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P/+MANDE2
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 » Personal collection » Acorn ADFS disks » Electron_User_Group » EUG_29.ADF |
| Filename: | P/+MANDE2 |
| Read OK: | ✔ |
| File size: | 0E8E bytes |
| Load address: | 2B204556 |
| Exec address: | 444E414D |
File contents
560-570 data for the colour arrays (16 colours only)
the first number gives the colour (0-3) which is plotted
on the main screen, the second gives the colours for
the shadow screen, and so on for the others (third =
main colour, fourth = shadow colour etc...) The "sea"
of the mandelbrot is usually black (0,0), blue or white
(colour selection depends on lines 1320-1410)
Therefore you can select your preferred colour scheme
within the colours defined for the mode by changing these
lines. You will need 32 numbers for 16 colour
mode 1, or 72 for 36 colour mode 2.
580 Blank
590-730 This is the clever bit - the Mandelbrot algorithm.
The idea of the Mandelbrot set is to iterate the
equation Z = Z^2 + C, where Z is a complex number,
given by X + iY. Points which go infinite before
MI% iterations have been done are plotted in a colour
from the array, whereas points which have not gone
infinite are plotted in the "sea" colour (the first
colour in the array is reserved for the sea, so that
you can plot a 2-colour picture by *LOADing SHVPIC1
at &3000 and doing VDU19s to set colours 1,2 and 3
to the same colour (with 16 colour mode switched off
with *FX13,4))
To square a complex number, the X component becomes
X squared - Y squared (because i is the square root
of -1), and the Y component becomes 2 * X * Y.
The complex constant C is added to Z. C is made up
of the coordinates of the pixel. Apologies to the
those who hate maths!
The Mandelbrot set is a 'map' of "Julia sets" (plot
these by changing line 640 to:
640 I%=0:X1=X:Y1=Y
and removing the "+ X" or "+ Y" from lines 670 and
680. The best Julia sets to plot are found at the
edge of the "sea" area of the Mandelbrot set.
HLT is a flag which indicates that the iterated
complex number Z has gone theoretically infinite
- a value of X^2+Y^2 of more than 16 is judged to
be infinite. an alternative here is to use
700 HLT=(ABS(X)+ABS(Y)>4)
which gives a similar effect, except that plotting
from -4 to +4 on both axes gives a diamond as the
first-iteration shape, rather than an ovoid.
I% is the number of iterations performed. If Z
has gone infinite, the sea colour (0) is chosen,
otherwise a number from 1 to 15 (1 to 3 for non-
shadow-RAM machines).
N.B. For the Sea-horse Valley pictures I added lines
610-620. These cut out the bottom left corner
and part of the right hand side respectively.
Since 600 iterations takes so long to plot, I
thought that adding two tests to every point
plotted was an insignificant delay compared to
the benefit of removing 3/8 of 65536 (=24566)
points at the full 600 iterations!
I would advise you to do something similar if
you intend to plot at more than 100 iterations
with any significant sea area.
740 Blank
750-790 Calculate the pixel offset - interpolate between
pixels to give the array of decimal values of
points to feed into the algorithm.
800 Blank
810-1500 The 16-colour source code. An explanation of this
is given separately.
