Home » Archimedes archive » Acorn User » AU 1996-06.adf » Regulars » StarInfo/Green/!PPlane/!Help
StarInfo/Green/!PPlane/!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 » Acorn User » AU 1996-06.adf » Regulars |
| Filename: | StarInfo/Green/!PPlane/!Help |
| Read OK: | ✔ |
| File size: | 11BA bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
PPlane by Darren Green � 1996 ====== == ====== ===== = ==== Introduction ============ PPlane is a graph drawing utility for RISCOS. The purpose of PPlane is to draw "phase plane" vector field diagrams. You enter equations for dx/dt and dy/dt (where "d" is a curly d, ie "dye") and the application will draw a graph showing how the magnitude and direction of [dx/dt,dy/dt] varies over the limits entered for the graph. Interactive help is supported. Instructions ============ To run the application double click on its icon in the filer window. To begin click select over the PPlane icon: this brings up the main window, containing the graph. Clicking menu over either the PPlane icon, or the main window will bring up the PPlane menu. Clicking adjust over the PPlane icon will bring up the integrate window. This is also accessible from the menu. Other windows which are available from the menu are the save window, the info window and the main window. Click quit on the menu to quit PPlane. In the control window you can enter the limits for the axes of your graph, and enter the equations for dx/dt and dy/dt. These should be entered as expressions containing x and y. You can also enter the number of points shown on the graph along each axis. Arrow scale determines the relative length of the vector arrows drawn from each point on the graph. If "Set arrow lengths all the same" is selected, then all of the arrows on the graph are drawn as if |[dx/dt,dy/dt]|=1, ie have a length of 1. This means that the arrows then only show the direction of the vector, not the magnitude, but can lead to less confusing graphs. Click OK to draw a graph, or redraw the current graph. In the integrate window you can specify the coordinates of a point to start integrating at, and a step value, dt. Click OK then to carry out the operation. This involves repeatedly calculating dx/dt and dy/dt at this point, multiplying these values by the value of dt, and adding them on to the current x and y. This plots a curve over the graph, which is drawn when it is finished. Calculating this can take a very long time, or if the path enters a loop or a stable node, forever. Pressing ESCAPE ends the calculation and returns control to the user. If "Stop when out of range" is selected then calculation will stop when the value of x or y exceeds the limits of the graph. Clicking on the main window with select also enters integrate mode. Integration begins at the point on the graph where the user clicks select, and uses the dt value in the dt icon on the integration window. If the integrate function is working strangely, it is possible that the values of dx/dt and dy/dt are large. Try reducing the value of dt. If the integrate function is working too slowly, try increasing the value of dt. Note the smaller the value of dt, the more accurate the plot, but the slower it is to calculate. The current main screen can be saved as a sprite file. Enter the filename in the icon on the save as window, and either click OK, or drag the sprite icon to the destination window. The sprite file contains a single sprite, called "Screen" with a default desktop palette. Things to try ====== == === Why not try the following to demonstrate PPlane: 1. Scale x: -1 to 3 y: -1 to 3 dx/dt: x*y-x dy/dt: y-x*y 2. Scale x: -10 to 10 y: -10 to 10 dx/dt: x*x-y*y dy/dt: 2*x*y Things to look out for ====== == ==== === === One of the most commmon problems encountered with this application is the error "Division by Zero". This generally occurs upon drawing a graph. Try adjusting your equations so that this does not occur, eg by adding on a small constant eg 1E-10, or adjust the graph scales. Copyright ========= � Darren Green (Pinkmongoose Software.) version 2.00 You may distribute this program freely, as long as it is distributed intact, with all the files mentioned below included, in an unaltered state. This program may not be re-sold without written permission from the author. If distributed no more than a nominal charge of 3 pounds sterling may be charged for distribution costs. Files included are: !Run !Help !RUNimage !Sprites Messages Palette Templates Disclaimer ========== No liability for damage or loss ensuing as a result of the use or misuse of this software can be accepted by the author. No guarantee of the quality and accuracy of the plots produced by this software is given. To contact the author for suggestions, reports of bugs, etc. write to: Darren Green. 18 O'Hanlon Avenue Brigg South Humberside. DN20 8DE.
