b 5f 20 |pen dial|og..ok_ |
|00003950| 66 65 72 6e 20 67 72 65 | 65 6e 20 63 6f 6c 6f 72 |fern gre|en color|
|00003960| 20 6f 6e 20 6f 75 74 6c | 69 6e 65 73 20 64 72 61 | on outl|ines dra|
|00003970| 77 0d c7 70 72 6f 67 72 | 61 6d 20 6c 6f 61 64 73 |w..progr|am loads|
|00003980| 20 74 68 65 20 6d 61 70 | 73 20 66 6f 72 20 74 68 | the map|s for th|
|00003990| 65 20 66 65 72 6e 2c 20 | 64 72 61 77 73 20 74 68 |e fern, |draws th|
|000039a0| 65 20 6f 75 74 6c 69 6e | 65 73 20 6f 66 20 74 68 |e outlin|es of th|
|000039b0| 65 20 6d 61 70 73 2c 20 | 77 61 69 74 73 20 66 6f |e maps, |waits fo|
|000039c0| 72 20 61 20 6b 65 79 70 | 72 65 73 73 2c 20 61 6e |r a keyp|ress, an|
|000039d0| 64 20 64 72 61 77 73 20 | 74 68 65 20 66 65 72 6e |d draws |the fern|
|000039e0| 20 69 6e 20 67 72 65 65 | 6e 20 75 6e 74 69 6c 20 | in gree|n until |
|000039f0| 74 68 65 20 75 73 65 72 | 20 70 72 65 73 73 65 73 |the user| presses|
|00003a00| 20 61 20 6b 65 79 c8 20 | 0d 6f 6b 5f 20 6d 6f 75 | a key. |.ok_ mou|
|00003a10| 73 65 0d c7 70 72 6f 67 | 72 61 6d 20 73 68 6f 77 |se..prog|ram show|
|00003a20| 73 20 74 68 65 20 74 72 | 75 65 20 63 6f 6f 72 64 |s the tr|ue coord|
|00003a30| 69 6e 61 74 65 73 20 6f | 66 20 74 68 65 20 6d 6f |inates o|f the mo|
|00003a40| 75 73 65 20 70 6f 69 6e | 74 65 72 20 75 6e 74 69 |use poin|ter unti|
|00003a50| 6c 20 74 68 65 20 75 73 | 65 72 20 70 72 65 73 73 |l the us|er press|
|00003a60| 65 73 20 61 20 6b 65 79 | c8 0d 6f 6b 5f 20 73 65 |es a key|..ok_ se|
|00003a70| 74 74 69 6e 67 73 0d 43 | 75 72 72 65 6e 74 20 70 |ttings.C|urrent p|
|00003a80| 6c 6f 74 20 6f 72 69 67 | 69 6e 20 28 20 30 2e 30 |lot orig|in ( 0.0|
|00003a90| 30 30 30 30 20 2c 20 30 | 2e 30 30 30 30 30 20 29 |0000 , 0|.00000 )|
|00003aa0| 20 5c 68 66 69 6c 20 5c | 62 72 65 61 6b 0d 43 75 | \hfil \|break.Cu|
|00003ab0| 72 72 65 6e 74 20 73 63 | 72 65 65 6e 20 6f 72 69 |rrent sc|reen ori|
|00003ac0| 67 69 6e 20 28 20 31 30 | 30 20 2c 20 33 33 30 20 |gin ( 10|0 , 330 |
|00003ad0| 29 20 5c 68 66 69 6c 20 | 5c 62 72 65 61 6b 0d 43 |) \hfil |\break.C|
|00003ae0| 75 72 72 65 6e 74 20 78 | 20 5c 26 20 79 20 73 63 |urrent x| \& y sc|
|00003af0| 61 6c 65 20 69 73 20 31 | 2e 30 30 30 30 20 3a 20 |ale is 1|.0000 : |
|00003b00| 31 2e 30 30 30 30 20 5c | 68 66 69 6c 20 5c 62 72 |1.0000 \|hfil \br|
|00003b10| 65 61 6b 0d 41 78 65 73 | 20 61 72 65 20 63 75 72 |eak.Axes| are cur|
|00003b20| 72 65 6e 74 6c 79 20 4f | 46 46 20 5c 68 66 69 6c |rently O|FF \hfil|
|00003b30| 20 5c 62 72 65 61 6b 0d | 44 72 61 77 20 4f 75 74 | \break.|Draw Out|
|00003b40| 6c 69 6e 65 73 20 69 73 | 20 63 75 72 72 65 6e 74 |lines is| current|
|00003b50| 6c 79 20 4f 4e 20 5c 68 | 66 69 6c 20 5c 62 72 65 |ly ON \h|fil \bre|
|00003b60| 61 6b 0d 43 75 72 72 65 | 6e 74 20 6e 75 6d 62 65 |ak.Curre|nt numbe|
|00003b70| 72 20 6f 66 20 6d 61 70 | 73 20 3d 20 35 20 5c 68 |r of map|s = 5 \h|
|00003b80| 66 69 6c 20 5c 62 72 65 | 61 6b 0d 6f 6b 5f 20 6f |fil \bre|ak.ok_ o|
|00003b90| 66 66 20 6f 75 74 6c 69 | 6e 65 73 20 30 2e 31 37 |ff outli|nes 0.17|
|00003ba0| 38 20 30 2e 30 33 34 20 | 6f 72 69 67 69 6e 20 2e |8 0.034 |origin .|
|00003bb0| 32 35 20 72 61 6e 67 65 | 20 63 64 72 61 77 0d c7 |25 range| cdraw..|
|00003bc0| 70 72 6f 67 72 61 6d 20 | 7a 6f 6f 6d 73 20 69 6e |program |zooms in|
|00003bd0| 20 74 6f 20 74 68 65 20 | 73 65 63 6f 6e 64 20 6c | to the |second l|
|00003be0| 65 61 66 6c 65 74 20 61 | 6e 64 20 67 65 6e 65 72 |eaflet a|nd gener|
|00003bf0| 61 74 65 73 20 61 20 6d | 61 67 6e 69 66 69 65 64 |ates a m|agnified|
|00003c00| 20 69 6d 61 67 65 20 75 | 73 69 6e 67 20 61 20 64 | image u|sing a d|
|00003c10| 69 66 66 65 72 65 6e 74 | 20 63 6f 6c 6f 72 20 66 |ifferent| color f|
|00003c20| 6f 72 20 65 61 63 68 20 | 6d 61 70 20 75 6e 74 69 |or each |map unti|
|00003c30| 6c 20 61 20 6b 65 79 70 | 72 65 73 73 c8 0d 6f 6b |l a keyp|ress..ok|
|00003c40| 5f 20 62 79 65 0d c7 70 | 72 6f 67 72 61 6d 20 65 |_ bye..p|rogram e|
|00003c50| 78 69 74 73 c8 0d 0d 28 | 20 74 68 65 20 6d 61 6e |xits...(| the man|
|00003c60| 61 75 6c 20 63 6f 6e 74 | 69 6e 75 65 73 20 69 6e |aul cont|inues in|
|00003c70| 20 66 69 6c 65 20 27 50 | 61 72 74 20 32 27 29 2e | file 'P|art 2').|
|00003c80| 2e 2e 2e 2e 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003c90| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003ca0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003cb0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003cc0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003cd0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003ce0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003cf0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003d00| 00 00 01 00 00 00 8b 74 | 00 00 8a 74 00 00 00 a6 |.......t|...t....|
|00003d10| 00 40 00 58 00 4c 20 54 | 70 00 10 28 00 2d 4a 80 |.@.X.L T|p..(.-J.|
|00003d20| 60 48 20 54 70 00 10 28 | 00 2e 4a 80 60 3c 20 54 |`H Tp..(|..J.`< T|
|00003d30| 13 4d 61 6e 75 61 6c 20 | 33 2e 30 20 28 50 61 72 |.Manual |3.0 (Par|
|00003d40| 74 20 31 29 02 00 00 00 | 54 45 58 54 74 74 78 74 |t 1)....|TEXTttxt|
|00003d50| 00 00 54 45 58 54 74 74 | 78 74 01 00 00 3b 01 8c |..TEXTtt|xt...;..|
|00003d60| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003d70| 00 00 a9 ad ff d0 00 00 | 3c 04 00 00 8c 1a 00 12 |........|<.......|
|00003d80| 26 6e 00 0c 28 6e 00 08 | 30 06 04 40 0b ec 67 00 |&n..(n..|0..@..g.|
|00003d90| 01 1e 04 40 4d 24 67 18 | 5d 40 67 00 00 c4 5b 40 |...@M$g.|]@g...[@|
|00003da0| 67 00 00 a6 04 40 00 ef | 67 00 01 46 60 00 01 d2 |g....@..|g..F`...|
|00003db0| 41 ee ff 00 42 10 48 78 | 0b ea 48 6e ff 00 2f 0c |A...B.Hx|..Hn../.|
|00003dc0| 20 54 20 50 22 68 00 54 | 4e 91 48 6e fd fe 48 6e | T P"h.T|N.Hn..Hn|
|00003dd0| fe fe 48 6e ff 00 70 00 | 2f 00 2f 2d ff 72 4e ba |..Hn..p.|/./-.rN.|
|00003de0| 04 4c 3a 00 48 c5 2f 05 | 4e ad 05 2a 70 00 2f 00 |.L:.H./.|N..*p./.|
|00003df0| 2f 2e fe 06 48 6e fd fe | 4e ad 00 3a 42 47 4f ef |/...Hn..|N..:BGO.|
|00003e00| 00 00 00 48 00 09 4d 6f | 6e 61 63 6f 00 80 42 28 |...H..Mo|naco..B(|
|00003e10| 00 1b 08 e8 00 00 00 00 | 00 06 00 5c c7 ee 00 60 |........|...\...`|
|00003e20| 61 34 00 63 e8 9a 00 04 | 00 04 00 28 00 03 01 7d |a4.c....|...(...}|
|00003e30| 01 f9 00 28 00 03 01 7d | 01 f9 00 12 0d d4 00 00 |...(...}|........|
|00003e40| 51 d6 00 00 51 d6 00 00 | 51 ba 01 00 00 00 19 36 |Q...Q...|Q......6|
|00003e50| 19 36 00 95 00 0b 01 04 | 01 ec 00 11 02 ff 0c 00 |.6......|........|
|00003e60| ff ff ff ff 00 0b 00 00 | 00 95 00 00 01 ec 00 00 |........|........|
|00003e70| 01 04 00 00 00 00 00 00 | 00 01 00 0a 00 95 00 0b |........|........|
|00003e80| 01 04 01 ec 00 98 80 f2 | 00 95 00 0b 01 04 01 ec |........|........|
|00003e90| 00 00 00 00 00 00 00 00 | 00 48 00 00 00 48 00 00 |........|.H...H..|
|00003ea0| 00 00 00 04 00 01 00 04 | 00 00 00 00 00 59 68 08 |........|.....Yh.|