Mark Bellis
118, The Lawns,
Rolleston-on-Dove,
Burton-on-Trent,
Staffs,
DE13 9DE
00000000 0d 35 36 30 2d 35 37 30 20 20 20 20 64 61 74 61 |.560-570 data| 00000010 20 66 6f 72 20 74 68 65 20 63 6f 6c 6f 75 72 20 | for the colour | 00000020 61 72 72 61 79 73 20 28 31 36 20 63 6f 6c 6f 75 |arrays (16 colou| 00000030 72 73 20 6f 6e 6c 79 29 0d 20 20 20 20 20 20 20 |rs only). | 00000040 20 20 20 20 74 68 65 20 66 69 72 73 74 20 6e 75 | the first nu| 00000050 6d 62 65 72 20 67 69 76 65 73 20 74 68 65 20 63 |mber gives the c| 00000060 6f 6c 6f 75 72 20 28 30 2d 33 29 20 77 68 69 63 |olour (0-3) whic| 00000070 68 20 69 73 20 70 6c 6f 74 74 65 64 0d 20 20 20 |h is plotted. | 00000080 20 20 20 20 20 20 20 20 6f 6e 20 74 68 65 20 6d | on the m| 00000090 61 69 6e 20 73 63 72 65 65 6e 2c 20 74 68 65 20 |ain screen, the | 000000a0 73 65 63 6f 6e 64 20 67 69 76 65 73 20 74 68 65 |second gives the| 000000b0 20 63 6f 6c 6f 75 72 73 20 66 6f 72 0d 20 20 20 | colours for. | 000000c0 20 20 20 20 20 20 20 20 74 68 65 20 73 68 61 64 | the shad| 000000d0 6f 77 20 73 63 72 65 65 6e 2c 20 61 6e 64 20 73 |ow screen, and s| 000000e0 6f 20 6f 6e 20 66 6f 72 20 74 68 65 20 6f 74 68 |o on for the oth| 000000f0 65 72 73 20 28 74 68 69 72 64 20 3d 0d 20 20 20 |ers (third =. | 00000100 20 20 20 20 20 20 20 20 6d 61 69 6e 20 63 6f 6c | main col| 00000110 6f 75 72 2c 20 66 6f 75 72 74 68 20 3d 20 73 68 |our, fourth = sh| 00000120 61 64 6f 77 20 63 6f 6c 6f 75 72 20 65 74 63 2e |adow colour etc.| 00000130 2e 2e 29 20 20 54 68 65 20 22 73 65 61 22 0d 20 |..) The "sea". | 00000140 20 20 20 20 20 20 20 20 20 20 6f 66 20 74 68 65 | of the| 00000150 20 6d 61 6e 64 65 6c 62 72 6f 74 20 69 73 20 75 | mandelbrot is u| 00000160 73 75 61 6c 6c 79 20 62 6c 61 63 6b 20 28 30 2c |sually black (0,| 00000170 30 29 2c 20 62 6c 75 65 20 6f 72 20 77 68 69 74 |0), blue or whit| 00000180 65 0d 20 20 20 20 20 20 20 20 20 20 20 28 63 6f |e. (co| 00000190 6c 6f 75 72 20 73 65 6c 65 63 74 69 6f 6e 20 64 |lour selection d| 000001a0 65 70 65 6e 64 73 20 6f 6e 20 6c 69 6e 65 73 20 |epends on lines | 000001b0 31 33 32 30 2d 31 34 31 30 29 0d 20 20 20 20 20 |1320-1410). | 000001c0 20 20 20 20 20 20 54 68 65 72 65 66 6f 72 65 20 | Therefore | 000001d0 79 6f 75 20 63 61 6e 20 73 65 6c 65 63 74 20 79 |you can select y| 000001e0 6f 75 72 20 70 72 65 66 65 72 72 65 64 20 63 6f |our preferred co| 000001f0 6c 6f 75 72 20 73 63 68 65 6d 65 0d 20 20 20 20 |lour scheme. | 00000200 20 20 20 20 20 20 