00000000 50 50 6c 61 6e 65 20 62 79 20 44 61 72 72 65 6e |PPlane by Darren| 00000010 20 47 72 65 65 6e 20 a9 20 31 39 39 36 0a 3d 3d | Green . 1996.==| 00000020 3d 3d 3d 3d 20 3d 3d 20 3d 3d 3d 3d 3d 3d 20 3d |==== == ====== =| 00000030 3d 3d 3d 3d 20 3d 20 3d 3d 3d 3d 0a 0a 49 6e 74 |==== = ====..Int| 00000040 72 6f 64 75 63 74 69 6f 6e 0a 3d 3d 3d 3d 3d 3d |roduction.======| 00000050 3d 3d 3d 3d 3d 3d 0a 0a 20 50 50 6c 61 6e 65 20 |======.. PPlane | 00000060 69 73 20 61 20 67 72 61 70 68 20 64 72 61 77 69 |is a graph drawi| 00000070 6e 67 20 75 74 69 6c 69 74 79 20 66 6f 72 20 52 |ng utility for R| 00000080 49 53 43 4f 53 2e 20 54 68 65 20 70 75 72 70 6f |ISCOS. The purpo| 00000090 73 65 20 6f 66 20 50 50 6c 61 6e 65 20 69 73 20 |se of PPlane is | 000000a0 74 6f 20 64 72 61 77 20 22 70 68 61 73 65 20 70 |to draw "phase p| 000000b0 6c 61 6e 65 22 20 76 65 63 74 6f 72 20 66 69 65 |lane" vector fie| 000000c0 6c 64 20 64 69 61 67 72 61 6d 73 2e 20 59 6f 75 |ld diagrams. You| 000000d0 20 65 6e 74 65 72 20 65 71 75 61 74 69 6f 6e 73 | enter equations| 000000e0 20 66 6f 72 20 64 78 2f 64 74 20 61 6e 64 20 64 | for dx/dt and d| 000000f0 79 2f 64 74 20 28 77 68 65 72 65 20 22 64 22 20 |y/dt (where "d" | 00000100 69 73 20 61 20 63 75 72 6c 79 20 64 2c 20 69 65 |is a curly d, ie| 00000110 20 22 64 79 65 22 29 20 61 6e 64 20 74 68 65 20 | "dye") and the | 00000120 61 70 70 6c 69 63 61 74 69 6f 6e 20 77 69 6c 6c |application will| 00000130 20 64 72 61 77 20 61 20 67 72 61 70 68 20 73 68 | draw a graph sh| 00000140 6f 77 69 6e 67 20 68 6f 77 20 74 68 65 20 6d 61 |owing how the ma| 00000150 67 6e 69 74 75 64 65 20 61 6e 64 20 64 69 72 65 |gnitude and dire| 00000160 63 74 69 6f 6e 20 6f 66 20 5b 64 78 2f 64 74 2c |ction of [dx/dt,| 00000170 64 79 2f 64 74 5d 20 76 61 72 69 65 73 20 6f 76 |dy/dt] varies ov| 00000180 65 72 20 74 68 65 20 6c 69 6d 69 74 73 20 65 6e |er the limits en| 00000190 74 65 72 65 64 20 66 6f 72 20 74 68 65 20 67 72 |tered for the gr| 000001a0 61 70 68 2e 20 49 6e 74 65 72 61 63 74 69 76 65 |aph. Interactive| 000001b0 20 68 65 6c 70 20 69 73 20 73 75 70 70 6f 72 74 | help is support| 000001c0 65 64 2e 0a 0a 49 6e 73 74 72 75 63 74 69 6f 6e |ed...Instruction| 000001d0 73 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 0a |s.============..| 000001e0 20 54 6f 20 72 75 6e 20 74 68 65 20 61 70 70 6c | To run the appl| 000001f0 69 63 61 74 69 6f 6e 20 64 6f 75 62 6c 65 20 63 |ication double c| 00000200 6c 69 63 6b 20 6f 6e 20 69 74 73 20 69 63 6f 6e |lick on its icon| 00000210 20 69 6e 20 74 68 65 20 66 69 6c 65 72 20 77 69 | in the filer wi| 00000220 6e 64 6f 77 2e 20 54 6f 20 62 65 67 69 6e 20 63 |ndow. To begin c| 00000230 6c 69 63 6b 20 73 65 6c 65 63 74 20 6f 76 65 72 |lick select over| 00000240 20 74 68 65 20 50 50 6c 61 6e 65 20 69 63 6f 6e | the PPlane icon| 00000250 3a 20 74 68 69 73 20 62 72 69 6e 67 73 20 75 70 |: this brings up| 00000260 20 74 68 65 20 6d 61 69 6e 20 77 69 6e 64 6f 77 | the main window| 00000270 2c 20 63 6f 6e 74 61 69 6e 69 6e 67 20 74 68 65 |, containing the| 00000280 20 67 72 61 70 68 2e 20 43 6c 69 