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Hudson/ReadMe
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 » Recent acquisitions » Acorn ADFS disks » adfs_AcornUser_199312.adf » !StarInfo_StarInfo |
| Filename: | Hudson/ReadMe |
| Read OK: | ✔ |
| File size: | 0A41 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
Riemann:
This particular Riemann sphere has every single complex number
on it. Beginning at 0 at the front, the real numbers go +ve to
the right and -ve to the left, stretching around the sphere. If
0 is at the front, then 1 is on the rightmost point and -1 on
the leftmost point. The numbers continue to rise sharply as you
continue around to the back; directly behind the 0 point on the
front is a +/- infinity point on the back. Going up and over the
sphere are the positive imaginary numbers, and down and under
the negative ones, with the +/- infinite imaginary numbers
joining up with the +/- infinite real numbers at the back. This
can be hard to visualise - see DRAW file.
Note about complex numbers:
These are numbers with a normal (or "real") part and an
imaginary part. The imaginary part doesn't really exist, and is
shown as a multiple of the square root of -1, called i.
For more advanced readers, the Riemann sphere in this case is
produced by mapping an Argand diagram through an arctangent, and
then wrapping around a sphere. Equal moduli form concentric
circles around the sphere, with the Great circle being modulus
of 1.
The Julia set is just an ordinary Julia set, and has been
explained in Acorn User/ BBC Acorn user in 1986, 1987, 1988,
1989, 1990, 1991, 1992 and 1993, along with 1983, so I won't go
into it again.
Here are some run-time statistics which show the speed
improvements made by my fast algorithm (although I don't want to
boast:)
Type of Julia set Coords Time Time % speed
without with increase
lots of low iteration area 1,1 225.17 32.24 86
loads of detail, no blue .3,.6 506.89 504.24 .5
About 50% blue area .3,.5 1091.68 602.98 45
Mostly blue -.75,0 1612.39 273.94 83
(All the above sets were plotted head-on with la & lo =0)
The times are in seconds. "Time without" represents the time
taken to plot the complete globe scanning every pixel on the
screen. "Time with" shows the time taken using my fast(er)
algorithm. All screens with lots of colour the same benefit
greaty from the algorithm. Even the Cantor dust at 0.3, 0.6 is
not worse than the original pixel by pixel plot.
The following times show how the speed of the plot vary with the
variable z%, which controls the scanning square size.
Square size time (seconds)
8 583
12 499
16 492
20 515
24 532
28 559
32 575