20 77 69 74 68 69 6e 20 74 68 | within th| 00000210 65 20 63 6f 6c 6f 75 72 73 20 64 65 66 69 6e 65 |e colours define| 00000220 64 20 66 6f 72 20 74 68 65 20 6d 6f 64 65 20 62 |d for the mode b| 00000230 79 20 63 68 61 6e 67 69 6e 67 20 74 68 65 73 65 |y changing these| 00000240 0d 20 20 20 20 20 20 20 20 20 20 20 6c 69 6e 65 |. line| 00000250 73 2e 20 20 59 6f 75 20 77 69 6c 6c 20 6e 65 65 |s. You will nee| 00000260 64 20 33 32 20 6e 75 6d 62 65 72 73 20 66 6f 72 |d 32 numbers for| 00000270 20 31 36 20 63 6f 6c 6f 75 72 0d 20 20 20 20 20 | 16 colour. | 00000280 20 20 20 20 20 20 6d 6f 64 65 20 31 2c 20 6f 72 | mode 1, or| 00000290 20 37 32 20 66 6f 72 20 33 36 20 63 6f 6c 6f 75 | 72 for 36 colou| 000002a0 72 20 6d 6f 64 65 20 32 2e 0d 0d 35 38 30 20 20 |r mode 2...580 | 000002b0 20 20 20 20 20 20 42 6c 61 6e 6b 0d 0d 35 39 30 | Blank..590| 000002c0 2d 37 33 30 20 20 20 20 54 68 69 73 20 69 73 20 |-730 This is | 000002d0 74 68 65 20 63 6c 65 76 65 72 20 62 69 74 20 2d |the clever bit -| 000002e0 20 74 68 65 20 4d 61 6e 64 65 6c 62 72 6f 74 20 | the Mandelbrot | 000002f0 61 6c 67 6f 72 69 74 68 6d 2e 0d 20 20 20 20 20 |algorithm.. | 00000300 20 20 20 20 20 20 54 68 65 20 69 64 65 61 20 6f | The idea o| 00000310 66 20 74 68 65 20 4d 61 6e 64 65 6c 62 72 6f 74 |f the Mandelbrot| 00000320 20 73 65 74 20 69 73 20 74 6f 20 69 74 65 72 61 | set is to itera| 00000330 74 65 20 74 68 65 0d 20 20 20 20 20 20 20 20 20 |te the. | 00000340 20 20 65 71 75 61 74 69 6f 6e 20 5a 20 3d 20 5a | equation Z = Z| 00000350 5e 32 20 2b 20 43 2c 20 77 68 65 72 65 20 5a 20 |^2 + C, where Z | 00000360 69 73 20 61 20 63 6f 6d 70 6c 65 78 20 6e 75 6d |is a complex num| 00000370 62 65 72 2c 0d 20 20 20 20 20 20 20 20 20 20 20 |ber,. | 00000380 67 69 76 65 6e 20 62 79 20 58 20 2b 20 69 59 2e |given by X + iY.| 00000390 20 20 50 6f 69 6e 74 73 20 77 68 69 63 68 20 67 | Points which g| 000003a0 6f 20 69 6e 66 69 6e 69 74 65 20 62 65 66 6f 72 |o infinite befor| 000003b0 65 0d 20 20 20 20 20 20 20 20 20 20 20 4d 49 25 |e. MI%| 000003c0 20 69 74 65 72 61 74 69 6f 6e 73 20 68 61 76 65 | iterations have| 000003d0 20 62 65 65 6e 20 64 6f 6e 65 20 61 72 65 20 70 | been done are p| 000003e0 6c 6f 74 74 65 64 20 69 6e 20 61 20 63 6f 6c 6f |lotted in a colo| 000003f0 75 72 0d 20 20 20 20 20 20 20 20 20 20 20 66 72 |ur. fr| 00000400 6f 6d 20 74 68 65 20 61 72 72 61 79 2c 20 77 68 |om the array, wh| 00000410 65 72 65 61 73 20 70 6f 69 6e 74 73 20 77 68 69 |ereas points