63 6b 69 6e 67 | graph. Clicking| 00000290 20 6d 65 6e 75 20 6f 76 65 72 20 65 69 74 68 65 | menu over eithe| 000002a0 72 20 74 68 65 20 50 50 6c 61 6e 65 20 69 63 6f |r the PPlane ico| 000002b0 6e 2c 20 6f 72 20 74 68 65 20 6d 61 69 6e 20 77 |n, or the main w| 000002c0 69 6e 64 6f 77 20 77 69 6c 6c 20 62 72 69 6e 67 |indow will bring| 000002d0 20 75 70 20 74 68 65 20 50 50 6c 61 6e 65 20 6d | up the PPlane m| 000002e0 65 6e 75 2e 20 43 6c 69 63 6b 69 6e 67 20 61 64 |enu. Clicking ad| 000002f0 6a 75 73 74 20 6f 76 65 72 20 74 68 65 20 50 50 |just over the PP| 00000300 6c 61 6e 65 20 69 63 6f 6e 20 77 69 6c 6c 20 62 |lane icon will b| 00000310 72 69 6e 67 20 75 70 20 74 68 65 20 69 6e 74 65 |ring up the inte| 00000320 67 72 61 74 65 20 77 69 6e 64 6f 77 2e 20 54 68 |grate window. Th| 00000330 69 73 20 69 73 20 61 6c 73 6f 20 61 63 63 65 73 |is is also acces| 00000340 73 69 62 6c 65 20 66 72 6f 6d 20 74 68 65 20 6d |sible from the m| 00000350 65 6e 75 2e 20 4f 74 68 65 72 20 77 69 6e 64 6f |enu. Other windo| 00000360 77 73 20 77 68 69 63 68 20 61 72 65 20 61 76 61 |ws which are ava| 00000370 69 6c 61 62 6c 65 20 66 72 6f 6d 20 74 68 65 20 |ilable from the | 00000380 6d 65 6e 75 20 61 72 65 20 74 68 65 20 73 61 76 |menu are the sav| 00000390 65 20 77 69 6e 64 6f 77 2c 20 74 68 65 20 69 6e |e window, the in| 000003a0 66 6f 20 77 69 6e 64 6f 77 20 61 6e 64 20 74 68 |fo window and th| 000003b0 65 20 6d 61 69 6e 20 77 69 6e 64 6f 77 2e 20 43 |e main window. C| 000003c0 6c 69 63 6b 20 71 75 69 74 20 6f 6e 20 74 68 65 |lick quit on the| 000003d0 20 6d 65 6e 75 20 74 6f 20 71 75 69 74 20 50 50 | menu to quit PP| 000003e0 6c 61 6e 65 2e 0a 20 49 6e 20 74 68 65 20 63 6f |lane.. In the co| 000003f0 6e 74 72 6f 6c 20 77 69 6e 64 6f 77 20 79 6f 75 |ntrol window you| 00000400 20 63 61 6e 20 65 6e 74 65 72 20 74 68 65 20 6c | can enter the l| 00000410 69 6d 69 74 73 20 66 6f 72 20 74 68 65 20 61 78 |imits for the ax| 00000420 65 73 20 6f 66 20 79 6f 75 72 20 67 72 61 70 68 |es of your graph| 00000430 2c 20 61 6e 64 20 65 6e 74 65 72 20 74 68 65 20 |, and enter the | 00000440 65 71 75 61 74 69 6f 6e 73 20 66 6f 72 20 64 78 |equations for dx| 00000450 2f 64 74 20 61 6e 64 20 64 79 2f 64 74 2e 20 54 |/dt and dy/dt. T| 00000460 68 65 73 65 20 73 68 6f 75 6c 64 20 62 65 20 65 |hese should be e| 00000470 6e 74 65 72 65 64 20 61 73 20 65 78 70 72 65 73 |ntered as expres| 00000480 73 69 6f 6e 73 20 63 6f 6e 74 61 69 6e 69 6e 67 |sions containing| 00000490 20 78 20 61 6e 64 20 79 2e 20 59 6f 75 20 63 61 | x and y. You ca| 000004a0 6e 20 61 6c 73 6f 20 65 6e 74 65 72 20 74 68 65 |n also enter the| 000004b0 20 6e 75 6d 62 65 72 20 6f 66 20 70 6f 69 6e 74 | number of point| 000004c0 73 20 73 68 6f 77 6e 20 6f 6e 20 74 68 65 20 67 |s shown on the g| 000004d0 72 61 70 68 20 61 6c 6f 6e 67 20 65 61 63 68 20 |raph along each | 000004e0 61 78 69 73 2e 20 41 72 72 6f 77 20 73 63 61 6c |axis. Arrow scal| 000004f0 65 20 64 65 74 65 72 6d 69 6e 65 73 20 74 68 65 |e determines the| 00000500 20 72 65 6c 61 74 69 76 65 20 6c 65 6e 67 74 68 | relative length| 00000510 20 6f 66 20 