|00003eb0| 00 00 00 00 00 00 04 bf | 80 00 00 0f 08 00 ff ff |........|........|
|00003ec0| ff ff ff ff 20 00 bb bb | bb bb bb bb 20 00 99 99 |.... ...|.... ...|
|00003ed0| 66 66 33 33 20 00 66 66 | 33 33 00 00 20 00 00 00 |ff33 .ff|33.. ...|
|00003ee0| 66 66 00 00 20 00 33 33 | cc cc 33 33 20 00 00 00 |ff.. .33|..33 ...|
|00003ef0| 99 99 ff ff 20 00 00 00 | 00 00 dd dd 20 00 33 33 |.... ...|.... .33|
|00003f00| 00 00 99 99 20 00 f2 d7 | 08 56 84 ec 20 00 dd dd |.... ...|.V.. ...|
|00003f10| 00 00 00 00 20 00 ff ff | 66 66 00 00 20 00 aa aa |.... ...|ff.. ...|
|00003f20| aa aa aa aa 20 00 ff ff | ff ff 00 00 20 00 55 55 |.... ...|.... .UU|
|00003f30| 55 55 55 55 08 00 00 00 | 00 00 00 00 00 95 00 0b |UUUU....|........|
|00003f40| 01 04 01 ec 00 95 00 0b | 01 04 01 ec 00 00 04 81 |........|........|
|00003f50| 00 8f 00 04 81 00 8f 00 | 04 81 00 8f 00 04 81 00 |........|........|
|00003f60| 8f 00 04 81 00 8f 00 04 | 81 00 8f 00 39 ba 00 00 |........|....9...|
|00003f70| f0 f4 00 00 0f f7 00 00 | f0 fb 00 00 0f c8 00 02 |........|........|
|00003f80| f0 0f ff fb 00 00 f0 f4 | 00 00 f0 f8 00 00 0f fe |........|........|
|00003f90| 00 00 0f f7 00 00 f0 fb | 00 00 f0 fe 00 05 f0 0f |........|........|
|00003fa0| ff f0 00 0f f1 00 8c fe | 00 00 0f fd ff 00 f0 ee |........|........|
|00003fb0| 00 04 ff ff 00 0f f0 f2 | 00 01 ff ff f7 00 06 ff |........|........|
|00003fc0| ff 00 00 0f ff ff fe 00 | 05 0f f0 00 00 ff ff f9 |........|........|
|00003fd0| 00 01 0f f0 fe 00 00 ff | fc 00 01 0f f0 fd 00 03 |........|........|
|00003fe0| ff f0 00 ff ed 00 04 ff | ff 00 0f f0 f3 00 02 0f |........|........|
|00003ff0| ff f0 f8 00 07 0f ff 00 | 00 0f ff f0 0f fc 00 05 |........|........|
|00004000| 0f f0 00 00 ff ff f9 00 | 00 0f fe 00 01 0f f0 fc |........|........|
|00004010| 00 00 ff fe 00 00 f0 fe | 00 00 ff fc 00 12 0f f0 |........|........|
|00004020| 00 00 ff f0 00 00 0f 00 | 00 0f ff ff 00 f0 00 00 |........|........|
|00004030| f0 f2 00 8d fd 00 05 0f | f0 00 00 ff f0 ef 00 04 |........|........|
|00004040| 0f ff 00 0f ff f2 00 01 | 0f ff f6 00 05 ff f0 00 |........|........|
|00004050| 00 0f f0 fe 00 05 0f f0 | 00 00 0f ff f9 00 00 ff |........|........|
|00004060| fe 00 01 ff ff fc 00 01 | 0f f0 fe 00 05 ff 00 ff |........|........|
|00004070| 00 0f f0 ee 00 04 0f ff | 00 0f ff f2 00 01 ff f0 |........|........|
|00004080| f8 00 07 ff 00 ff 00 0f | ff 00 0f fc 00 05 0f f0 |........|........|
|00004090| 00 00 0f ff f9 00 05 ff | 00 00 0f ff f0 fc 00 08 |........|........|
|000040a0| ff 00 00 0f f0 00 00 ff | ff fc 00 12 0f f0 00 ff |........|........|
|000040b0| 00 ff f0 00 0f f0 00 0f | ff f0 00 f0 00 00 ff f2 |........|........|
|000040c0| 00 8f fd 00 05 0f f0 00 | 00 0f ff ef 00 04 0f ff |........|........|
|000040d0| 00 0f f0 f2 00 01 0f ff | f6 00 04 ff f0 00 00 0f |........|........|
|000040e0| fd 00 05 0f f0 00 00 0f | ff f9 00 05 ff 00 00 0f |........|........|
|000040f0| 0f ff fc 00 0a 0f f0 00 | 00 0f 00 00 ff 00 0f f0 |........|........|
|00004100| ee 00 04 0f ff 00 0f f0 | f2 00 01 ff f0 f9 00 08 |........|........|
|00004110| 0f 00 00 0f f0 00 ff 00 | 0f fc 00 05 0f f0 00 00 |........|........|
|00004120| 0f ff fa 00 06 0f f0 00 | 00 f0 ff f0 fc 00 08 ff |........|........|
|00004130| 00 00 ff 00 00 0f 0f ff | fc 00 13 0f f0 0f ff 00 |........|........|
|00004140| 0f ff 00 00 ff 00 00 ff | 00 00 f0 00 00 0f f0 f3 |........|........|
|00004150| 00 8d fd 00 01 ff f0 fe | 00 00 ff ef 00 01 0f ff |........|........|
|00004160| ef 00 01 0f ff f7 00 05 | 0f ff f0 00 00 ff fd 00 |........|........|
|00004170| 00 ff fe 00 01 0f ff fa | 00 01 0f f0 fe 00 01 0f |........|........|
|00004180| ff fc 00 00 ff fe 00 06 | f0 00 00 ff 00 00 ff ee |........|........|
|00004190| 00 01 0f ff ef 00 01 ff | f0 f9 00 09 0f ff 00 0f |........|........|
|000041a0| f0 00 f0 00 ff f0 fd 00 | 00 ff fe 00 01 0f ff fa |........|........|
|000041b0| 00 01 0f f0 fe 00 01 ff | f0 fd 00 04 0f f0 00 00 |........|........|
|000041c0| ff fe 00 01 0f ff fc 00 | 13 ff 00 0f ff 00 0f ff |........|........|
|000041d0| 00 00 ff 00 00 f0 00 0f | ff 00 00 0f f0 f3 00 8f |........|........|
|000041e0| fd 00 00 ff fd 00 00 ff | ef 00 01 0f ff ef 00 01 |........|........|
|000041f0| 0f ff f7 00 05 0f 00 ff | 00 00 f0 fe 00 01 0f ff |........|........|
|00004200| fe 00 01 0f ff fa 00 01 | ff f0 fe 00 01 0f ff fd |........|........|
|00004210| 00 0c 0f ff 00 00 0f f0 | 00 00 ff 00 00 ff f0 ef |........|........|
|00004220| 00 01 0f ff ef 00 01 ff | f0 f9 00 09 0f ff 00 0f |........|........|
|00004230| f0 00 f0 00 f0 f0 fe 00 | 01 0f ff fe 00 01 0f ff |........|........|
|00004240| fa 00 00 ff fd 00 01 ff | f0 fd 00 04 0f f0 00 0f |........|........|
|00004250| f0 fe 00 01 0f ff fc 00 | 0f ff 00 00 ff 00 0f ff |........|........|
|00004260| 00 00 0f f0 00 f0 00 ff | 0f fe 00 00 ff f3 00 b3 |........|........|
|00004270| fd 00 00 ff fd 00 00 ff | ef 00 01 0f ff fd 00 06 |........|........|
|00004280| ff f0 ff ff 00 0f ff fa | 00 06 0f ff 00 ff ff 0f |........|........|
|00004290| ff fc 00 05 0f 00 ff f0 | 00 f0 fe 00 01 0f f0 fe |........|........|
|000042a0| 00 09 0f ff 00 ff f0 ff | f0 00 00 ff fd 00 01 0f |........|........|
|000042b0| ff fd 00 0c 0f f0 00 00 | 0f 00 00 0f f0 00 00 0f |........|........|
|000042c0| f0 ef 00 01 0f ff fd 00 | 06 ff f0 ff ff 00 0f ff |........|........|
|000042d0| fa 00 06 ff f0 0f ff f0 | ff f0 fe 00 09 0f f0 00 |........|........|
|000042e0| 0f f0 0f f0 00 ff f0 fe | 00 01 0f f0 fe 00 09 0f |........|........|
|000042f0| ff 00 ff f0 ff f0 00 00 | ff fd 00 01 ff f0 fd 00 |........|........|
|00004300| 04 0f 00 00 0f f0 fe 00 | 01 0f ff fc 00 00 f0 fd |........|........|
|00004310| 00 0a 0f f0 00 00 0f f0 | 0f f0 00 ff ff fe 00 00 |........|........|
|00004320| ff f3 00 b8 fd 00 00 ff | fd 00 00 ff fd 00 fa ff |........|........|
|00004330| fa 00 0d 0f ff 00 ff ff | 00 0f ff f0 0f f0 f0 0f |........|........|
|00004340| f0 fb 00 07 0f ff 00 0f | ff f0 0f f0 fd 00 05 0f |........|........|
|00004350| 00 ff f0 00 f0 fe 00 01 | 0f f0 fe 00 09 0f ff 00 |........|........|
|00004360| 0f ff f0 ff 00 00 ff fd | 00 01 0f ff fd 00 0c 0f |........|........|
|00004370| f0 00 00 0f 0f ff ff f0 | 00 00 0f f0 fe 00 00 0f |........|........|
|00004380| fb ff 00 f0 fa 00 0d 0f | ff 00 ff ff 00 0f ff f0 |........|........|
|00004390| 0f f0 f0 0f f0 fb 00 06 | ff f0 00 ff ff 00 ff fb |........|........|
|000043a0| 00 01 0f f0 f9 00 01 0f | f0 fe 00 09 0f ff 00 0f |........|........|
|000043b0| ff f0 ff 00 00 ff fd 00 | 01 ff f0 fd 00 04 ff 00 |........|........|
|000043c0| 00 0f f0 fe 00 01 0f ff | fd 00 01 0f f0 fd 00 00 |........|........|
|000043d0| ff fe 00 01 0f f0 f9 00 | 00 ff f3 00 b9 fe 00 01 |........|........|
|000043e0| 0f ff fe 00 01 0f ff fd | 00 fa ff fa 00 0d 0f ff |........|........|