whi| 00000420 63 68 20 68 61 76 65 20 6e 6f 74 20 67 6f 6e 65 |ch have not gone| 00000430 0d 20 20 20 20 20 20 20 20 20 20 20 69 6e 66 69 |. infi| 00000440 6e 69 74 65 20 61 72 65 20 70 6c 6f 74 74 65 64 |nite are plotted| 00000450 20 69 6e 20 74 68 65 20 22 73 65 61 22 20 63 6f | in the "sea" co| 00000460 6c 6f 75 72 20 28 74 68 65 20 66 69 72 73 74 0d |lour (the first.| 00000470 20 20 20 20 20 20 20 20 20 20 20 63 6f 6c 6f 75 | colou| 00000480 72 20 69 6e 20 74 68 65 20 61 72 72 61 79 20 69 |r in the array i| 00000490 73 20 72 65 73 65 72 76 65 64 20 66 6f 72 20 74 |s reserved for t| 000004a0 68 65 20 73 65 61 2c 20 73 6f 20 74 68 61 74 0d |he sea, so that.| 000004b0 20 20 20 20 20 20 20 20 20 20 20 79 6f 75 20 63 | you c| 000004c0 61 6e 20 70 6c 6f 74 20 61 20 32 2d 63 6f 6c 6f |an plot a 2-colo| 000004d0 75 72 20 70 69 63 74 75 72 65 20 62 79 20 2a 4c |ur picture by *L| 000004e0 4f 41 44 69 6e 67 20 53 48 56 50 49 43 31 0d 20 |OADing SHVPIC1. | 000004f0 20 20 20 20 20 20 20 20 20 20 61 74 20 26 33 30 | at &30| 00000500 30 30 20 61 6e 64 20 64 6f 69 6e 67 20 56 44 55 |00 and doing VDU| 00000510 31 39 73 20 74 6f 20 73 65 74 20 63 6f 6c 6f 75 |19s to set colou| 00000520 72 73 20 31 2c 32 20 61 6e 64 20 33 0d 20 20 20 |rs 1,2 and 3. | 00000530 20 20 20 20 20 20 20 20 74 6f 20 74 68 65 20 73 | to the s| 00000540 61 6d 65 20 63 6f 6c 6f 75 72 20 28 77 69 74 68 |ame colour (with| 00000550 20 31 36 20 63 6f 6c 6f 75 72 20 6d 6f 64 65 20 | 16 colour mode | 00000560 73 77 69 74 63 68 65 64 20 6f 66 66 0d 20 20 20 |switched off. | 00000570 20 20 20 20 20 20 20 20 77 69 74 68 20 2a 46 58 | with *FX| 00000580 31 33 2c 34 29 29 0d 0d 20 20 20 20 20 20 20 20 |13,4)).. | 00000590 20 20 20 54 6f 20 73 71 75 61 72 65 20 61 20 63 | To square a c| 000005a0 6f 6d 70 6c 65 78 20 6e 75 6d 62 65 72 2c 20 74 |omplex number, t| 000005b0 68 65 20 58 20 63 6f 6d 70 6f 6e 65 6e 74 20 62 |he X component b| 000005c0 65 63 6f 6d 65 73 0d 20 20 20 20 20 20 20 20 20 |ecomes. | 000005d0 20 20 58 20 73 71 75 61 72 65 64 20 2d 20 59 20 | X squared - Y | 000005e0 73 71 75 61 72 65 64 20 28 62 65 63 61 75 73 65 |squared (because| 000005f0 20 69 20 69 73 20 74 68 65 20 73 71 75 61 72 65 | i is the square| 00000600 20 72 6f 6f 74 0d 20 20 20 20 20 20 20 20 20 20 | root. | 00000610 20 6f 66 20 2d 31 29 2c 20 61 6e 64 20 74 68 65 | of -1), and the| 00000620 20 59 20 63 6f 6d 70 6f 6e 65 6e 74 20 62 65 63 | Y component bec| 00000630 6f 6d 65 73 20 32 20 2a 20 58 20 2a 20 59 2e 0d |omes 2 * X * Y..