74 68 65 20 76 65 63 74 6f 72 20 61 | of the vector a| 00000520 72 72 6f 77 73 20 64 72 61 77 6e 20 66 72 6f 6d |rrows drawn from| 00000530 20 65 61 63 68 20 70 6f 69 6e 74 20 6f 6e 20 74 | each point on t| 00000540 68 65 20 67 72 61 70 68 2e 20 49 66 20 22 53 65 |he graph. If "Se| 00000550 74 20 61 72 72 6f 77 20 6c 65 6e 67 74 68 73 20 |t arrow lengths | 00000560 61 6c 6c 20 74 68 65 20 73 61 6d 65 22 20 69 73 |all the same" is| 00000570 20 73 65 6c 65 63 74 65 64 2c 20 74 68 65 6e 20 | selected, then | 00000580 61 6c 6c 20 6f 66 20 74 68 65 20 61 72 72 6f 77 |all of the arrow| 00000590 73 20 6f 6e 20 74 68 65 20 67 72 61 70 68 20 61 |s on the graph a| 000005a0 72 65 20 64 72 61 77 6e 20 61 73 20 69 66 20 7c |re drawn as if || 000005b0 5b 64 78 2f 64 74 2c 64 79 2f 64 74 5d 7c 3d 31 |[dx/dt,dy/dt]|=1| 000005c0 2c 20 69 65 20 68 61 76 65 20 61 20 6c 65 6e 67 |, ie have a leng| 000005d0 74 68 20 6f 66 20 31 2e 20 54 68 69 73 20 6d 65 |th of 1. This me| 000005e0 61 6e 73 20 74 68 61 74 20 74 68 65 20 61 72 72 |ans that the arr| 000005f0 6f 77 73 20 74 68 65 6e 20 6f 6e 6c 79 20 73 68 |ows then only sh| 00000600 6f 77 20 74 68 65 20 64 69 72 65 63 74 69 6f 6e |ow the direction| 00000610 20 6f 66 20 74 68 65 20 76 65 63 74 6f 72 2c 20 | of the vector, | 00000620 6e 6f 74 20 74 68 65 20 6d 61 67 6e 69 74 75 64 |not the magnitud| 00000630 65 2c 20 62 75 74 20 63 61 6e 20 6c 65 61 64 20 |e, but can lead | 00000640 74 6f 20 6c 65 73 73 20 63 6f 6e 66 75 73 69 6e |to less confusin| 00000650 67 20 67 72 61 70 68 73 2e 20 43 6c 69 63 6b 20 |g graphs. Click | 00000660 4f 4b 20 74 6f 20 64 72 61 77 20 61 20 67 72 61 |OK to draw a gra| 00000670 70 68 2c 20 6f 72 20 72 65 64 72 61 77 20 74 68 |ph, or redraw th| 00000680 65 20 63 75 72 72 65 6e 74 20 67 72 61 70 68 2e |e current graph.| 00000690 0a 20 49 6e 20 74 68 65 20 69 6e 74 65 67 72 61 |. In the integra| 000006a0 74 65 20 77 69 6e 64 6f 77 20 79 6f 75 20 63 61 |te window you ca| 000006b0 6e 20 73 70 65 63 69 66 79 20 74 68 65 20 63 6f |n specify the co| 000006c0 6f 72 64 69 6e 61 74 65 73 20 6f 66 20 61 20 70 |ordinates of a p| 000006d0 6f 69 6e 74 20 74 6f 20 73 74 61 72 74 20 69 6e |oint to start in| 000006e0 74 65 67 72 61 74 69 6e 67 20 61 74 2c 20 61 6e |tegrating at, an| 000006f0 64 20 61 20 73 74 65 70 20 76 61 6c 75 65 2c 20 |d a step value, | 00000700 64 74 2e 20 43 6c 69 63 6b 20 4f 4b 20 74 68 65 |dt. Click OK the| 00000710 6e 20 74 6f 20 63 61 72 72 79 20 6f 75 74 20 74 |n to carry out t| 00000720 68 65 20 6f 70 65 72 61 74 69 6f 6e 2e 20 54 68 |he operation. Th| 00000730 69 73 20 69 6e 76 6f 6c 76 65 73 20 72 65 70 65 |is involves repe| 00000740 61 74 65 64 6c 79 20 63 61 6c 63 75 6c 61 74 69 |atedly calculati| 00000750 6e 67 20 64 78 2f 64 74 20 61 6e 64 20 64 79 2f |ng dx/dt and dy/| 00000760 64 74 20 61 74 20 74 68 69 73 20 70 6f 69 6e 74 |dt at this point| 00000770 2c 20 6d 75 6c 74 69 70 6c 79 69 6e 67 20 74 68 |, multiplying th| 00000780 65 73 65 20 76 61 6c 75 65 73 20 62 79 20 74 68 |ese values by th| 00000790 65 20 76 61 6c 75 65 20 6f 66 20 64 74 2c 20 61 |e value of dt, a| 