|000043f0| 00 0f ff 00 0f ff 00 0f | ff 00 00 ff fb 00 07 0f |........|........|
|00004400| ff 00 0f ff 00 0f ff fd | 00 05 ff 00 0f f0 0f f0 |........|........|
|00004410| fe 00 00 ff fd 00 09 0f | ff 00 0f ff 00 0f f0 00 |........|........|
|00004420| ff fd 00 01 0f ff fd 00 | 00 ff fe 00 08 0f 00 ff |........|........|
|00004430| ff f0 00 00 0f f0 fe 00 | 00 0f fb ff 00 f0 fa 00 |........|........|
|00004440| 0d 0f ff 00 0f ff 00 0f | ff 00 0f ff 00 00 ff fb |........|........|
|00004450| 00 07 ff f0 00 ff f0 00 | ff f0 fc 00 00 ff f8 00 |........|........|
|00004460| 00 ff fd 00 09 0f ff 00 | 0f ff 00 0f f0 00 ff fd |........|........|
|00004470| 00 01 ff f0 fd 00 04 ff | 00 00 0f f0 fe 00 01 0f |........|........|
|00004480| ff fd 00 01 0f f0 fe 00 | 01 ff ff fe 00 01 0f f0 |........|........|
|00004490| f9 00 00 ff f3 00 aa fe | 00 01 0f f0 fe 00 01 0f |........|........|
|000044a0| ff ef 00 0d 0f ff 00 0f | ff 00 0f f0 00 0f ff 00 |........|........|
|000044b0| 00 ff fb 00 07 0f ff 00 | 0f ff 00 0f ff fd 00 04 |........|........|
|000044c0| f0 00 00 ff 0f fd 00 00 | ff fd 00 09 0f ff 00 0f |........|........|
|000044d0| f0 00 0f f0 00 ff fd 00 | 01 0f ff fd 00 00 ff fe |........|........|
|000044e0| 00 08 f0 00 00 0f f0 00 | 00 0f f0 ef 00 0d 0f ff |........|........|
|000044f0| 00 0f ff 00 0f f0 00 0f | ff 00 00 ff fb 00 07 ff |........|........|
|00004500| f0 00 ff f0 00 ff f0 fc | 00 00 ff f8 00 00 ff fd |........|........|
|00004510| 00 09 0f ff 00 0f f0 00 | 0f f0 00 ff fd 00 01 ff |........|........|
|00004520| f0 fd 00 04 f0 00 00 0f | f0 fe 00 01 0f ff fd 00 |........|........|
|00004530| 00 0f fc 00 05 0f f0 00 | 00 0f f0 f9 00 00 ff f3 |........|........|
|00004540| 00 ab fe 00 01 0f f0 fe | 00 01 0f ff ef 00 0d 0f |........|........|
|00004550| ff 00 0f ff 00 0f f0 00 | 0f ff 00 00 ff fb 00 07 |........|........|
|00004560| 0f ff 00 0f ff 00 0f ff | fd 00 04 f0 00 00 ff 0f |........|........|
|00004570| fd 00 00 ff fd 00 09 0f | ff 00 0f f0 00 0f f0 00 |........|........|
|00004580| ff fd 00 01 0f ff fd 00 | 00 ff fe 00 08 f0 00 00 |........|........|
|00004590| 0f f0 00 00 0f f0 ef 00 | 0d 0f ff 00 0f ff 00 0f |........|........|
|000045a0| f0 00 0f ff 00 00 ff fb | 00 07 ff f0 00 ff f0 00 |........|........|
|000045b0| ff f0 fd 00 01 0f f0 f8 | 00 00 ff fd 00 09 0f ff |........|........|
|000045c0| 00 0f f0 00 0f f0 00 ff | fd 00 01 ff f0 fe 00 05 |........|........|
|000045d0| 0f f0 00 00 0f f0 fe 00 | 01 0f ff fd 00 00 ff fb |........|........|
|000045e0| 00 04 ff 00 00 0f f0 f9 | 00 00 ff f3 00 b0 fe 00 |........|........|
|000045f0| 01 0f f0 fe 00 01 0f f0 | ef 00 0d 0f ff 00 0f ff |........|........|
|00004600| 00 0f f0 00 0f ff 00 00 | ff fb 00 07 0f ff 00 0f |........|........|
|00004610| ff 00 0f ff fd 00 04 f0 | 00 00 ff 0f fe 00 01 0f |........|........|
|00004620| f0 fd 00 09 0f ff 00 0f | f0 00 0f f0 00 ff fd 00 |........|........|
|00004630| 01 0f ff fe 00 01 0f f0 | fe 00 08 f0 00 00 0f f0 |........|........|
|00004640| 00 00 0f f0 ef 00 0d 0f | ff 00 0f ff 00 0f f0 00 |........|........|
|00004650| 0f ff 00 00 ff fb 00 07 | ff f0 00 ff f0 00 ff f0 |........|........|
|00004660| fd 00 00 ff f8 00 01 0f | f0 fd 00 09 0f ff 00 0f |........|........|
|00004670| f0 00 0f f0 00 ff fd 00 | 01 ff f0 fe 00 05 0f f0 |........|........|
|00004680| 00 00 0f f0 fe 00 01 0f | ff fd 00 0b ff 00 00 0f |........|........|
|00004690| f0 00 00 ff 00 00 0f f0 | f9 00 00 ff f3 00 b4 fe |........|........|
|000046a0| 00 01 0f f0 fe 00 01 ff | f0 ef 00 0d 0f ff 00 0f |........|........|
|000046b0| ff 00 0f f0 00 0f ff 00 | 00 ff fb 00 07 0f ff 00 |........|........|
|000046c0| 0f ff 00 0f ff fd 00 04 | f0 00 00 ff ff fe 00 01 |........|........|
|000046d0| 0f f0 fd 00 09 0f ff 00 | 0f f0 00 0f f0 00 ff fd |........|........|
|000046e0| 00 01 0f ff fe 00 01 0f | f0 fe 00 08 f0 00 00 ff |........|........|
|000046f0| f0 00 00 0f f0 ef 00 0d | 0f ff 00 0f ff 00 0f f0 |........|........|
|00004700| 00 0f ff 00 00 ff fb 00 | 07 ff f0 00 ff f0 00 ff |........|........|
|00004710| f0 fe 00 03 0f f0 00 f0 | fa 00 01 0f f0 fd 00 09 |........|........|
|00004720| 0f ff 00 0f f0 00 0f f0 | 00 ff fd 00 01 ff f0 fe |........|........|
|00004730| 00 00 ff fe 00 01 0f f0 | fe 00 01 0f ff fe 00 0c |........|........|
|00004740| 0f f0 00 00 0f ff 00 00 | ff 00 00 0f f0 f9 00 00 |........|........|
|00004750| ff f3 00 be fe 00 00 ff | fe 00 01 0f ff fc 00 fa |........|........|
|00004760| ff fa 00 0d 0f ff 00 0f | ff 00 0f f0 00 0f ff 00 |........|........|
|00004770| 00 ff fb 00 07 0f ff 00 | 0f ff 00 0f ff fe 00 00 |........|........|
|00004780| 0f fe 00 01 0f f0 fe 00 | 00 0f fc 00 09 0f ff 00 |........|........|
|00004790| 0f f0 00 0f f0 00 ff fd | 00 01 0f ff fe 00 00 0f |........|........|
|000047a0| fe 00 04 0f f0 00 00 ff | fe 00 01 0f f0 fe 00 00 |........|........|
|000047b0| 0f fb ff 00 f0 fa 00 0d | 0f ff 00 0f ff 00 0f f0 |........|........|
|000047c0| 00 0f ff 00 00 ff fb 00 | 07 ff f0 00 ff f0 00 ff |........|........|
|000047d0| f0 fe 00 03 ff 00 00 f0 | fa 00 00 0f fc 00 09 0f |........|........|
|000047e0| ff 00 0f f0 00 0f f0 00 | ff fd 00 01 ff f0 fe 00 |........|........|
|000047f0| 00 ff fe 00 01 0f f0 fe | 00 01 0f ff fe 00 0c 0f |........|........|
|00004800| f0 00 00 0f ff 00 00 ff | 00 00 0f f0 f9 00 00 ff |........|........|
|00004810| f3 00 b1 fe 00 00 ff fe | 00 01 ff f0 ee 00 0d 0f |........|........|
|00004820| ff 00 0f ff 00 0f f0 00 | 0f ff 00 00 ff fb 00 07 |........|........|
|00004830| 0f ff 00 0f ff 00 0f ff | fe 00 00 0f fe 00 01 0f |........|........|
|00004840| f0 fe 00 00 ff fc 00 09 | 0f ff 00 0f f0 00 0f f0 |........|........|
|00004850| 00 ff fd 00 01 0f ff fe | 00 00 ff fe 00 04 0f f0 |........|........|
|00004860| 00 0f f0 fe 00 01 0f f0 | ef 00 0d 0f ff 00 0f ff |........|........|
|00004870| 00 0f f0 00 0f ff 00 00 | ff fb 00 07 ff f0 00 ff |........|........|
|00004880| f0 00 ff f0 fe 00 fe ff | 00 f0 fa 00 00 ff fc 00 |........|........|
|00004890| 09 0f ff 00 0f f0 00 0f | f0 00 ff fd 00 01 ff f0 |........|........|
|000048a0| fe 00 00 ff fe 00 01 0f | f0 fe 00 01 0f ff fe 00 |........|........|
|000048b0| 0c 0f f0 00 00 0f f0 00 | 0f f0 00 00 0f f0 f9 00 |........|........|
|000048c0| 00 ff f3 00 ad 01 00 00 | fc ff 00 f0 ed 00 0e ff |........|........|
|000048d0| ff f0 ff ff f0 ff ff f0 | ff ff f0 ff ff f0 fc 00 |........|........|
|000048e0| 0c ff ff f0 ff ff f0 ff | ff f0 00 0f ff ff fe 00 |........|........|
|000048f0| 04 f0 00 00 0f ff fc 00 | 02 ff ff f0 fc ff 05 00 |........|........|
|00004900| ff f0 00 00 0f fe ff 02 | 00 0f ff fe 00 03 0f 0f |........|........|
|00004910| ff ff fd 00 01 ff f0 ef | 00 0e ff ff f0 ff ff f0 |........|........|