| 00000640 20 20 20 20 20 20 20 20 20 20 20 54 68 65 20 63 | The c| 00000650 6f 6d 70 6c 65 78 20 63 6f 6e 73 74 61 6e 74 20 |omplex constant | 00000660 43 20 69 73 20 61 64 64 65 64 20 74 6f 20 5a 2e |C is added to Z.| 00000670 20 20 43 20 69 73 20 6d 61 64 65 20 75 70 0d 20 | C is made up. | 00000680 20 20 20 20 20 20 20 20 20 20 6f 66 20 74 68 65 | of the| 00000690 20 63 6f 6f 72 64 69 6e 61 74 65 73 20 6f 66 20 | coordinates of | 000006a0 74 68 65 20 70 69 78 65 6c 2e 20 20 41 70 6f 6c |the pixel. Apol| 000006b0 6f 67 69 65 73 20 74 6f 20 74 68 65 0d 20 20 20 |ogies to the. | 000006c0 20 20 20 20 20 20 20 20 74 68 6f 73 65 20 77 68 | those wh| 000006d0 6f 20 68 61 74 65 20 6d 61 74 68 73 21 0d 0d 20 |o hate maths!.. | 000006e0 20 20 20 20 20 20 20 20 20 20 54 68 65 20 4d 61 | The Ma| 000006f0 6e 64 65 6c 62 72 6f 74 20 73 65 74 20 69 73 20 |ndelbrot set is | 00000700 61 20 27 6d 61 70 27 20 6f 66 20 22 4a 75 6c 69 |a 'map' of "Juli| 00000710 61 20 73 65 74 73 22 20 28 70 6c 6f 74 0d 20 20 |a sets" (plot. | 00000720 20 20 20 20 20 20 20 20 20 74 68 65 73 65 20 62 | these b| 00000730 79 20 63 68 61 6e 67 69 6e 67 20 6c 69 6e 65 20 |y changing line | 00000740 36 34 30 20 74 6f 3a 0d 20 20 20 20 20 20 20 20 |640 to:. | 00000750 20 20 20 36 34 30 20 49 25 3d 30 3a 58 31 3d 58 | 640 I%=0:X1=X| 00000760 3a 59 31 3d 59 0d 20 20 20 20 20 20 20 20 20 20 |:Y1=Y. | 00000770 20 61 6e 64 20 72 65 6d 6f 76 69 6e 67 20 74 68 | and removing th| 00000780 65 20 22 2b 20 58 22 20 6f 72 20 22 2b 20 59 22 |e "+ X" or "+ Y"| 00000790 20 66 72 6f 6d 20 6c 69 6e 65 73 20 36 37 30 20 | from lines 670 | 000007a0 61 6e 64 0d 20 20 20 20 20 20 20 20 20 20 20 36 |and. 6| 000007b0 38 30 2e 20 20 54 68 65 20 62 65 73 74 20 4a 75 |80. The best Ju| 000007c0 6c 69 61 20 73 65 74 73 20 74 6f 20 70 6c 6f 74 |lia sets to plot| 000007d0 20 61 72 65 20 66 6f 75 6e 64 20 61 74 20 74 68 | are found at th| 000007e0 65 0d 20 20 20 20 20 20 20 20 20 20 20 65 64 67 |e. edg| 000007f0 65 20 6f 66 20 74 68 65 20 22 73 65 61 22 20 61 |e of the "sea" a| 00000800 72 65 61 20 6f 66 20 74 68 65 20 4d 61 6e 64 65 |rea of the Mande| 00000810 6c 62 72 6f 74 20 73 65 74 2e 0d 0d 20 20 20 20 |lbrot set... | 00000820 20 20 20 20 20 20 20 48 4c 54 20 69 73 20 61 20 | HLT is a | 00000830 66 6c 61 67 20 77 68 69 63 68 20 69 6e 64 69 63 |flag which indic| 00000840 61 74 65 73 20 74 68 61 74 20 74 68 65 20 69 74 |ates that the it| 00000850 65 72 61 74 65 