000007a0 6e 64 20 61 64 64 69 6e 67 20 74 68 65 6d 20 6f |nd adding them o| 000007b0 6e 20 74 6f 20 74 68 65 20 63 75 72 72 65 6e 74 |n to the current| 000007c0 20 78 20 61 6e 64 20 79 2e 20 54 68 69 73 20 70 | x and y. This p| 000007d0 6c 6f 74 73 20 61 20 63 75 72 76 65 20 6f 76 65 |lots a curve ove| 000007e0 72 20 74 68 65 20 67 72 61 70 68 2c 20 77 68 69 |r the graph, whi| 000007f0 63 68 20 69 73 20 64 72 61 77 6e 20 77 68 65 6e |ch is drawn when| 00000800 20 69 74 20 69 73 20 66 69 6e 69 73 68 65 64 2e | it is finished.| 00000810 20 43 61 6c 63 75 6c 61 74 69 6e 67 20 74 68 69 | Calculating thi| 00000820 73 20 63 61 6e 20 74 61 6b 65 20 61 20 76 65 72 |s can take a ver| 00000830 79 20 6c 6f 6e 67 20 74 69 6d 65 2c 20 6f 72 20 |y long time, or | 00000840 69 66 20 74 68 65 20 70 61 74 68 20 65 6e 74 65 |if the path ente| 00000850 72 73 20 61 20 6c 6f 6f 70 20 6f 72 20 61 20 73 |rs a loop or a s| 00000860 74 61 62 6c 65 20 6e 6f 64 65 2c 20 66 6f 72 65 |table node, fore| 00000870 76 65 72 2e 20 50 72 65 73 73 69 6e 67 20 45 53 |ver. Pressing ES| 00000880 43 41 50 45 20 65 6e 64 73 20 74 68 65 20 63 61 |CAPE ends the ca| 00000890 6c 63 75 6c 61 74 69 6f 6e 20 61 6e 64 20 72 65 |lculation and re| 000008a0 74 75 72 6e 73 20 63 6f 6e 74 72 6f 6c 20 74 6f |turns control to| 000008b0 20 74 68 65 20 75 73 65 72 2e 20 49 66 20 22 53 | the user. If "S| 000008c0 74 6f 70 20 77 68 65 6e 20 6f 75 74 20 6f 66 20 |top when out of | 000008d0 72 61 6e 67 65 22 20 69 73 20 73 65 6c 65 63 74 |range" is select| 000008e0 65 64 20 74 68 65 6e 20 63 61 6c 63 75 6c 61 74 |ed then calculat| 000008f0 69 6f 6e 20 77 69 6c 6c 20 73 74 6f 70 20 77 68 |ion will stop wh| 00000900 65 6e 20 74 68 65 20 76 61 6c 75 65 20 6f 66 20 |en the value of | 00000910 78 20 6f 72 20 79 20 65 78 63 65 65 64 73 20 74 |x or y exceeds t| 00000920 68 65 20 6c 69 6d 69 74 73 20 6f 66 20 74 68 65 |he limits of the| 00000930 20 67 72 61 70 68 2e 0a 20 43 6c 69 63 6b 69 6e | graph.. Clickin| 00000940 67 20 6f 6e 20 74 68 65 20 6d 61 69 6e 20 77 69 |g on the main wi| 00000950 6e 64 6f 77 20 77 69 74 68 20 73 65 6c 65 63 74 |ndow with select| 00000960 20 61 6c 73 6f 20 65 6e 74 65 72 73 20 69 6e 74 | also enters int| 00000970 65 67 72 61 74 65 20 6d 6f 64 65 2e 20 49 6e 74 |egrate mode. Int| 00000980 65 67 72 61 74 69 6f 6e 20 62 65 67 69 6e 73 20 |egration begins | 00000990 61 74 20 74 68 65 20 70 6f 69 6e 74 20 6f 6e 20 |at the point on | 000009a0 74 68 65 20 67 72 61 70 68 20 77 68 65 72 65 20 |the graph where | 000009b0 74 68 65 20 75 73 65 72 20 63 6c 69 63 6b 73 20 |the user clicks | 000009c0 73 65 6c 65 63 74 2c 20 61 6e 64 20 75 73 65 73 |select, and uses| 000009d0 20 74 68 65 20 64 74 20 76 61 6c 75 65 20 69 6e | the dt value in| 000009e0 20 74 68 65 20 64 74 20 69 63 6f 6e 20 6f 6e 20 | the dt icon on | 000009f0 74 68 65 20 69 6e 74 65 67 72 61 74 69 6f 6e 20 |the integration | 00000a00 77 69 6e 64 6f 77 2e 0a 20 49 66 20 74 68 65 20 |window.. If the | 00000a10 69 6e 74 65 67 72 61 74 65 20 66 75 6e 63 74 69 |integrate functi| 00000a20 6f 6e 20 69 73 20 77 6f 72 6b 69 6e 67 20 