|00004920| ff ff f0 ff ff f0 ff ff | f0 fd 00 0b 0f ff ff 0f |........|........|
|00004930| ff ff 0f ff ff 00 00 0f | fe ff 00 f0 fb 00 01 0f |........|........|
|00004940| ff fc 00 02 ff ff f0 fc | ff 01 00 ff fe 00 fe ff |........|........|
|00004950| 03 f0 00 0f f0 fe 00 04 | 0f f0 00 00 0f fe ff 02 |........|........|
|00004960| 00 00 ff fd 00 fe ff fe | 00 01 0f f0 f9 00 00 ff |........|........|
|00004970| f3 00 39 be 00 01 0f f0 | f3 00 01 0f f0 fa 00 01 |..9.....|........|
|00004980| 0f f0 fe 00 00 0f fa 00 | 00 ff c5 00 01 0f f0 f3 |........|........|
|00004990| 00 01 0f f0 fa 00 01 0f | f0 fd 00 00 ff f9 00 00 |........|........|
|000049a0| ff f7 00 00 ff f9 00 01 | 0f f0 f3 00 39 be 00 01 |........|....9...|
|000049b0| 0f f0 f2 00 00 ff fa 00 | 01 0f f0 fe 00 00 f0 fb |........|........|
|000049c0| 00 01 0f f0 c5 00 01 0f | f0 f3 00 01 0f f0 fa 00 |........|........|
|000049d0| 01 0f f0 fd 00 00 ff f9 | 00 00 ff f7 00 00 ff f9 |........|........|
|000049e0| 00 01 0f f0 f3 00 36 be | 00 00 ff f1 00 00 ff fa |......6.|........|
|000049f0| 00 00 ff fd 00 00 f0 fb | 00 01 0f f0 c5 00 00 ff |........|........|
|00004a00| f1 00 00 ff fa 00 00 ff | fc 00 01 0f f0 fb 00 01 |........|........|
|00004a10| 0f f0 f8 00 01 0f f0 f9 | 00 00 ff f2 00 34 be 00 |........|.....4..|
|00004a20| 00 ff f1 00 01 0f f0 fb | 00 00 ff fd 00 00 f0 fb |........|........|
|00004a30| 00 00 ff c4 00 00 ff f1 | 00 00 0f fa 00 00 ff fb |........|........|
|00004a40| 00 00 f0 fb 00 01 0f f0 | f8 00 00 0f f8 00 00 f0 |........|........|
|00004a50| f2 00 2e be 00 00 f0 f0 | 00 00 0f fb 00 00 f0 f7 |........|........|
|00004a60| 00 00 0f c3 00 00 f0 f0 | 00 00 f0 fb 00 00 f0 fb |........|........|
|00004a70| 00 00 0f fb 00 00 0f f7 | 00 00 f0 f9 00 00 0f f1 |........|........|
|00004a80| 00 20 e8 00 03 f0 0f ff | f0 f7 00 05 0f f0 00 00 |. ......|........|
|00004a90| 0f f0 b4 00 02 f0 0f ff | f6 00 00 ff fe 00 00 ff |........|........|
|00004aa0| 9c 00 2c e9 00 04 0f ff | ff 00 f0 fb 00 0a 0f 00 |..,.....|........|
|00004ab0| 00 0f ff ff f0 0f f0 0f | f0 b6 00 03 0f ff f0 0f |........|........|
|00004ac0| fa 00 02 0f 00 00 fe ff | 03 00 ff 00 ff 9d 00 2c |........|.......,|
|00004ad0| e9 00 04 0f ff f0 00 f0 | fb 00 0a 0f f0 00 0f 00 |........|........|
|00004ae0| 00 ff ff 00 00 f0 b6 00 | 03 0f ff 00 0f fa 00 09 |........|........|
|00004af0| 0f f0 00 f0 00 0f ff f0 | 00 0f 9d 00 29 e8 00 04 |........|....)...|
|00004b00| ff 00 00 f0 00 fa ff 08 | 00 0f 00 00 0f f0 00 00 |........|........|
|00004b10| f0 b5 00 04 ff 00 0f 00 | 00 fa ff 07 00 f0 00 00 |........|........|
|00004b20| ff 00 00 0f 9d 00 2b e8 | 00 03 f0 00 0f ff fb 00 |......+.|........|
|00004b30| 0a 0f f0 00 0f 00 00 0f | ff 00 00 f0 b5 00 03 f0 |........|........|
|00004b40| 00 ff f0 fb 00 09 0f f0 | 00 f0 00 00 ff f0 00 0f |........|........|
|00004b50| 9d 00 2b e8 00 03 f0 00 | ff 0f fb 00 0a 0f 00 00 |..+.....|........|
|00004b60| 0f 00 00 f0 0f f0 0f f0 | b5 00 03 f0 00 f0 f0 fb |........|........|
|00004b70| 00 09 0f 00 00 f0 00 0f | 00 ff 00 ff 9d 00 25 e9 |........|......%.|
|00004b80| 00 04 0f f0 00 ff ff f7 | 00 05 ff ff 00 00 ff ff |........|........|
|00004b90| b5 00 04 0f f0 00 ff f0 | f8 00 06 0f ff f0 00 0f |........|........|
|00004ba0| ff f0 9d 00 04 81 00 8f | 00 04 81 00 8f 00 04 81 |........|........|
|00004bb0| 00 8f 00 04 81 00 8f 00 | 04 81 00 8f 00 04 81 00 |........|........|
|00004bc0| 8f 00 04 81 00 8f 00 04 | 81 00 8f 00 04 81 00 8f |........|........|
|00004bd0| 00 04 81 00 8f 00 04 81 | 00 8f 00 04 81 00 8f 00 |........|........|
|00004be0| 04 81 00 8f 00 04 81 00 | 8f 00 04 81 00 8f 00 04 |........|........|
|00004bf0| 81 00 8f 00 04 81 00 8f | 00 04 81 00 8f 00 04 81 |........|........|
|00004c00| 00 8f 00 04 81 00 8f 00 | 04 81 00 8f 00 04 81 00 |........|........|
|00004c10| 8f 00 04 81 00 8f 00 04 | 81 00 8f 00 04 81 00 8f |........|........|
|00004c20| 00 04 81 00 8f 00 04 81 | 00 8f 00 04 81 00 8f 00 |........|........|
|00004c30| 04 81 00 8f 00 04 81 00 | 8f 00 04 81 00 8f 00 04 |........|........|
|00004c40| 81 00 8f 00 04 81 00 8f | 00 04 81 00 8f 00 04 81 |........|........|
|00004c50| 00 8f 00 04 81 00 8f 00 | 04 81 00 8f 00 04 81 00 |........|........|
|00004c60| 8f 00 04 81 00 8f 00 04 | 81 00 8f 00 04 81 00 8f |........|........|
|00004c70| 00 04 81 00 8f 00 04 81 | 00 8f 00 04 81 00 8f 00 |........|........|
|00004c80| 0a b6 00 00 0f c8 00 00 | 0f 95 00 7a fe 00 00 0f |........|...z....|
|00004c90| fd ff 00 f0 ee 00 04 ff | ff 00 0f f0 ea 00 01 ff |........|........|
|00004ca0| ff f7 00 01 ff f0 fc 00 | 00 ff f8 00 01 ff ff f8 |........|........|
|00004cb0| 00 02 0f ff f0 f2 00 01 | ff ff f7 00 01 ff f0 fc |........|........|
|00004cc0| 00 05 ff 00 00 0f ff f0 | f8 00 01 0f ff f0 00 01 |........|........|
|00004cd0| 0f ff fa 00 01 0f f0 fe | 00 01 ff f0 fe 00 01 0f |........|........|
|00004ce0| f0 fe 00 01 0f ff fe 00 | 01 0f ff fd 00 04 ff f0 |........|........|
|00004cf0| 00 00 f0 fd 00 08 0f 00 | 00 0f 00 00 0f ff f0 fe |........|........|
|00004d00| 00 01 0f f0 f0 00 85 fd | 00 05 0f f0 00 00 ff f0 |........|........|
|00004d10| ef 00 04 0f ff 00 0f ff | ea 00 01 0f ff f8 00 03 |........|........|
|00004d20| ff 00 ff f0 fd 00 00 ff | f8 00 01 0f ff f8 00 02 |........|........|
|00004d30| ff 00 ff f2 00 01 0f ff | f8 00 03 ff 00 ff f0 fd |........|........|
|00004d40| 00 00 ff fe 00 01 ff f0 | f9 00 03 0f f0 0f ff f2 |........|........|
|00004d50| 00 03 0f ff 0f ff fc 00 | 1e 0f f0 0f 00 00 ff 00 |........|........|
|00004d60| ff f0 00 0f f0 0f f0 00 | 0f ff 0f ff 00 00 ff 00 |........|........|
|00004d70| ff 00 00 ff f0 ff f0 00 | fd ff 01 f0 0f fe ff 09 |........|........|
|00004d80| 00 00 ff 00 ff 00 00 0f | f0 0f f0 00 8b fd 00 05 |........|........|
|00004d90| 0f f0 00 00 0f ff ef 00 | 04 0f ff 00 0f f0 ea 00 |........|........|
|00004da0| 01 0f ff f9 00 00 0f fe | 00 00 ff fd 00 00 ff f8 |........|........|
|00004db0| 00 01 0f ff f9 00 04 0f | ff 00 ff f0 f3 00 01 0f |........|........|
|00004dc0| ff f9 00 00 0f fe 00 00 | ff fd 00 00 ff fe 00 01 |........|........|
|00004dd0| ff f0 f9 00 04 ff f0 00 | ff f0 f3 00 03 0f 00 00 |........|........|
|00004de0| 0f fc 00 1e ff 00 ff f0 | 0f ff 00 0f ff 00 0f 00 |........|........|
|00004df0| 00 f0 00 ff 00 00 0f 00 | 0f 00 00 0f f0 0f f0 00 |........|........|
|00004e00| 00 f0 00 fd ff 0f f0 0f | ff ff 00 00 0f ff 00 ff |........|........|
|00004e10| f0 00 ff 00 ff f0 f1 00 | 8b fd 00 01 ff f0 fe 00 |........|........|
|00004e20| 00 ff ef 00 01 0f ff e7 | 00 01 0f ff f9 00 04 0f |........|........|
|00004e30| ff 00 00 ff fe 00 01 0f | f0 f8 00 01 0f ff f9 00 |........|........|
|00004e40| 04 0f ff 00 ff f0 f3 00 | 01 0f ff f9 00 04 0f ff |........|........|
|00004e50| 00 00 ff fe 00 01 0f f0 | fe 00 01 ff f0 f9 00 04 |........|........|