00000000 52 69 65 6d 61 6e 6e 3a 0a 0a 54 68 69 73 20 70 |Riemann:..This p| 00000010 61 72 74 69 63 75 6c 61 72 20 52 69 65 6d 61 6e |articular Rieman| 00000020 6e 20 73 70 68 65 72 65 20 68 61 73 20 65 76 65 |n sphere has eve| 00000030 72 79 20 73 69 6e 67 6c 65 20 63 6f 6d 70 6c 65 |ry single comple| 00000040 78 20 6e 75 6d 62 65 72 0a 6f 6e 20 69 74 2e 20 |x number.on it. | 00000050 42 65 67 69 6e 6e 69 6e 67 20 61 74 20 30 20 61 |Beginning at 0 a| 00000060 74 20 74 68 65 20 66 72 6f 6e 74 2c 20 74 68 65 |t the front, the| 00000070 20 72 65 61 6c 20 6e 75 6d 62 65 72 73 20 67 6f | real numbers go| 00000080 20 2b 76 65 20 74 6f 0a 74 68 65 20 72 69 67 68 | +ve to.the righ| 00000090 74 20 61 6e 64 20 2d 76 65 20 74 6f 20 74 68 65 |t and -ve to the| 000000a0 20 6c 65 66 74 2c 20 73 74 72 65 74 63 68 69 6e | left, stretchin| 000000b0 67 20 61 72 6f 75 6e 64 20 74 68 65 20 73 70 68 |g around the sph| 000000c0 65 72 65 2e 20 49 66 0a 30 20 69 73 20 61 74 20 |ere. If.0 is at | 000000d0 74 68 65 20 66 72 6f 6e 74 2c 20 74 68 65 6e 20 |the front, then | 000000e0 31 20 69 73 20 6f 6e 20 74 68 65 20 72 69 67 68 |1 is on the righ| 000000f0 74 6d 6f 73 74 20 70 6f 69 6e 74 20 61 6e 64 20 |tmost point and | 00000100 2d 31 20 6f 6e 0a 74 68 65 20 6c 65 66 74 6d 6f |-1 on.the leftmo| 00000110 73 74 20 70 6f 69 6e 74 2e 20 54 68 65 20 6e 75 |st point. The nu| 00000120 6d 62 65 72 73 20 63 6f 6e 74 69 6e 75 65 20 74 |mbers continue t| 00000130 6f 20 72 69 73 65 20 73 68 61 72 70 6c 79 20 61 |o rise sharply a| 00000140 73 20 79 6f 75 0a 63 6f 6e 74 69 6e 75 65 20 61 |s you.continue a| 00000150 72 6f 75 6e 64 20 74 6f 20 74 68 65 20 62 61 63 |round to the bac| 00000160 6b 3b 20 64 69 72 65 63 74 6c 79 20 62 65 68 69 |k; directly behi| 00000170 6e 64 20 74 68 65 20 30 20 70 6f 69 6e 74 20 6f |nd the 0 point o| 00000180 6e 20 74 68 65 0a 66 72 6f 6e 74 20 69 73 20 61 |n the.front is a| 00000190 20 2b 2f 2d 20 69 6e 66 69 6e 69 74 79 20 70 6f | +/- infinity po| 000001a0 69 6e 74 20 6f 6e 20 74 68 65 20 62 61 63 6b 2e |int on the back.| 000001b0 20 47 6f 69 6e 67 20 75 70 20 61 6e 64 20 6f 76 | Going up and ov| 000001c0 65 72 20 74 68 65 0a 73 70 68 65 72 65 20 61 72 |er the.sphere ar| 000001d0 65 20 74 68 65 20 70 6f 73 69 74 69 76 65 20 69 |e the positive i| 000001e0 6d 61 67 69 6e 61 72 79 20 6e 75 6d 62 65 72 73 |maginary numbers| 000001f0 2c 20 61 6e 64 20 64 6f 77 6e 20 61 6e 64 20 75 |, and down and u| 00000200 6e 64 65 72 0a 74 68 65 20 6e 65 67 61 74 69 76 |nder.the negativ| 00000210 65 20 6f 6e 65 73 2c 20 77 69 74 68 20 74 68 65 |e ones, with the| 00000220 20 2b 2f 2d 20 69 6e 66 69 6e 69 74 65 20 69 6d | +/- infinite im| 00000230 61 67 69 6e 61 72 79 20 6e 75 6d 62 65 72 73 0a |aginary numbers.| 00000240 6a 6f 69 6e 69 6e 67 20 75 70 20 77 69 74 68 20 |joining up with | 00000250 74 68 65 20 2b 2f 2d 20 69 6e 66 69 6e 69 74 65 |the +/- infinite| 00000260 20 72 65 61 6c 20 6e 75 6d 62 65 72 73 20 61 74 | real numbers at| 00000270 20 74 68 65 20 62 61 63 6b 2e 20 54 68 69 73 0a | the back. This.