64 0d 20 20 20 20 20 20 20 20 20 |erated. | 00000860 20 20 63 6f 6d 70 6c 65 78 20 6e 75 6d 62 65 72 | complex number| 00000870 20 5a 20 68 61 73 20 67 6f 6e 65 20 74 68 65 6f | Z has gone theo| 00000880 72 65 74 69 63 61 6c 6c 79 20 69 6e 66 69 6e 69 |retically infini| 00000890 74 65 0d 20 20 20 20 20 20 20 20 20 20 20 2d 20 |te. - | 000008a0 61 20 76 61 6c 75 65 20 6f 66 20 58 5e 32 2b 59 |a value of X^2+Y| 000008b0 5e 32 20 6f 66 20 6d 6f 72 65 20 74 68 61 6e 20 |^2 of more than | 000008c0 31 36 20 69 73 20 6a 75 64 67 65 64 20 74 6f 0d |16 is judged to.| 000008d0 20 20 20 20 20 20 20 20 20 20 20 62 65 20 69 6e | be in| 000008e0 66 69 6e 69 74 65 2e 20 20 61 6e 20 61 6c 74 65 |finite. an alte| 000008f0 72 6e 61 74 69 76 65 20 68 65 72 65 20 69 73 20 |rnative here is | 00000900 74 6f 20 75 73 65 0d 20 20 20 20 20 20 20 20 20 |to use. | 00000910 20 20 37 30 30 20 48 4c 54 3d 28 41 42 53 28 58 | 700 HLT=(ABS(X| 00000920 29 2b 41 42 53 28 59 29 3e 34 29 0d 20 20 20 20 |)+ABS(Y)>4). | 00000930 20 20 20 20 20 20 20 77 68 69 63 68 20 67 69 76 | which giv| 00000940 65 73 20 61 20 73 69 6d 69 6c 61 72 20 65 66 66 |es a similar eff| 00000950 65 63 74 2c 20 65 78 63 65 70 74 20 74 68 61 74 |ect, except that| 00000960 20 70 6c 6f 74 74 69 6e 67 0d 20 20 20 20 20 20 | plotting. | 00000970 20 20 20 20 20 66 72 6f 6d 20 2d 34 20 74 6f 20 | from -4 to | 00000980 2b 34 20 6f 6e 20 62 6f 74 68 20 61 78 65 73 20 |+4 on both axes | 00000990 67 69 76 65 73 20 61 20 64 69 61 6d 6f 6e 64 20 |gives a diamond | 000009a0 61 73 20 74 68 65 0d 20 20 20 20 20 20 20 20 20 |as the. | 000009b0 20 20 66 69 72 73 74 2d 69 74 65 72 61 74 69 6f | first-iteratio| 000009c0 6e 20 73 68 61 70 65 2c 20 72 61 74 68 65 72 20 |n shape, rather | 000009d0 74 68 61 6e 20 61 6e 20 6f 76 6f 69 64 2e 0d 0d |than an ovoid...| 000009e0 20 20 20 20 20 20 20 20 20 20 20 49 25 20 69 73 | I% is| 000009f0 20 74 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 69 | the number of i| 00000a00 74 65 72 61 74 69 6f 6e 73 20 70 65 72 66 6f 72 |terations perfor| 00000a10 6d 65 64 2e 20 20 49 66 20 5a 0d 20 20 20 20 20 |med. If Z. | 00000a20 20 20 20 20 20 20 68 61 73 20 67 6f 6e 65 20 69 | has gone i| 00000a30 6e 66 69 6e 69 74 65 2c 20 74 68 65 20 73 65 61 |nfinite, the sea| 00000a40 20 63 6f 6c 6f 75 72 20 28 30 29 20 69 73 20 63 | colour (0) is c| 00000a50 68 6f 73 65 6e 2c 0d 20 20 20 20 20 20 20 20 20 |hosen,. | 00000a60 20 20 6f 74 68 65 72 77 69 73 65 20 61 20 6e 75 | otherwise