73 74 |on is working st| 00000a30 72 61 6e 67 65 6c 79 2c 20 69 74 20 69 73 20 70 |rangely, it is p| 00000a40 6f 73 73 69 62 6c 65 20 74 68 61 74 20 74 68 65 |ossible that the| 00000a50 20 76 61 6c 75 65 73 20 6f 66 20 64 78 2f 64 74 | values of dx/dt| 00000a60 20 61 6e 64 20 64 79 2f 64 74 20 61 72 65 20 6c | and dy/dt are l| 00000a70 61 72 67 65 2e 20 54 72 79 20 72 65 64 75 63 69 |arge. Try reduci| 00000a80 6e 67 20 74 68 65 20 76 61 6c 75 65 20 6f 66 20 |ng the value of | 00000a90 64 74 2e 20 49 66 20 74 68 65 20 69 6e 74 65 67 |dt. If the integ| 00000aa0 72 61 74 65 20 66 75 6e 63 74 69 6f 6e 20 69 73 |rate function is| 00000ab0 20 77 6f 72 6b 69 6e 67 20 74 6f 6f 20 73 6c 6f | working too slo| 00000ac0 77 6c 79 2c 20 74 72 79 20 69 6e 63 72 65 61 73 |wly, try increas| 00000ad0 69 6e 67 20 74 68 65 20 76 61 6c 75 65 20 6f 66 |ing the value of| 00000ae0 20 64 74 2e 20 4e 6f 74 65 20 74 68 65 20 73 6d | dt. Note the sm| 00000af0 61 6c 6c 65 72 20 74 68 65 20 76 61 6c 75 65 20 |aller the value | 00000b00 6f 66 20 64 74 2c 20 74 68 65 20 6d 6f 72 65 20 |of dt, the more | 00000b10 61 63 63 75 72 61 74 65 20 74 68 65 20 70 6c 6f |accurate the plo| 00000b20 74 2c 20 62 75 74 20 74 68 65 20 73 6c 6f 77 65 |t, but the slowe| 00000b30 72 20 69 74 20 69 73 20 74 6f 20 63 61 6c 63 75 |r it is to calcu| 00000b40 6c 61 74 65 2e 0a 20 54 68 65 20 63 75 72 72 65 |late.. The curre| 00000b50 6e 74 20 6d 61 69 6e 20 73 63 72 65 65 6e 20 63 |nt main screen c| 00000b60 61 6e 20 62 65 20 73 61 76 65 64 20 61 73 20 61 |an be saved as a| 00000b70 20 73 70 72 69 74 65 20 66 69 6c 65 2e 20 45 6e | sprite file. En| 00000b80 74 65 72 20 74 68 65 20 66 69 6c 65 6e 61 6d 65 |ter the filename| 00000b90 20 69 6e 20 74 68 65 20 69 63 6f 6e 20 6f 6e 20 | in the icon on | 00000ba0 74 68 65 20 73 61 76 65 20 61 73 20 77 69 6e 64 |the save as wind| 00000bb0 6f 77 2c 20 61 6e 64 20 65 69 74 68 65 72 20 63 |ow, and either c| 00000bc0 6c 69 63 6b 20 4f 4b 2c 20 6f 72 20 64 72 61 67 |lick OK, or drag| 00000bd0 20 74 68 65 20 73 70 72 69 74 65 20 69 63 6f 6e | the sprite icon| 00000be0 20 74 6f 20 74 68 65 20 64 65 73 74 69 6e 61 74 | to the destinat| 00000bf0 69 6f 6e 20 77 69 6e 64 6f 77 2e 20 54 68 65 20 |ion window. The | 00000c00 73 70 72 69 74 65 20 66 69 6c 65 20 63 6f 6e 74 |sprite file cont| 00000c10 61 69 6e 73 20 61 20 73 69 6e 67 6c 65 20 73 70 |ains a single sp| 00000c20 72 69 74 65 2c 20 63 61 6c 6c 65 64 20 22 53 63 |rite, called "Sc| 00000c30 72 65 65 6e 22 20 77 69 74 68 20 61 20 64 65 66 |reen" with a def| 00000c40 61 75 6c 74 20 64 65 73 6b 74 6f 70 20 70 61 6c |ault desktop pal| 00000c50 65 74 74 65 2e 0a 0a 54 68 69 6e 67 73 20 74 6f |ette...Things to| 00000c60 20 74 72 79 0a 3d 3d 3d 3d 3d 3d 20 3d 3d 20 3d | try.====== == =| 00000c70 3d 3d 0a 57 68 79 20 6e 6f 74 20 74 72 79 20 74 |==.Why not try t| 00000c80 68 65 20 66 6f 6c 6c 6f 77 69 6e 67 20 74 6f 20 |he following to | 00000c90 64 65 6d 6f 6e 73 74 72 61 74 65 20 50 50 6c 61 |demonstrate PPla| 00000ca0 6e 65 3a 0a 31 2e 0a 53 63 61 6c 65 20 78 3a 20 |ne:.1..Scale x: | 00000cb0 2d 31 20 74 6f 20 33 20 79 3a 20 2d 31 20 74 6f |-1 to 3 y: -1 to| 00000cc0 20 33 0a 64 78 2f 64 74 3a 20 78 2a 79 2d 78 0a | 3.dx/dt: x*y-x.