| 00000280 63 61 6e 20 62 65 20 68 61 72 64 20 74 6f 20 76 |can be hard to v| 00000290 69 73 75 61 6c 69 73 65 20 2d 20 73 65 65 20 44 |isualise - see D| 000002a0 52 41 57 20 66 69 6c 65 2e 0a 0a 4e 6f 74 65 20 |RAW file...Note | 000002b0 61 62 6f 75 74 20 63 6f 6d 70 6c 65 78 20 6e 75 |about complex nu| 000002c0 6d 62 65 72 73 3a 0a 0a 54 68 65 73 65 20 61 72 |mbers:..These ar| 000002d0 65 20 6e 75 6d 62 65 72 73 20 77 69 74 68 20 61 |e numbers with a| 000002e0 20 6e 6f 72 6d 61 6c 20 28 6f 72 20 22 72 65 61 | normal (or "rea| 000002f0 6c 22 29 20 70 61 72 74 20 61 6e 64 20 61 6e 0a |l") part and an.| 00000300 69 6d 61 67 69 6e 61 72 79 20 70 61 72 74 2e 20 |imaginary part. | 00000310 54 68 65 20 69 6d 61 67 69 6e 61 72 79 20 70 61 |The imaginary pa| 00000320 72 74 20 64 6f 65 73 6e 27 74 20 72 65 61 6c 6c |rt doesn't reall| 00000330 79 20 65 78 69 73 74 2c 20 61 6e 64 20 69 73 0a |y exist, and is.| 00000340 73 68 6f 77 6e 20 61 73 20 61 20 6d 75 6c 74 69 |shown as a multi| 00000350 70 6c 65 20 6f 66 20 74 68 65 20 73 71 75 61 72 |ple of the squar| 00000360 65 20 72 6f 6f 74 20 6f 66 20 2d 31 2c 20 63 61 |e root of -1, ca| 00000370 6c 6c 65 64 20 69 2e 0a 0a 46 6f 72 20 6d 6f 72 |lled i...For mor| 00000380 65 20 61 64 76 61 6e 63 65 64 20 72 65 61 64 65 |e advanced reade| 00000390 72 73 2c 20 74 68 65 20 52 69 65 6d 61 6e 6e 20 |rs, the Riemann | 000003a0 73 70 68 65 72 65 20 69 6e 20 74 68 69 73 20 63 |sphere in this c| 000003b0 61 73 65 20 69 73 0a 70 72 6f 64 75 63 65 64 20 |ase is.produced | 000003c0 62 79 20 6d 61 70 70 69 6e 67 20 61 6e 20 41 72 |by mapping an Ar| 000003d0 67 61 6e 64 20 64 69 61 67 72 61 6d 20 74 68 72 |gand diagram thr| 000003e0 6f 75 67 68 20 61 6e 20 61 72 63 74 61 6e 67 65 |ough an arctange| 000003f0 6e 74 2c 20 61 6e 64 0a 74 68 65 6e 20 77 72 61 |nt, and.then wra| 00000400 70 70 69 6e 67 20 61 72 6f 75 6e 64 20 61 20 73 |pping around a s| 00000410 70 68 65 72 65 2e 20 45 71 75 61 6c 20 6d 6f 64 |phere. Equal mod| 00000420 75 6c 69 20 66 6f 72 6d 20 63 6f 6e 63 65 6e 74 |uli form concent| 00000430 72 69 63 0a 63 69 72 63 6c 65 73 20 61 72 6f 75 |ric.circles arou| 00000440 6e 64 20 74 68 65 20 73 70 68 65 72 65 2c 20 77 |nd the sphere, w| 00000450 69 74 68 20 74 68 65 20 47 72 65 61 74 20 63 69 |ith the Great ci| 00000460 72 63 6c 65 20 62 65 69 6e 67 20 6d 6f 64 75 6c |rcle being modul| 00000470 75 73 0a 6f 66 20 31 2e 0a 0a 54 68 65 20 4a 75 |us.of 1...The Ju| 00000480 6c 69 61 20 73 65 74 20 69 73 20 6a 75 73 74 20 |lia set is just | 00000490 61 6e 20 6f 72 64 69 6e 61 72 79 20 4a 75 6c 69 |an ordinary Juli| 000004a0 61 20 73 65 74 2c 20 61 6e 64 20 68 61 73 20 62 |a set, and has b| 000004b0 65 65 6e 0a 65 78 70 6c 61 69 6e 65 64 20 69 6e |een.explained in| 000004c0 20 41 63 6f 72 6e 20 55 73 65 72 2f 20 42 42 43 | Acorn User/ BBC| 000004d0 20 41 63 6f 72 6e 20 75 73 65 72 20 69 6e 20 31 | Acorn user in 1| 000004e0 39 38 36 2c 20 31 39 38 37 2c 20 31 39 38 38 2c |986, 1987, 1988,| 000004f0 0a 31 39 38 39 2c 20 31 39 39 30 2c 20 31 39 39 |.1989, 1990, 199| 00000500 31 2c 20 31 39 39 32 20 61 6e 64 20 31 39 39 33 |1, 1992 and 1993| 00000510 2c 20 61 6c 6f 6e 67 20 77 69 74 68 20 31 39 38 |, along with 198| 00000520 33 2c 20 73 6f 20 49 20 77 6f 6e 27 74 20 67 6f |3, so I won't go| 00000530 0a 69 6e 74 6f 20 69 74 20 61 67 61 69 6e 2e 0a |.into it again..