|00004e60| ff f0 00 ff f0 f3 00 04 | ff 00 00 0f f0 fd 00 24 |........|.......$|
|00004e70| f0 00 ff f0 0f ff 00 0f | ff 00 ff 00 00 ff 00 ff |........|........|
|00004e80| 00 00 0f f0 0f ff 00 0f | f0 0f f0 00 00 ff 00 f0 |........|........|
|00004e90| 00 00 0f 00 0f fd 00 09 | 0f ff 00 ff f0 00 f0 00 |........|........|
|00004ea0| ff f0 f1 00 85 fd 00 00 | ff fd 00 00 ff ef 00 01 |........|........|
|00004eb0| 0f ff e7 00 01 0f ff f9 | 00 04 0f ff 00 00 ff fe |........|........|
|00004ec0| 00 01 0f f0 f8 00 01 0f | ff f8 00 03 ff 00 ff f0 |........|........|
|00004ed0| f3 00 01 0f ff f9 00 04 | 0f ff 00 00 ff fe 00 01 |........|........|
|00004ee0| 0f f0 fe 00 01 ff f0 f9 | 00 04 0f f0 00 ff f0 f3 |........|........|
|00004ef0| 00 04 ff 00 00 0f f0 fe | 00 01 0f f0 fd 00 1f ff |........|........|
|00004f00| 00 0f ff 00 ff 00 00 ff | 00 ff 00 00 0f f0 0f ff |........|........|
|00004f10| 00 0f f0 0f f0 00 00 ff | 00 f0 00 00 f0 00 0f fc |........|........|
|00004f20| 00 05 ff 00 ff f0 0f f0 | ee 00 aa fd 00 00 ff fd |........|........|
|00004f30| 00 00 ff ef 00 01 0f ff | fd 00 06 ff f0 ff ff 00 |........|........|
|00004f40| 0f ff f9 00 03 ff 00 ff | f0 fe 00 06 0f ff 00 ff |........|........|
|00004f50| ff 0f ff fe 00 04 0f f0 | 00 00 ff fe 00 07 0f 00 |........|........|
|00004f60| 00 0f f0 00 ff f0 fe 00 | 06 0f ff 00 ff f0 ff f0 |........|........|
|00004f70| fb 00 00 ff f2 00 06 0f | ff 00 ff ff 0f ff fe 00 |........|........|
|00004f80| 04 0f f0 00 00 ff fe 00 | 00 0f fd 00 06 ff f0 0f |........|........|
|00004f90| ff f0 ff f0 fb 00 00 ff | f2 00 04 ff 00 00 0f f0 |........|........|
|00004fa0| fe 00 03 0f f0 ff f0 fd | 00 16 0f f0 00 ff 00 00 |........|........|
|00004fb0| ff 00 ff 00 00 0f f0 0f | f0 00 0f f0 0f f0 00 00 |........|........|
|00004fc0| ff fe 00 05 0f f0 00 0f | 0f ff fc 00 05 ff 00 0f |........|........|
|00004fd0| f0 ff f0 f0 00 bf fd 00 | 00 ff fd 00 00 ff fd 00 |........|........|
|00004fe0| fa ff fa 00 0d 0f ff 00 | ff ff 00 0f ff f0 0f f0 |........|........|
|00004ff0| f0 0f f0 fb 00 04 0f 0f | ff f0 ff fe 00 07 0f ff |........|........|
|00005000| 00 0f ff f0 0f f0 fb 00 | 00 ff fe 00 07 ff 00 00 |........|........|
|00005010| f0 ff ff 00 ff fe 00 06 | 0f ff 00 0f ff f0 ff fc |........|........|
|00005020| 00 01 0f f0 fd 00 00 0f | fb ff 00 f0 fe 00 07 0f |........|........|
|00005030| ff 00 0f ff f0 0f f0 fb | 00 00 ff fe 00 00 ff fd |........|........|
|00005040| 00 06 ff f0 00 ff ff 00 | ff fc 00 01 0f f0 fd 00 |........|........|
|00005050| 00 0f fb ff 00 f0 fe 00 | 04 ff 00 00 0f f0 fe 00 |........|........|
|00005060| 03 0f ff 00 ff fd 00 0c | ff 00 00 ff 00 00 ff 00 |........|........|
|00005070| ff 00 00 0f f0 fe 00 06 | 0f f0 0f f0 00 00 ff fe |........|........|
|00005080| 00 06 0f 00 00 0f ff 0f | ff fe 00 06 0f f0 00 0f |........|........|
|00005090| ff 00 ff f0 00 c9 fe 00 | 01 0f ff fe 00 01 0f ff |........|........|
|000050a0| fd 00 fa ff fa 00 0d 0f | ff 00 0f ff 00 0f ff 00 |........|........|
|000050b0| 0f ff 00 00 ff fb 00 04 | 0f 0f f0 00 ff fe 00 07 |........|........|
|000050c0| 0f ff 00 0f ff 00 0f ff | fc 00 01 0f f0 fe 00 07 |........|........|
|000050d0| ff 00 00 f0 ff f0 00 ff | fe 00 07 0f ff 00 0f ff |........|........|
|000050e0| 00 0f f0 fe 00 02 0f ff | f0 fd 00 00 0f fb ff 00 |........|........|
|000050f0| f0 fe 00 07 0f ff 00 0f | ff 00 0f ff fc 00 01 0f |........|........|
|00005100| f0 fe 00 00 ff fd 00 07 | ff f0 00 ff f0 00 ff f0 |........|........|
|00005110| fe 00 02 0f ff f0 fd 00 | 00 0f fb ff 00 f0 fe 00 |........|........|
|00005120| 04 ff 00 00 0f f0 fe 00 | 14 0f f0 00 0f f0 00 00 |........|........|
|00005130| ff ff 00 00 ff 00 00 ff | 00 ff 00 00 0f f0 fe 00 |........|........|
|00005140| 06 ff 00 0f f0 00 00 ff | fe 00 11 ff 00 00 0f 00 |........|........|
|00005150| 00 ff f0 00 0f ff f0 00 | 0f f0 00 0f f0 f1 00 af |........|........|
|00005160| fe 00 01 0f f0 fe 00 01 | 0f ff ef 00 0d 0f ff 00 |........|........|
|00005170| 0f ff 00 0f f0 00 0f ff | 00 00 ff fb 00 04 0f 0f |........|........|
|00005180| f0 00 ff fe 00 07 0f ff | 00 0f ff 00 0f ff fc 00 |........|........|
|00005190| 01 ff f0 fe 00 07 f0 00 | 00 f0 ff 00 00 ff fe 00 |........|........|
|000051a0| 07 0f ff 00 0f f0 00 0f | f0 fc 00 00 ff f2 00 07 |........|........|
|000051b0| 0f ff 00 0f ff 00 0f ff | fc 00 01 ff f0 fe 00 00 |........|........|
|000051c0| f0 fd 00 07 ff f0 00 ff | f0 00 ff f0 fc 00 00 ff |........|........|
|000051d0| f2 00 04 ff 00 00 0f f0 | fe 00 04 0f f0 00 0f f0 |........|........|
|000051e0| fe 00 0c 0f f0 00 ff 00 | 00 ff 00 0f f0 00 ff f0 |........|........|
|000051f0| fe 00 0a ff 00 00 ff 00 | 0f ff 00 00 0f ff fc 00 |........|........|
|00005200| 01 0f f0 fe 00 06 ff 00 | 0f f0 00 0f f0 f1 00 af |........|........|
|00005210| fe 00 01 0f f0 fe 00 01 | 0f ff ef 00 0d 0f ff 00 |........|........|
|00005220| 0f ff 00 0f f0 00 0f ff | 00 00 ff fa 00 03 ff f0 |........|........|
|00005230| 00 ff fe 00 07 0f ff 00 | 0f ff 00 0f ff fc 00 00 |........|........|
|00005240| ff fe 00 08 0f f0 00 00 | 0f ff 00 0f ff fe 00 07 |........|........|
|00005250| 0f ff 00 0f f0 00 0f f0 | fc 00 01 0f f0 f3 00 07 |........|........|
|00005260| 0f ff 00 0f ff 00 0f ff | fc 00 00 ff fe 00 01 0f |........|........|
|00005270| f0 fd 00 07 ff f0 00 ff | f0 00 ff f0 fc 00 01 0f |........|........|
|00005280| f0 f3 00 04 ff 00 00 0f | f0 fe 00 04 0f f0 00 0f |........|........|
|00005290| f0 fd 00 19 ff 00 ff 00 | 00 ff 00 00 ff ff 0f f0 |........|........|
|000052a0| 00 00 0f f0 00 00 0f ff | f0 ff 00 00 0f f0 fc 00 |........|........|
|000052b0| 01 0f f0 fe 00 06 0f f0 | 0f f0 00 0f f0 f1 00 b4 |........|........|
|000052c0| fe 00 01 0f f0 fe 00 01 | 0f f0 ef 00 0d 0f ff 00 |........|........|
|000052d0| 0f ff 00 0f f0 00 0f ff | 00 00 ff fa 00 03 ff 00 |........|........|
|000052e0| 00 ff fe 00 07 0f ff 00 | 0f ff 00 0f ff fd 00 01 |........|........|
|000052f0| 0f f0 fe 00 08 0f f0 00 | 00 0f ff 00 0f ff fe 00 |........|........|
|00005300| 0e 0f ff 00 0f f0 00 0f | f0 00 00 0f f0 00 0f f0 |........|........|
|00005310| f3 00 07 0f ff 00 0f ff | 00 0f ff fd 00 01 0f f0 |........|........|
|00005320| fe 00 01 0f f0 fd 00 0e | ff f0 00 ff f0 00 ff f0 |........|........|
|00005330| 00 00 ff 00 00 0f f0 f3 | 00 04 ff 00 00 0f f0 fe |........|........|
|00005340| 00 0e 0f f0 00 0f f0 0f | f0 00 00 ff 00 ff 00 00 |........|........|
|00005350| ff fd 00 04 0f f0 00 00 | ff fb 00 15 ff 00 00 0f |........|........|
|00005360| f0 00 00 ff 00 00 0f f0 | 0f f0 00 0f f0 0f f0 00 |........|........|
|00005370| 0f f0 f1 00 b7 fe 00 01 | 0f f0 fe 00 01 ff f0 ef |........|........|
|00005380| 00 0d 0f ff 00 0f ff 00 | 0f f0 00 0f ff 00 00 ff |........|........|
|00005390| fa 00 03 ff 00 0f ff fe | 00 07 0f ff 00 0f ff 00 |........|........|