| 00000cd0 64 79 2f 64 74 3a 20 79 2d 78 2a 79 0a 32 2e 0a |dy/dt: y-x*y.2..| 00000ce0 53 63 61 6c 65 20 78 3a 20 2d 31 30 20 74 6f 20 |Scale x: -10 to | 00000cf0 31 30 20 79 3a 20 2d 31 30 20 74 6f 20 31 30 0a |10 y: -10 to 10.| 00000d00 64 78 2f 64 74 3a 20 78 2a 78 2d 79 2a 79 0a 64 |dx/dt: x*x-y*y.d| 00000d10 79 2f 64 74 3a 20 32 2a 78 2a 79 0a 0a 54 68 69 |y/dt: 2*x*y..Thi| 00000d20 6e 67 73 20 74 6f 20 6c 6f 6f 6b 20 6f 75 74 20 |ngs to look out | 00000d30 66 6f 72 0a 3d 3d 3d 3d 3d 3d 20 3d 3d 20 3d 3d |for.====== == ==| 00000d40 3d 3d 20 3d 3d 3d 20 3d 3d 3d 0a 4f 6e 65 20 6f |== === ===.One o| 00000d50 66 20 74 68 65 20 6d 6f 73 74 20 63 6f 6d 6d 6d |f the most commm| 00000d60 6f 6e 20 70 72 6f 62 6c 65 6d 73 20 65 6e 63 6f |on problems enco| 00000d70 75 6e 74 65 72 65 64 20 77 69 74 68 20 74 68 69 |untered with thi| 00000d80 73 20 61 70 70 6c 69 63 61 74 69 6f 6e 20 69 73 |s application is| 00000d90 20 74 68 65 20 65 72 72 6f 72 20 22 44 69 76 69 | the error "Divi| 00000da0 73 69 6f 6e 20 62 79 20 5a 65 72 6f 22 2e 20 54 |sion by Zero". T| 00000db0 68 69 73 20 67 65 6e 65 72 61 6c 6c 79 20 6f 63 |his generally oc| 00000dc0 63 75 72 73 20 75 70 6f 6e 20 64 72 61 77 69 6e |curs upon drawin| 00000dd0 67 20 61 20 67 72 61 70 68 2e 20 54 72 79 20 61 |g a graph. Try a| 00000de0 64 6a 75 73 74 69 6e 67 20 79 6f 75 72 20 65 71 |djusting your eq| 00000df0 75 61 74 69 6f 6e 73 20 73 6f 20 74 68 61 74 20 |uations so that | 00000e00 74 68 69 73 20 64 6f 65 73 20 6e 6f 74 20 6f 63 |this does not oc| 00000e10 63 75 72 2c 20 65 67 20 62 79 20 61 64 64 69 6e |cur, eg by addin| 00000e20 67 20 6f 6e 20 61 20 73 6d 61 6c 6c 20 63 6f 6e |g on a small con| 00000e30 73 74 61 6e 74 20 65 67 20 31 45 2d 31 30 2c 20 |stant eg 1E-10, | 00000e40 6f 72 20 61 64 6a 75 73 74 20 74 68 65 20 67 72 |or adjust the gr| 00000e50 61 70 68 20 73 63 61 6c 65 73 2e 0a 20 0a 43 6f |aph scales.. .Co| 00000e60 70 79 72 69 67 68 74 0a 3d 3d 3d 3d 3d 3d 3d 3d |pyright.========| 00000e70 3d 0a 0a a9 20 44 61 72 72 65 6e 20 47 72 65 65 |=... Darren Gree| 00000e80 6e 20 28 50 69 6e 6b 6d 6f 6e 67 6f 6f 73 65 20 |n (Pinkmongoose | 00000e90 53 6f 66 74 77 61 72 65 2e 29 20 76 65 72 73 69 |Software.) versi| 00000ea0 6f 6e 20 32 2e 30 30 0a 59 6f 75 20 6d 61 79 20 |on 2.00.You may | 00000eb0 64 69 73 74 72 69 62 75 74 65 20 74 68 69 73 20 |distribute this | 00000ec0 70 72 6f 67 72 61 6d 20 66 72 65 65 6c 79 2c 20 |program freely, | 00000ed0 61 73 20 6c 6f 6e 67 20 61 73 20 69 74 20 69 73 |as long as it is| 00000ee0 20 64 69 73 74 72 69 62 75 74 65 64 20 69 6e 74 | distributed int| 00000ef0 61 63 74 2c 20 77 69 74 68 20 61 6c 6c 20 74 68 |act, with all th| 00000f00 65 20 66 69 6c 65 73 20 6d 65 6e 74 69 6f 6e 65 |e files mentione| 00000f10 64 20 62 65 6c 6f 77 20 69 6e 63 6c 75 64 65 64 |d below included| 00000f20 2c 20 69 6e 20 61 6e 20 75 6e 61 6c 74 65 72 65 |, in an unaltere| 00000f30 64 20 73 74 61 74 65 2e 20 54 68 69 73 20 70 72 |d state. This pr| 00000f40 