| 00000540 0a 48 65 72 65 20 61 72 65 20 73 6f 6d 65 20 72 |.Here are some r| 00000550 75 6e 2d 74 69 6d 65 20 73 74 61 74 69 73 74 69 |un-time statisti| 00000560 63 73 20 77 68 69 63 68 20 73 68 6f 77 20 74 68 |cs which show th| 00000570 65 20 73 70 65 65 64 0a 69 6d 70 72 6f 76 65 6d |e speed.improvem| 00000580 65 6e 74 73 20 6d 61 64 65 20 62 79 20 6d 79 20 |ents made by my | 00000590 66 61 73 74 20 61 6c 67 6f 72 69 74 68 6d 20 28 |fast algorithm (| 000005a0 61 6c 74 68 6f 75 67 68 20 49 20 64 6f 6e 27 74 |although I don't| 000005b0 20 77 61 6e 74 20 74 6f 0a 62 6f 61 73 74 3a 29 | want to.boast:)| 000005c0 0a 0a 54 79 70 65 20 6f 66 20 4a 75 6c 69 61 20 |..Type of Julia | 000005d0 73 65 74 20 20 20 20 20 20 20 20 20 20 43 6f 6f |set Coo| 000005e0 72 64 73 20 20 20 54 69 6d 65 20 20 20 20 20 20 |rds Time | 000005f0 54 69 6d 65 20 20 20 20 20 20 25 20 73 70 65 65 |Time % spee| 00000600 64 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |d. | 00000610 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000620 20 20 20 20 20 77 69 74 68 6f 75 74 20 20 20 20 | without | 00000630 77 69 74 68 20 20 20 20 20 69 6e 63 72 65 61 73 |with increas| 00000640 65 0a 0a 6c 6f 74 73 20 6f 66 20 6c 6f 77 20 69 |e..lots of low i| 00000650 74 65 72 61 74 69 6f 6e 20 61 72 65 61 20 20 31 |teration area 1| 00000660 2c 31 20 20 20 20 20 32 32 35 2e 31 37 20 20 20 |,1 225.17 | 00000670 20 33 32 2e 32 34 20 20 20 20 20 38 36 0a 6c 6f | 32.24 86.lo| 00000680 61 64 73 20 6f 66 20 64 65 74 61 69 6c 2c 20 6e |ads of detail, n| 00000690 6f 20 62 6c 75 65 20 20 20 20 2e 33 2c 2e 36 20 |o blue .3,.6 | 000006a0 20 20 35 30 36 2e 38 39 20 20 20 20 35 30 34 2e | 506.89 504.| 000006b0 32 34 20 20 20 20 2e 35 0a 41 62 6f 75 74 20 35 |24 .5.About 5| 000006c0 30 25 20 62 6c 75 65 20 61 72 65 61 20 20 20 20 |0% blue area | 000006d0 20 20 20 20 20 2e 33 2c 2e 35 20 20 20 31 30 39 | .3,.5 109| 000006e0 31 2e 36 38 20 20 20 36 30 32 2e 39 38 20 20 20 |1.68 602.98 | 000006f0 20 34 35 0a 4d 6f 73 74 6c 79 20 62 6c 75 65 20 | 45.Mostly blue | 00000700 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000710 2d 2e 37 35 2c 30 20 20 31 36 31 32 2e 33 39 20 |-.75,0 1612.39 | 00000720 20 20 32 37 33 2e 39 34 20 20 20 20 38 33 0a 0a | 273.94 83..| 00000730 28 41 6c 6c 20 74 68 65 20 61 62 6f 76 65 20 73 |(All the above s| 00000740 65 74 73 20 77 65 72 65 20 70 6c 6f 74 74 65 64 |ets were plotted| 00000750 20 68 65 61 64 2d 6f 6e 20 77 69 74 68 20 6c 61 | head-on with la| 00000760 20 26 20 6c 6f 20 3d 30 29 20 0a 54 68 65 20 74 | & lo =0) .The t| 00000770 69 6d 65 73 20 61 72 65 20 69 6e 20 73 65 63 6f |imes are in seco| 00000780 6e 64 73 2e 20 22 54 69 6d 65 20 77 69 74 68 6f |nds. "Time witho| 00000790 75 74 22 20 72 65 70 72 65 73 65 6e 74 73 20 74 |ut" represents t| 000007a0 68 65 20 74 69 6d 65 0a 74 61 6b 65 6e 20 74 6f |he time.taken to| 000007b0 20 70 6c 