|000053a0| 0f ff fd 00 05 ff 00 0f | 00 00 ff fe 00 04 0f ff |........|........|
|000053b0| 00 0f ff fe 00 0e 0f ff | 00 0f f0 00 0f f0 00 00 |........|........|
|000053c0| 0f ff 00 0f f0 f3 00 07 | 0f ff 00 0f ff 00 0f ff |........|........|
|000053d0| fd 00 05 ff 00 0f 00 00 | ff fc 00 0e ff f0 00 ff |........|........|
|000053e0| f0 00 ff f0 00 00 ff f0 | 00 0f f0 f3 00 04 ff 00 |........|........|
|000053f0| 00 0f f0 fe 00 33 0f f0 | 00 0f f0 0f ff 00 00 ff |.....3..|........|
|00005400| 00 ff 00 00 ff 00 0f 00 | 00 0f f0 00 0f f0 00 f0 |........|........|
|00005410| 00 f0 00 00 ff 00 00 ff | f0 00 00 ff 00 00 0f f0 |........|........|
|00005420| 0f ff 00 0f f0 0f f0 00 | 0f f0 f1 00 d8 fe 00 00 |........|........|
|00005430| ff fe 00 01 0f ff fc 00 | fa ff fa 00 0d 0f ff 00 |........|........|
|00005440| 0f ff 00 0f f0 00 0f ff | 00 00 ff fa 00 0e ff 00 |........|........|
|00005450| 0f f0 f0 00 00 0f ff 00 | 0f ff 00 0f ff fe 00 06 |........|........|
|00005460| ff f0 00 0f 00 00 ff fe | 00 16 0f f0 00 0f f0 f0 |........|........|
|00005470| 00 00 0f ff 00 0f f0 00 | 0f f0 00 00 0f ff 00 0f |........|........|
|00005480| f0 fe 00 00 0f fb ff 00 | f0 fe 00 07 0f ff 00 0f |........|........|
|00005490| ff 00 0f ff fe 00 06 ff | f0 00 0f 00 00 ff fc 00 |........|........|
|000054a0| 0e ff f0 00 ff f0 00 ff | f0 00 00 ff f0 00 0f f0 |........|........|
|000054b0| fe 00 00 0f fb ff 00 f0 | fe 00 3b ff 00 00 0f f0 |........|..;.....|
|000054c0| 00 ff 00 0f f0 00 0f f0 | 0f ff 00 00 ff 00 ff 00 |........|........|
|000054d0| 00 ff 00 ff f0 00 ff 00 | 00 ff 00 00 f0 0f ff 00 |........|........|
|000054e0| 0f f0 00 00 ff f0 00 00 | f0 00 00 ff f0 0f ff 00 |........|........|
|000054f0| 0f f0 0f f0 00 0f f0 fe | 00 00 ff fd 00 00 f0 fe |........|........|
|00005500| 00 00 0f fe 00 bf fe 00 | 00 ff fe 00 01 ff f0 ee |........|........|
|00005510| 00 0d 0f ff 00 0f ff 00 | 0f f0 00 0f ff 00 00 ff |........|........|
|00005520| fa 00 0e ff 00 0f f0 f0 | 00 00 0f ff 00 0f ff 00 |........|........|
|00005530| 0f ff fe 00 fd ff 02 00 | 00 ff fe 00 15 0f f0 00 |........|........|
|00005540| ff 00 f0 00 00 0f ff 00 | 0f f0 00 0f f0 00 00 0f |........|........|
|00005550| f0 00 ff f2 00 07 0f ff | 00 0f ff 00 0f ff fe 00 |........|........|
|00005560| fd ff 02 00 00 ff fc 00 | 0d ff f0 00 ff f0 00 ff |........|........|
|00005570| f0 00 00 ff 00 00 ff f2 | 00 1d 0f f0 00 ff 00 00 |........|........|
|00005580| ff 00 00 ff 00 ff 00 0f | f0 00 0f f0 00 0f f0 0f |........|........|
|00005590| f0 00 ff 00 0f f0 00 00 | fe ff 04 f0 0f f0 00 ff |........|........|
|000055a0| fe 00 11 ff f0 00 00 ff | 00 0f ff 00 0f f0 00 ff |........|........|
|000055b0| 00 00 ff 00 ff fd 00 00 | ff fe 00 01 0f ff fe 00 |........|........|
|000055c0| 01 ff f0 ff 00 bb 01 00 | 00 fc ff 00 f0 ed 00 0e |........|........|
|000055d0| ff ff f0 ff ff f0 ff ff | f0 ff ff f0 ff ff f0 fc |........|........|
|000055e0| 00 04 0f f0 00 0f ff fe | 00 0a ff ff f0 ff ff f0 |........|........|
|000055f0| ff ff f0 00 0f fd ff 02 | 00 0f f0 fe 00 04 ff 00 |........|........|
|00005600| 00 0f ff fe 00 02 ff ff | f0 fc ff fe 00 02 ff ff |........|........|
|00005610| f0 f2 00 0a ff ff f0 ff | ff f0 ff ff f0 00 0f fd |........|........|
|00005620| ff 02 00 0f f0 fd 00 0e | 0f ff ff 0f ff ff 0f ff |........|........|
|00005630| ff 00 00 0f ff ff f0 f1 | 00 0c ff ff f0 00 00 ff |........|........|
|00005640| 00 00 0f ff f0 00 00 fe | ff fe 00 09 ff ff 00 00 |........|........|
|00005650| 0f ff ff 00 00 0f fe ff | 04 f0 00 ff ff f0 fe 00 |........|........|
|00005660| 11 ff f0 00 00 0f ff ff | f0 00 00 ff ff f0 00 00 |........|........|
|00005670| 0f ff f0 fd 00 00 ff fd | 00 00 f0 fe 00 00 0f fe |........|........|
|00005680| 00 0c b9 00 01 0f f0 c9 | 00 01 0f f0 93 00 0c b9 |........|........|
|00005690| 00 01 0f f0 c9 00 01 0f | f0 93 00 0a b9 00 00 ff |........|........|
|000056a0| c8 00 00 ff 92 00 0a b9 | 00 00 ff c8 00 00 ff 92 |........|........|
|000056b0| 00 0a b9 00 00 f0 c8 00 | 00 f0 92 00 14 e8 00 03 |........|........|
|000056c0| f0 0f ff f0 f7 00 05 0f | f0 00 00 0f f0 81 00 bc |........|........|
|000056d0| 00 1a e9 00 04 0f ff ff | 00 f0 fb 00 0a 0f 00 00 |........|........|
|000056e0| 0f ff ff f0 0f f0 0f f0 | 81 00 bd 00 1a e9 00 04 |........|........|
|000056f0| 0f ff f0 00 f0 fb 00 0a | 0f f0 00 0f 00 00 ff ff |........|........|
|00005700| 00 00 f0 81 00 bd 00 18 | e8 00 04 ff 00 00 f0 00 |........|........|
|00005710| fa ff 08 00 0f 00 00 0f | f0 00 00 f0 81 00 bd 00 |........|........|
|00005720| 19 e8 00 03 f0 00 0f ff | fb 00 0a 0f f0 00 0f 00 |........|........|
|00005730| 00 0f ff 00 00 f0 81 00 | bd 00 19 e8 00 03 f0 00 |........|........|
|00005740| ff 0f fb 00 0a 0f 00 00 | 0f 00 00 f0 0f f0 0f f0 |........|........|
|00005750| 81 00 bd 00 15 e9 00 04 | 0f f0 00 ff ff f7 00 05 |........|........|
|00005760| ff ff 00 00 ff ff 81 00 | bc 00 04 81 00 8f 00 04 |........|........|
|00005770| 81 00 8f 00 04 81 00 8f | 00 04 81 00 8f 00 04 81 |........|........|
|00005780| 00 8f 00 00 00 ff 00 00 | 08 20 08 20 00 6c 00 24 |........|. . .l.$|
|00005790| 01 42 01 df 00 11 02 ff | 0c 00 ff ff ff ff 00 24 |.B......|.......$|
|000057a0| 00 00 00 6c 00 00 01 df | 00 00 01 42 00 00 00 00 |...l....|...B....|
|000057b0| 00 00 00 01 00 0a 00 6c | 00 24 01 42 01 df 00 98 |.......l|.$.B....|
|000057c0| 80 de 00 6c 00 24 01 42 | 01 df 00 00 00 00 00 00 |...l.$.B|........|
|000057d0| 00 00 00 48 00 00 00 48 | 00 00 00 00 00 04 00 01 |...H...H|........|
|000057e0| 00 04 00 00 00 00 00 59 | 68 68 00 00 00 00 00 00 |.......Y|hh......|
|000057f0| 04 f4 80 00 00 0f 08 00 | ff ff ff ff ff ff 20 00 |........|...... .|
|00005800| bb bb bb bb bb bb 20 00 | 99 99 66 66 33 33 20 00 |...... .|..ff33 .|
|00005810| 66 66 33 33 00 00 20 00 | 00 00 66 66 00 00 20 00 |ff33.. .|..ff.. .|
|00005820| 33 33 cc cc 33 33 20 00 | 00 00 99 99 ff ff 20 00 |33..33 .|...... .|
|00005830| 00 00 00 00 dd dd 20 00 | 33 33 00 00 99 99 20 00 |...... .|33.... .|
|00005840| ff ff 00 00 cc cc 20 00 | dd dd 00 00 00 00 20 00 |...... .|...... .|
|00005850| ff ff 66 66 00 00 20 00 | aa aa aa aa aa aa 20 00 |..ff.. .|...... .|
|00005860| ff ff ff ff 00 00 20 00 | 55 55 55 55 55 55 08 00 |...... .|UUUUUU..|
|00005870| 00 00 00 00 00 00 00 6c | 00 24 01 42 01 df 00 6c |.......l|.$.B...l|
|00005880| 00 24 01 42 01 df 00 00 | 04 81 00 a3 00 04 81 00 |.$.B....|........|
|00005890| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|000058a0| 00 04 81 00 a3 00 08 02 | ff ff f0 81 00 a6 00 04 |........|........|
|000058b0| 81 00 a3 00 0c b5 00 00 | 0f fe ff 00 f0 81 00 f4 |........|........|
|000058c0| 00 11 b5 00 fd ff 00 f0 | f2 00 00 ff dc 00 01 0f |........|........|
|000058d0| f0 ab 00 14 b6 00 05 0f | ff 00 00 ff f0 f2 00 00 |........|........|