a nu| 00000a70 6d 62 65 72 20 66 72 6f 6d 20 31 20 74 6f 20 31 |mber from 1 to 1| 00000a80 35 20 28 31 20 74 6f 20 33 20 66 6f 72 20 6e 6f |5 (1 to 3 for no| 00000a90 6e 2d 0d 20 20 20 20 20 20 20 20 20 20 20 73 68 |n-. sh| 00000aa0 61 64 6f 77 2d 52 41 4d 20 6d 61 63 68 69 6e 65 |adow-RAM machine| 00000ab0 73 29 2e 0d 0d 20 20 4e 2e 42 2e 20 20 20 20 20 |s)... N.B. | 00000ac0 46 6f 72 20 74 68 65 20 53 65 61 2d 68 6f 72 73 |For the Sea-hors| 00000ad0 65 20 56 61 6c 6c 65 79 20 70 69 63 74 75 72 65 |e Valley picture| 00000ae0 73 20 49 20 61 64 64 65 64 20 6c 69 6e 65 73 0d |s I added lines.| 00000af0 20 20 20 20 20 20 20 20 20 20 20 36 31 30 2d 36 | 610-6| 00000b00 32 30 2e 20 20 54 68 65 73 65 20 63 75 74 20 6f |20. These cut o| 00000b10 75 74 20 74 68 65 20 62 6f 74 74 6f 6d 20 6c 65 |ut the bottom le| 00000b20 66 74 20 63 6f 72 6e 65 72 0d 20 20 20 20 20 20 |ft corner. | 00000b30 20 20 20 20 20 61 6e 64 20 70 61 72 74 20 6f 66 | and part of| 00000b40 20 74 68 65 20 72 69 67 68 74 20 68 61 6e 64 20 | the right hand | 00000b50 73 69 64 65 20 72 65 73 70 65 63 74 69 76 65 6c |side respectivel| 00000b60 79 2e 0d 20 20 20 20 20 20 20 20 20 20 20 53 69 |y.. Si| 00000b70 6e 63 65 20 36 30 30 20 69 74 65 72 61 74 69 6f |nce 600 iteratio| 00000b80 6e 73 20 74 61 6b 65 73 20 73 6f 20 6c 6f 6e 67 |ns takes so long| 00000b90 20 74 6f 20 70 6c 6f 74 2c 20 49 0d 20 20 20 20 | to plot, I. | 00000ba0 20 20 20 20 20 20 20 74 68 6f 75 67 68 74 20 74 | thought t| 00000bb0 68 61 74 20 61 64 64 69 6e 67 20 74 77 6f 20 74 |hat adding two t| 00000bc0 65 73 74 73 20 74 6f 20 65 76 65 72 79 20 70 6f |ests to every po| 00000bd0 69 6e 74 0d 20 20 20 20 20 20 20 20 20 20 20 70 |int. p| 00000be0 6c 6f 74 74 65 64 20 77 61 73 20 61 6e 20 69 6e |lotted was an in| 00000bf0 73 69 67 6e 69 66 69 63 61 6e 74 20 64 65 6c 61 |significant dela| 00000c00 79 20 63 6f 6d 70 61 72 65 64 20 74 6f 0d 20 20 |y compared to. | 00000c10 20 20 20 20 20 20 20 20 20 74 68 65 20 62 65 6e | the ben| 00000c20 65 66 69 74 20 6f 66 20 72 65 6d 6f 76 69 6e 67 |efit of removing| 00000c30 20 33 2f 38 20 6f 66 20 36 35 35 33 36 20 28 3d | 3/8 of 65536 (=| 00000c40 32 34 35 36 36 29 0d 20 20 20 20 20 20 20 20 20 |24566). | 00000c50 20 20 70 6f 69 6e 74 73 20 61 74 20 74 68 65 20 | points at the | 00000c60 66 75 6c 6c 20 36 30 30 20 69 74 65 72 61 74 69 |full 600 iterati| 00000c70 6f 6e 73 21 0d 0d 20 20 20 20 20 20 20 20 20 20 |ons!.. | 00000c80 20 49 20 77 6f 75 6c 64 20 61 64 