6f 74 20 74 68 65 20 63 6f 6d 70 6c 65 | plot the comple| 000007c0 74 65 20 67 6c 6f 62 65 20 73 63 61 6e 6e 69 6e |te globe scannin| 000007d0 67 20 65 76 65 72 79 20 70 69 78 65 6c 20 6f 6e |g every pixel on| 000007e0 20 74 68 65 0a 73 63 72 65 65 6e 2e 20 22 54 69 | the.screen. "Ti| 000007f0 6d 65 20 77 69 74 68 22 20 73 68 6f 77 73 20 74 |me with" shows t| 00000800 68 65 20 74 69 6d 65 20 74 61 6b 65 6e 20 75 73 |he time taken us| 00000810 69 6e 67 20 6d 79 20 66 61 73 74 28 65 72 29 0a |ing my fast(er).| 00000820 61 6c 67 6f 72 69 74 68 6d 2e 20 41 6c 6c 20 73 |algorithm. All s| 00000830 63 72 65 65 6e 73 20 77 69 74 68 20 6c 6f 74 73 |creens with lots| 00000840 20 6f 66 20 63 6f 6c 6f 75 72 20 74 68 65 20 73 | of colour the s| 00000850 61 6d 65 20 62 65 6e 65 66 69 74 0a 67 72 65 61 |ame benefit.grea| 00000860 74 79 20 66 72 6f 6d 20 74 68 65 20 61 6c 67 6f |ty from the algo| 00000870 72 69 74 68 6d 2e 20 45 76 65 6e 20 74 68 65 20 |rithm. Even the | 00000880 43 61 6e 74 6f 72 20 64 75 73 74 20 61 74 20 30 |Cantor dust at 0| 00000890 2e 33 2c 20 30 2e 36 20 69 73 0a 6e 6f 74 20 77 |.3, 0.6 is.not w| 000008a0 6f 72 73 65 20 74 68 61 6e 20 74 68 65 20 6f 72 |orse than the or| 000008b0 69 67 69 6e 61 6c 20 70 69 78 65 6c 20 62 79 20 |iginal pixel by | 000008c0 70 69 78 65 6c 20 70 6c 6f 74 2e 0a 0a 54 68 65 |pixel plot...The| 000008d0 20 66 6f 6c 6c 6f 77 69 6e 67 20 74 69 6d 65 73 | following times| 000008e0 20 73 68 6f 77 20 68 6f 77 20 74 68 65 20 73 70 | show how the sp| 000008f0 65 65 64 20 6f 66 20 74 68 65 20 70 6c 6f 74 20 |eed of the plot | 00000900 76 61 72 79 20 77 69 74 68 20 74 68 65 0a 76 61 |vary with the.va| 00000910 72 69 61 62 6c 65 20 7a 25 2c 20 77 68 69 63 68 |riable z%, which| 00000920 20 63 6f 6e 74 72 6f 6c 73 20 74 68 65 20 73 63 | controls the sc| 00000930 61 6e 6e 69 6e 67 20 73 71 75 61 72 65 20 73 69 |anning square si| 00000940 7a 65 2e 0a 0a 53 71 75 61 72 65 20 73 69 7a 65 |ze...Square size| 00000950 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 74 | t| 00000960 69 6d 65 20 28 73 65 63 6f 6e 64 73 29 0a 0a 38 |ime (seconds)..8| 00000970 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000980 20 20 20 20 20 20 20 20 20 35 38 33 0a 31 32 20 | 583.12 | 00000990 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000009a0 20 20 20 20 20 20 20 34 39 39 0a 31 36 20 20 20 | 499.16 | 000009b0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000009c0 20 20 20 20 20 34 39 32 0a 32 30 20 20 20 20 20 | 492.20 | 000009d0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 000009e0 20 20 20 35 31 35 0a 32 34 20 20 20 20 20 20 20 | 515.24 | 000009f0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000a00 20 35 33 32 0a 32 38 20 20 20 20 20 20 20 20 20 | 532.28 | 00000a10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 35 | 5| 00000a20 35 39 0a 33 32 20 20 20 20 20 20 20 20 20 20 20 |59.32 | 00000a30 20 20 20 20 20 20 20 20 20 20 20 20 20 35 37 35 | 575| 00000a40 0a |.| 00000a41
.