|000058e0| ff dc 00 01 0f f0 ab 00 | 14 b6 00 05 0f f0 00 00 |........|........|
|000058f0| 0f f0 f2 00 00 ff dc 00 | 01 0f f0 ab 00 3a b6 00 |........|.....:..|
|00005900| 00 ff fe 00 05 0f f0 00 | 0f ff ff fe 00 06 ff ff |........|........|
|00005910| 0f ff 00 00 0f fd ff 00 | f0 fe 00 09 ff ff 00 00 |........|........|
|00005920| 0f ff ff 00 ff ff f9 00 | 00 0f fe ff fe 00 04 0f |........|........|
|00005930| ff 00 00 0f fc ff ad 00 | 32 b6 00 00 ff fb 00 fd |........|2.......|
|00005940| ff 01 00 00 fc ff 01 00 | 0f fd ff 02 f0 00 00 fd |........|........|
|00005950| ff 01 00 0f fc ff 00 f0 | fb 00 00 0f fd ff 02 00 |........|........|
|00005960| 00 0f fe ff 01 f0 0f fc | ff ad 00 3a b6 00 00 ff |........|...:....|
|00005970| fb 00 03 ff f0 00 ff fe | 00 03 ff f0 00 ff fe 00 |........|........|
|00005980| 00 ff fc 00 03 ff f0 0f | ff fe 00 04 ff ff f0 0f |........|........|
|00005990| f0 fb 00 0f 0f ff 00 0f | ff 00 00 ff f0 00 ff f0 |........|........|
|000059a0| 00 00 0f f0 ab 00 35 b6 | 00 00 ff f8 00 07 0f f0 |......5.|........|
|000059b0| 00 00 ff 00 00 ff fe 00 | 00 ff fd 00 09 0f ff 00 |........|........|
|000059c0| 00 ff f0 00 00 ff f0 f8 | 00 07 0f f0 00 00 ff 00 |........|........|
|000059d0| 0f ff fe 00 04 ff 00 00 | 0f f0 ab 00 36 b6 00 00 |........|....6...|
|000059e0| ff fa 00 fe ff 06 f0 00 | 00 ff 00 00 ff fe 00 00 |........|........|
|000059f0| ff fd 00 09 0f f0 00 00 | 0f f0 00 00 ff f0 f8 00 |........|........|
|00005a00| 02 0f ff ff fe 00 01 0f | f0 fe 00 04 ff 00 00 0f |........|........|
|00005a10| f0 ab 00 33 b6 00 00 ff | fb 00 00 0f fe ff 06 f0 |...3....|........|
|00005a20| 00 00 ff 00 00 ff fe 00 | 00 ff fd 00 08 0f f0 00 |........|........|
|00005a30| 00 0f f0 00 00 ff f6 00 | fe ff 02 f0 00 0f fc ff |........|........|
|00005a40| 03 00 00 0f f0 ab 00 35 | b6 00 00 ff fe 00 0d 0f |.......5|........|
|00005a50| f0 00 ff f0 00 0f f0 00 | 00 ff 00 00 ff fe 00 00 |........|........|
|00005a60| ff fd 00 08 0f f0 00 00 | 0f f0 00 00 ff f4 00 03 |........|........|
|00005a70| ff ff 00 0f fc ff 03 00 | 00 0f f0 ab 00 3a b6 00 |........|.....:..|
|00005a80| 11 0f f0 00 00 0f f0 00 | ff 00 00 0f f0 00 00 ff |........|........|
|00005a90| 00 00 ff fe 00 0d ff 00 | 0f f0 00 0f f0 00 00 0f |........|........|
|00005aa0| f0 00 00 ff f7 00 07 0f | f0 00 00 ff 00 0f f0 fb |........|........|
|00005ab0| 00 03 0f f0 00 ff ad 00 | 3d b6 00 11 0f ff 00 00 |........|=.......|
|00005ac0| ff f0 00 ff 00 00 ff f0 | 00 00 ff 00 00 ff fe 00 |........|........|
|00005ad0| 0d ff 00 0f f0 00 0f ff | 00 00 ff f0 00 00 ff f7 |........|........|
|00005ae0| 00 11 0f f0 00 00 ff 00 | 0f ff f0 00 00 ff 00 00 |........|........|
|00005af0| 0f f0 00 ff ad 00 33 b5 | 00 fd ff 01 00 00 fc ff |......3.|........|
|00005b00| 00 f0 fe ff 0a 0f ff ff | 00 00 0f ff ff f0 00 00 |........|........|
|00005b10| fd ff 01 00 0f fd ff f9 | 00 00 0f fd ff 01 00 00 |........|........|
|00005b20| fc ff 02 00 00 0f fe ff | ad 00 3a b5 00 06 0f ff |........|..:.....|
|00005b30| ff f0 00 00 0f fd ff 00 | f0 fe ff 07 0f ff ff 00 |........|........|
|00005b40| 00 0f ff ff fe 00 05 0f | ff ff f0 00 0f fd ff f9 |........|........|
|00005b50| 00 00 0f fe ff 00 f0 fe | 00 fe ff 00 f0 fe 00 02 |........|........|
|00005b60| ff ff f0 ad 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005b70| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005b80| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005b90| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005ba0| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005bb0| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005bc0| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005bd0| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005be0| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005bf0| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005c00| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005c10| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005c20| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005c30| a3 00 08 fe 00 81 ff ab | ff fc 00 08 fe 00 81 ff |........|........|
|00005c40| ab ff fc 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005c50| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005c60| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005c70| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005c80| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005c90| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005ca0| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005cb0| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005cc0| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005cd0| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005ce0| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005cf0| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005d00| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005d10| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005d20| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005d30| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005d40| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005d50| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 0e fe 00 b8 |........|........|
|00005d60| ff be 00 00 0f b9 ff 00 | f0 fc 00 04 81 00 a3 00 |........|........|
|00005d70| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005d80| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005d90| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005da0| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005db0| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005dc0| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005dd0| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005de0| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005df0| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005e00| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005e10| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005e20| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005e30| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005e40| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005e50| 00 1a fe 00 ec ff 00 f0 | e4 00 00 0f ec ff bf 00 |........|........|
|00005e60| 00 0f ec ff e2 00 ec ff | 00 f0 fc 00 1a fe 00 ec |........|........|
|00005e70| ff 00 f0 e4 00 00 0f ec | ff bf 00 00 0f ec ff e2 |........|........|
|00005e80| 00 ec ff 00 f0 fc 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005e90| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005ea0| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005eb0| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005ec0| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005ed0| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 04 81 00 a3 |........|........|