6f 67 72 61 6d 20 6d 61 79 20 6e 6f 74 20 62 65 |ogram may not be| 00000f50 20 72 65 2d 73 6f 6c 64 20 77 69 74 68 6f 75 74 | re-sold without| 00000f60 20 77 72 69 74 74 65 6e 20 70 65 72 6d 69 73 73 | written permiss| 00000f70 69 6f 6e 20 66 72 6f 6d 20 74 68 65 20 61 75 74 |ion from the aut| 00000f80 68 6f 72 2e 20 49 66 20 64 69 73 74 72 69 62 75 |hor. If distribu| 00000f90 74 65 64 20 6e 6f 20 6d 6f 72 65 20 74 68 61 6e |ted no more than| 00000fa0 20 61 20 6e 6f 6d 69 6e 61 6c 20 63 68 61 72 67 | a nominal charg| 00000fb0 65 20 6f 66 20 33 20 70 6f 75 6e 64 73 20 73 74 |e of 3 pounds st| 00000fc0 65 72 6c 69 6e 67 20 6d 61 79 20 62 65 20 63 68 |erling may be ch| 00000fd0 61 72 67 65 64 20 66 6f 72 20 64 69 73 74 72 69 |arged for distri| 00000fe0 62 75 74 69 6f 6e 20 63 6f 73 74 73 2e 0a 0a 46 |bution costs...F| 00000ff0 69 6c 65 73 20 69 6e 63 6c 75 64 65 64 20 61 72 |iles included ar| 00001000 65 3a 0a 20 21 52 75 6e 0a 20 21 48 65 6c 70 0a |e:. !Run. !Help.| 00001010 20 21 52 55 4e 69 6d 61 67 65 0a 20 21 53 70 72 | !RUNimage. !Spr| 00001020 69 74 65 73 0a 20 4d 65 73 73 61 67 65 73 0a 20 |ites. Messages. | 00001030 50 61 6c 65 74 74 65 0a 20 54 65 6d 70 6c 61 74 |Palette. Templat| 00001040 65 73 0a 0a 44 69 73 63 6c 61 69 6d 65 72 0a 3d |es..Disclaimer.=| 00001050 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 0a 4e 6f 20 6c 69 |=========..No li| 00001060 61 62 69 6c 69 74 79 20 66 6f 72 20 64 61 6d 61 |ability for dama| 00001070 67 65 20 6f 72 20 6c 6f 73 73 20 65 6e 73 75 69 |ge or loss ensui| 00001080 6e 67 20 61 73 20 61 20 72 65 73 75 6c 74 20 6f |ng as a result o| 00001090 66 20 74 68 65 20 75 73 65 20 6f 72 20 6d 69 73 |f the use or mis| 000010a0 75 73 65 20 6f 66 0a 74 68 69 73 20 73 6f 66 74 |use of.this soft| 000010b0 77 61 72 65 20 63 61 6e 20 62 65 20 61 63 63 65 |ware can be acce| 000010c0 70 74 65 64 20 62 79 20 74 68 65 20 61 75 74 68 |pted by the auth| 000010d0 6f 72 2e 20 4e 6f 20 67 75 61 72 61 6e 74 65 65 |or. No guarantee| 000010e0 20 6f 66 20 74 68 65 20 71 75 61 6c 69 74 79 20 | of the quality | 000010f0 61 6e 64 20 61 63 63 75 72 61 63 79 20 6f 66 20 |and accuracy of | 00001100 74 68 65 20 70 6c 6f 74 73 20 70 72 6f 64 75 63 |the plots produc| 00001110 65 64 20 62 79 20 74 68 69 73 20 73 6f 66 74 77 |ed by this softw| 00001120 61 72 65 20 69 73 20 67 69 76 65 6e 2e 0a 0a 20 |are is given... | 00001130 54 6f 20 63 6f 6e 74 61 63 74 20 74 68 65 20 61 |To contact the a| 00001140 75 74 68 6f 72 20 66 6f 72 20 73 75 67 67 65 73 |uthor for sugges| 00001150 74 69 6f 6e 73 2c 20 72 65 70 6f 72 74 73 20 6f |tions, reports o| 00001160 66 20 62 75 67 73 2c 20 65 74 63 2e 0a 77 72 69 |f bugs, etc..wri| 00001170 74 65 20 74 6f 3a 0a 44 61 72 72 65 6e 20 47 72 |te to:.Darren Gr| 00001180 65 65 6e 2e 0a 31 38 20 4f 27 48 61 6e 6c 6f 6e |een..18 O'Hanlon| 00001190 20 41 76 65 6e 75 65 0a 42 72 69 67 67 0a 53 6f | Avenue.Brigg.So| 000011a0 75 74 68 20 48 75 6d 62 65 72 73 69 64 65 2e 0a |uth Humberside..| 000011b0 44 4e 32 30 20 38 44 45 2e 0a |DN20 8DE..| 000011ba
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