Home » Archimedes archive » Micro User » MU 1991-07.adf » PD-Stuff » Fractals/!Martin/!Help
Fractals/!Martin/!Help
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Micro User » MU 1991-07.adf » PD-Stuff |
| Filename: | Fractals/!Martin/!Help |
| Read OK: | ✔ |
| File size: | 0348 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
Help file for !Martin v1.0 !Martin uses the algorithm discovered by the man of the same name - Dr Barry Martin, and was originally published in the Scientific American. I gather it works due to rounding errors caused by the use of floating point numbers. These numbers are only stored approximately by the programming language / computer, and thus errors gradually creep in by the repeated calculation. Performing the same calculation using a different floating point mechanism will produce different results. The key to the routine is the SGN term - without it nothing spectacular happens. You can try different calculations to produce a similar effect. The amazing thing about the routine is its simplicity and speed. In fact you can reduce this program to just 1 line of BASIC code! Mike Curnow, Archimedes Fractal Group, April 1991
00000000 48 65 6c 70 20 66 69 6c 65 20 66 6f 72 20 21 4d |Help file for !M| 00000010 61 72 74 69 6e 20 76 31 2e 30 0a 0a 21 4d 61 72 |artin v1.0..!Mar| 00000020 74 69 6e 20 75 73 65 73 20 74 68 65 20 61 6c 67 |tin uses the alg| 00000030 6f 72 69 74 68 6d 20 64 69 73 63 6f 76 65 72 65 |orithm discovere| 00000040 64 20 62 79 20 74 68 65 20 6d 61 6e 20 6f 66 20 |d by the man of | 00000050 74 68 65 20 73 61 6d 65 20 6e 61 6d 65 20 2d 20 |the same name - | 00000060 44 72 20 42 61 72 72 79 0a 4d 61 72 74 69 6e 2c |Dr Barry.Martin,| 00000070 20 61 6e 64 20 77 61 73 20 6f 72 69 67 69 6e 61 | and was origina| 00000080 6c 6c 79 20 70 75 62 6c 69 73 68 65 64 20 69 6e |lly published in| 00000090 20 74 68 65 20 53 63 69 65 6e 74 69 66 69 63 20 | the Scientific | 000000a0 41 6d 65 72 69 63 61 6e 2e 20 49 20 67 61 74 68 |American. I gath| 000000b0 65 72 20 69 74 0a 77 6f 72 6b 73 20 64 75 65 20 |er it.works due | 000000c0 74 6f 20 72 6f 75 6e 64 69 6e 67 20 65 72 72 6f |to rounding erro| 000000d0 72 73 20 63 61 75 73 65 64 20 62 79 20 74 68 65 |rs caused by the| 000000e0 20 75 73 65 20 6f 66 20 66 6c 6f 61 74 69 6e 67 | use of floating| 000000f0 20 70 6f 69 6e 74 20 6e 75 6d 62 65 72 73 2e 0a | point numbers..| 00000100 54 68 65 73 65 20 6e 75 6d 62 65 72 73 20 61 72 |These numbers ar| 00000110 65 20 6f 6e 6c 79 20 73 74 6f 72 65 64 20 61 70 |e only stored ap| 00000120 70 72 6f 78 69 6d 61 74 65 6c 79 20 62 79 20 74 |proximately by t| 00000130 68 65 20 70 72 6f 67 72 61 6d 6d 69 6e 67 20 6c |he programming l| 00000140 61 6e 67 75 61 67 65 20 2f 0a 63 6f 6d 70 75 74 |anguage /.comput| 00000150 65 72 2c 20 61 6e 64 20 74 68 75 73 20 65 72 72 |er, and thus err| 00000160 6f 72 73 20 67 72 61 64 75 61 6c 6c 79 20 63 72 |ors gradually cr| 00000170 65 65 70 20 69 6e 20 62 79 20 74 68 65 20 72 65 |eep in by the re| 00000180 70 65 61 74 65 64 20 63 61 6c 63 75 6c 61 74 69 |peated calculati| 00000190 6f 6e 2e 0a 0a 50 65 72 66 6f 72 6d 69 6e 67 20 |on...Performing | 000001a0 74 68 65 20 73 61 6d 65 20 63 61 6c 63 75 6c 61 |the same calcula| 000001b0 74 69 6f 6e 20 75 73 69 6e 67 20 61 20 64 69 66 |tion using a dif| 000001c0 66 65 72 65 6e 74 20 66 6c 6f 61 74 69 6e 67 20 |ferent floating | 000001d0 70 6f 69 6e 74 20 6d 65 63 68 61 6e 69 73 6d 0a |point mechanism.| 000001e0 77 69 6c 6c 20 70 72 6f 64 75 63 65 20 64 69 66 |will produce dif| 000001f0 66 65 72 65 6e 74 20 72 65 73 75 6c 74 73 2e 0a |ferent results..| 00000200 0a 54 68 65 20 6b 65 79 20 74 6f 20 74 68 65 20 |.The key to the | 00000210 72 6f 75 74 69 6e 65 20 69 73 20 74 68 65 20 53 |routine is the S| 00000220 47 4e 20 74 65 72 6d 20 2d 20 77 69 74 68 6f 75 |GN term - withou| 00000230 74 20 69 74 20 6e 6f 74 68 69 6e 67 20 73 70 65 |t it nothing spe| 00000240 63 74 61 63 75 6c 61 72 0a 68 61 70 70 65 6e 73 |ctacular.happens| 00000250 2e 20 59 6f 75 20 63 61 6e 20 74 72 79 20 64 69 |. You can try di| 00000260 66 66 65 72 65 6e 74 20 63 61 6c 63 75 6c 61 74 |fferent calculat| 00000270 69 6f 6e 73 20 74 6f 20 70 72 6f 64 75 63 65 20 |ions to produce | 00000280 61 20 73 69 6d 69 6c 61 72 20 65 66 66 65 63 74 |a similar effect| 00000290 2e 0a 0a 54 68 65 20 61 6d 61 7a 69 6e 67 20 74 |...The amazing t| 000002a0 68 69 6e 67 20 61 62 6f 75 74 20 74 68 65 20 72 |hing about the r| 000002b0 6f 75 74 69 6e 65 20 69 73 20 69 74 73 20 73 69 |outine is its si| 000002c0 6d 70 6c 69 63 69 74 79 20 61 6e 64 20 73 70 65 |mplicity and spe| 000002d0 65 64 2e 20 49 6e 20 66 61 63 74 20 79 6f 75 0a |ed. In fact you.| 000002e0 63 61 6e 20 72 65 64 75 63 65 20 74 68 69 73 20 |can reduce this | 000002f0 70 72 6f 67 72 61 6d 20 74 6f 20 6a 75 73 74 20 |program to just | 00000300 31 20 6c 69 6e 65 20 6f 66 20 42 41 53 49 43 20 |1 line of BASIC | 00000310 63 6f 64 65 21 0a 0a 4d 69 6b 65 20 43 75 72 6e |code!..Mike Curn| 00000320 6f 77 2c 0a 41 72 63 68 69 6d 65 64 65 73 20 46 |ow,.Archimedes F| 00000330 72 61 63 74 61 6c 20 47 72 6f 75 70 2c 0a 41 70 |ractal Group,.Ap| 00000340 72 69 6c 20 31 39 39 31 |ril 1991| 00000348
.