|00005ee0| 00 04 81 00 a3 00 04 81 | 00 a3 00 04 81 00 a3 00 |........|........|
|00005ef0| 04 81 00 a3 00 04 81 00 | a3 00 04 81 00 a3 00 04 |........|........|
|00005f00| 81 00 a3 00 04 81 00 a3 | 00 04 81 00 a3 00 04 81 |........|........|
|00005f10| 00 a3 00 04 81 00 a3 00 | 04 81 00 a3 00 04 81 00 |........|........|
|00005f20| a3 00 04 81 00 a3 00 04 | 81 00 a3 00 0c 81 00 bf |........|........|
|00005f30| 00 f8 ff fd 00 f8 ff fb | 00 04 81 00 a3 00 14 81 |........|........|
|00005f40| 00 f4 00 00 0f f9 ff 00 | f0 fe 00 00 0f f9 ff 00 |........|........|
|00005f50| f0 c7 00 10 cc 00 00 0f | f9 ff 00 f0 fd 00 f8 ff |........|........|
|00005f60| 81 00 ef 00 10 cc 00 00 | 0f f9 ff 00 f0 fd 00 f8 |........|........|
|00005f70| ff 81 00 ef 00 11 01 00 | 00 f8 ff fd 00 00 0f f9 |........|........|
|00005f80| ff 00 f0 81 00 bc 00 11 | 01 00 00 f8 ff fd 00 00 |........|........|
|00005f90| 0f f9 ff 00 f0 81 00 bc | 00 04 81 00 a3 00 04 81 |........|........|
|00005fa0| 00 a3 00 04 81 00 a3 00 | 00 ff 00 00 0f aa 0f aa |........|........|
|00005fb0| 00 a9 00 36 00 f9 01 b0 | 00 11 02 ff 0c 00 ff ff |...6....|........|
|00005fc0| ff ff 00 36 00 00 00 a9 | 00 00 01 b0 00 00 00 f9 |...6....|........|
|00005fd0| 00 00 00 00 00 00 00 01 | 00 0a 00 a9 00 36 00 f9 |........|.....6..|
|00005fe0| 01 b0 00 98 80 be 00 a9 | 00 36 00 f9 01 b0 00 00 |........|.6......|
|00005ff0| 00 00 00 00 00 00 00 48 | 00 00 00 48 00 00 00 00 |.......H|...H....|
|00006000| 00 04 00 01 00 04 00 00 | 00 00 00 59 67 cc 00 00 |........|...Yg...|
|00006010| 00 00 00 00 04 f4 80 00 | 00 0f 08 00 ff ff ff ff |........|........|
|00006020| ff ff 20 00 bb bb bb bb | bb bb 20 00 99 99 66 66 |.. .....|.. ...ff|
|00006030| 33 33 20 00 66 66 33 33 | 00 00 20 00 00 00 66 66 |33 .ff33|.. ...ff|
|00006040| 00 00 20 00 33 33 cc cc | 33 33 20 00 00 00 99 99 |.. .33..|33 .....|
|00006050| ff ff 20 00 00 00 00 00 | dd dd 20 00 33 33 00 00 |.. .....|.. .33..|
|00006060| 99 99 20 00 ff ff 00 00 | cc cc 20 00 dd dd 00 00 |.. .....|.. .....|
|00006070| 00 00 20 00 ff ff 66 66 | 00 00 20 00 aa aa aa aa |.. ...ff|.. .....|
|00006080| aa aa 20 00 ff ff ff ff | 00 00 20 00 55 55 55 55 |.. .....|.. .UUUU|
|00006090| 55 55 08 00 00 00 00 00 | 00 00 00 a9 00 36 00 f9 |UU......|.....6..|
|000060a0| 01 b0 00 a9 00 36 00 f9 | 01 b0 00 00 04 81 00 c3 |.....6..|........|
|000060b0| 00 04 81 00 c3 00 04 81 | 00 c3 00 04 81 00 c3 00 |........|........|
|000060c0| 04 81 00 c3 00 04 81 00 | c3 00 04 81 00 c3 00 04 |........|........|
|000060d0| 81 00 c3 00 22 fa 00 00 | ff ec 00 00 ff e3 00 00 |...."...|........|
|000060e0| ff df 00 00 ff f1 00 00 | ff ef 00 00 ff e4 00 00 |........|........|
|000060f0| ff ef 00 00 ff f8 00 2a | fb 00 01 0f f0 ec 00 01 |.......*|........|
|00006100| 0f f0 e5 00 01 0f f0 df | 00 01 0f f0 f3 00 01 0f |........|........|
|00006110| f0 ef 00 01 0f f0 e6 00 | 01 0f f0 ef 00 01 0f f0 |........|........|
|00006120| f9 00 2a fb 00 01 0f f0 | ec 00 01 0f f0 e5 00 01 |..*.....|........|
|00006130| 0f f0 df 00 01 0f f0 f3 | 00 01 0f f0 ef 00 01 0f |........|........|
|00006140| f0 e6 00 01 0f f0 ef 00 | 01 0f f0 f9 00 22 fb 00 |........|....."..|
|00006150| 00 ff ea 00 00 ff e5 00 | 00 ff dd 00 00 ff f3 00 |........|........|
|00006160| 00 ff ed 00 00 ff e6 00 | 00 ff ed 00 00 ff f9 00 |........|........|
|00006170| 33 fc 00 01 0f f0 f2 00 | 00 ff fa 00 01 0f f0 e7 |3.......|........|
|00006180| 00 01 0f f0 e7 00 01 ff | f0 f9 00 01 0f f0 f5 00 |........|........|
|00006190| 01 0f f0 ed 00 01 0f f0 | e8 00 01 0f f0 ed 00 01 |........|........|
|000061a0| 0f f0 fa 00 33 fc 00 01 | 0f f0 f2 00 00 ff fa 00 |....3...|........|
|000061b0| 01 0f f0 e7 00 01 0f f0 | e8 00 01 ff ff f8 00 01 |........|........|
|000061c0| 0f f0 f5 00 01 0f f0 ed | 00 01 0f f0 e8 00 01 0f |........|........|
|000061d0| f0 ed 00 01 0f f0 fa 00 | 2b fc 00 00 ff f2 00 01 |........|+.......|
|000061e0| 0f ff f9 00 00 ff e7 00 | 00 ff e6 00 00 ff f7 00 |........|........|
|000061f0| 00 ff f5 00 00 ff eb 00 | 00 ff e8 00 00 ff eb 00 |........|........|
|00006200| 00 ff fa 00 34 fd 00 01 | 0f ff f2 00 01 0f ff f9 |....4...|........|
|00006210| 00 01 ff f0 e9 00 01 0f | ff e7 00 01 0f f0 f7 00 |........|........|
|00006220| 01 ff f0 f7 00 01 0f ff | eb 00 01 ff f0 ea 00 01 |........|........|
|00006230| 0f ff eb 00 01 ff f0 fb | 00 34 fd 00 01 0f f0 f2 |........|.4......|
|00006240| 00 01 0f f0 f9 00 01 0f | f0 e9 00 01 0f f0 e7 00 |........|........|
|00006250| 01 0f f0 f7 00 01 0f f0 | f7 00 01 0f f0 eb 00 01 |........|........|
|00006260| 0f f0 ea 00 01 0f f0 eb | 00 01 0f f0 fb 00 34 fd |........|......4.|
|00006270| 00 01 ff f0 f2 00 01 0f | f0 f9 00 01 0f ff e9 00 |........|........|
|00006280| 01 ff f0 e7 00 01 0f f0 | f7 00 01 0f ff f7 00 01 |........|........|
|00006290| ff f0 eb 00 01 0f ff ea | 00 01 ff f0 eb 00 01 0f |........|........|
|000062a0| ff fb 00 2b fd 00 00 ff | f1 00 00 ff f7 00 00 ff |...+....|........|
|000062b0| e9 00 00 ff e6 00 01 0f | f0 f6 00 00 ff f7 00 00 |........|........|
|000062c0| ff e9 00 00 ff ea 00 00 | ff e9 00 00 ff fb 00 43 |........|.......C|
|000062d0| fd 00 00 ff f6 00 05 ff | 00 ff f0 00 ff f7 00 00 |........|........|
|000062e0| ff e9 00 00 ff f6 00 02 | ff f0 0f f4 00 02 ff 00 |........|........|
|000062f0| ff f7 00 00 ff f7 00 00 | ff f6 00 03 ff 00 ff f0 |........|........|
|00006300| f8 00 00 ff ea 00 00 ff | f5 00 01 0f ff f7 00 00 |........|........|
|00006310| ff fb 00 51 fe 00 01 0f | ff f7 00 06 ff 0f ff f0 |...Q....|........|
|00006320| ff 00 f0 f7 00 01 ff f0 | eb 00 01 0f ff f7 00 03 |........|........|
|00006330| 0f f0 0f ff f4 00 03 ff | ff 0f ff f8 00 01 ff f0 |........|........|
|00006340| f9 00 01 0f ff f7 00 04 | ff 0f ff f0 ff f8 00 01 |........|........|
|00006350| ff f0 ec 00 01 0f ff f6 | 00 03 ff f0 0f f0 f8 00 |........|........|
|00006360| 01 ff f0 fc 00 52 fe 00 | 01 0f f0 f8 00 05 0f 00 |.....R..|........|
|00006370| 00 ff 00 ff f5 00 01 0f | f0 eb 00 01 0f f0 f7 00 |........|........|
|00006380| 03 ff 00 00 ff f4 00 03 | ff 00 00 ff f8 00 01 0f |........|........|
|00006390| f0 f9 00 01 0f f0 f8 00 | 05 0f 00 00 ff 00 ff f8 |........|........|
|000063a0| 00 01 0f f0 ec 00 01 0f | f0 f7 00 04 0f ff 00 00 |........|........|
|000063b0| f0 f8 00 01 0f f0 fc 00 | 53 fe 00 01 0f f0 f8 00 |........|S.......|
|000063c0| 05 0f 00 00 ff 00 ff f5 | 00 01 0f f0 eb 00 01 0f |........|........|
|000063d0| f0 f8 00 04 0f f0 00 00 | ff f4 00 03 ff 00 00 ff |........|........|
|000063e0| f8 00 01 0f f0 f9 00 01 | 0f f0 f8 00 05 0f 00 00 |........|........|
|000063f0| ff 00 ff f8 00 01 0f f0 | ec 00 01 0f f0 f7 00 04 |........|........|
+--------+-------------------------+-------------------------+--------+--------+
Only 25.0 KB of data is shown above.