76 69 73 65 20 | I would advise | 00000c90 79 6f 75 20 74 6f 20 64 6f 20 73 6f 6d 65 74 68 |you to do someth| 00000ca0 69 6e 67 20 73 69 6d 69 6c 61 72 20 69 66 0d 20 |ing similar if. | 00000cb0 20 20 20 20 20 20 20 20 20 20 79 6f 75 20 69 6e | you in| 00000cc0 74 65 6e 64 20 74 6f 20 70 6c 6f 74 20 61 74 20 |tend to plot at | 00000cd0 6d 6f 72 65 20 74 68 61 6e 20 31 30 30 20 69 74 |more than 100 it| 00000ce0 65 72 61 74 69 6f 6e 73 0d 20 20 20 20 20 20 20 |erations. | 00000cf0 20 20 20 20 77 69 74 68 20 61 6e 79 20 73 69 67 | with any sig| 00000d00 6e 69 66 69 63 61 6e 74 20 73 65 61 20 61 72 65 |nificant sea are| 00000d10 61 2e 0d 0d 37 34 30 20 20 20 20 20 20 20 20 42 |a...740 B| 00000d20 6c 61 6e 6b 0d 0d 37 35 30 2d 37 39 30 20 20 20 |lank..750-790 | 00000d30 20 43 61 6c 63 75 6c 61 74 65 20 74 68 65 20 70 | Calculate the p| 00000d40 69 78 65 6c 20 6f 66 66 73 65 74 20 2d 20 69 6e |ixel offset - in| 00000d50 74 65 72 70 6f 6c 61 74 65 20 62 65 74 77 65 65 |terpolate betwee| 00000d60 6e 0d 20 20 20 20 20 20 20 20 20 20 20 70 69 78 |n. pix| 00000d70 65 6c 73 20 74 6f 20 67 69 76 65 20 74 68 65 20 |els to give the | 00000d80 61 72 72 61 79 20 6f 66 20 64 65 63 69 6d 61 6c |array of decimal| 00000d90 20 76 61 6c 75 65 73 20 6f 66 0d 20 20 20 20 20 | values of. | 00000da0 20 20 20 20 20 20 70 6f 69 6e 74 73 20 74 6f 20 | points to | 00000db0 66 65 65 64 20 69 6e 74 6f 20 74 68 65 20 61 6c |feed into the al| 00000dc0 67 6f 72 69 74 68 6d 2e 0d 0d 38 30 30 20 20 20 |gorithm...800 | 00000dd0 20 20 20 20 20 42 6c 61 6e 6b 0d 0d 38 31 30 2d | Blank..810-| 00000de0 31 35 30 30 20 20 20 54 68 65 20 31 36 2d 63 6f |1500 The 16-co| 00000df0 6c 6f 75 72 20 73 6f 75 72 63 65 20 63 6f 64 65 |lour source code| 00000e00 2e 20 20 41 6e 20 65 78 70 6c 61 6e 61 74 69 6f |. An explanatio| 00000e10 6e 20 6f 66 20 74 68 69 73 0d 20 20 20 20 20 20 |n of this. | 00000e20 20 20 20 20 20 69 73 20 67 69 76 65 6e 20 73 65 | is given se| 00000e30 70 61 72 61 74 65 6c 79 2e 0d 0d 4d 61 72 6b 20 |parately...Mark | 00000e40 42 65 6c 6c 69 73 0d 31 31 38 2c 20 54 68 65 20 |Bellis.118, The | 00000e50 4c 61 77 6e 73 2c 0d 52 6f 6c 6c 65 73 74 6f 6e |Lawns,.Rolleston| 00000e60 2d 6f 6e 2d 44 6f 76 65 2c 0d 42 75 72 74 6f 6e |-on-Dove,.Burton| 00000e70 2d 6f 6e 2d 54 72 65 6e 74 2c 0d 53 74 61 66 66 |-on-Trent,.Staff| 00000e80 73 2c 0d 44 45 31 33 20 39 44 45 0d 0d 0d |s,.DE13 9DE...| 00000e8e
P/+MANDE2.m0
P/+MANDE2.m1
P/+MANDE2.m2
P/+MANDE2.m4
P/+MANDE2.m5
.