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Windsor/!Patterns/!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 1998-03 B.adf » StarInfo |
| Filename: | Windsor/!Patterns/!Help |
| Read OK: | ✔ |
| File size: | 240A bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
!Patterns - Version 1.00 ========================= !Patterns was written simply as an exercise in desktop programming. It isn't particularly useful, as far as I can see, unless you need regular polygons producing in DrawFile format. The algorithms for the 'Rose' and 'Epicycloid' section were adapted from some programs written by my Dad, Brian Windsor, some years ago in BASIC on the beeb, for class demonstrations. I decided to modernise them... The idea for the 'Limacon' section was also derived from one of his programs, although that only drew the envelope (the outline). The program produces four types of patterns in the Draw format. Files can be saved to disk, or dragged straight into Draw. The four object types have been named as follows: 1.Polygon ========= This quite simply produces a regular polygon that fits in a circle of the given radius. If you want a specific length of side, I am afraid you will have to work out the radius of the circle needed: I have tried to keep the options as simple as possible. 2.Mystic Rose ============= This is similar to the polygon option, in that the pattern is produced from a polygon of the given number of vertices. Again, this fits in the circle of the radius specified. The difference is that for a polygon, only adjacent points are connected, showing the sides, while the pattern produced here is generated by connecting every point to every other around the circumference. 3.Epicycloid ============ At this point, things become a little more complicated. Like the first two pattern types, this pattern is produced by drawing lines between regularly spaced points on a circle's circumference. It is the only one in which the bounding circle is drawn. If we number each point around the circle, point n is connected to the point (loops + 1) * n. So, if loops = 1, point 1 is connected to point 2, point 2 to point 4, point 3 to point 6, etc. Position numbers higher than the total number of points are mapped onto the existing positions, starting again from point zero. Within the figure, a definite path can be traced out which loops around a number of times. This number is the value contained in the "loops" box. To make this pattern more general, I have allowed non integer values of 'loops', but this should be used with care. The program continues to traverse the basic circle circumference until it has made a number of revolutions equal to the reciprocal of the fractional part of 'loops'. For this reason, selecting a fractional part which has a very high reciprocal will lead to a high number of revolutions and a lot of lines. As a general rule of thumb, values such as "x.5" or "x.25" produce acceptable results. Also worth noting is the fact that a fractional value with a non-integer reciprocal will produce a pattern that doesn't finish at the point at which it started. Technically speaking, an epicycloid is the pattern produced by following a point on the edge of a circle rolling around the circumference of another circle, in much the same way as a spirograph works. It is the envelope, or bounding path, of the pattern produced here. The number of loops produced is therefore dependent on the ratio of the sizes of the two circles: Circles the same size will produce a single loop (the cardioid, see below), two loops can be produced by using a rolling circle of half the radius of the fixed one, and so on. The case when two loops are produced is called a nephroid. When three or more loops are present, the figure is called a three cusped epicycloid, four cusped and so on; a cusp being the correct term for the loops observed. Despite this nomenclature suggesting the lower numbers of cusps are perhaps more special than higher ones, some very interesting patterns can be produced using much higher numbers of loops, where the cusps of the envelope can barely be seen. Try 15 loops, for instance, or 60, 61 and 89. 4.Limacon ========= As with the epicycloid, the limacon is actually the shape of the envelope around the pattern of circles seen here. The pattern is produced by starting from a circle (here called the 'basic' circle, as it is the basis for the pattern) and drawing a number of other circles with centres all on the circumference of the this circle. These points are all equally spaced around the circumference, as before. The second proviso is that each of the secondary circle's circumferences passes through the 'focus'. This point lies on the x-axis, and the value given is a fraction of the radius of the basic circle, i.e. "1.0" specifies a focus on the circumference of the basic circle, "2.0" specifies a point twice as far from the centre of the basic circle as its circumference and "0.5" specifies a point half way between the centre and the circumference. If 'Basic Circle' is selected, the basic circle will be drawn on the resulting diagram, otherwise it is left off. The member of the limacon family produced when the focus is on the basic circle circumference (i.e. focus = 1.0) is called a cardioid, the shape mentioned above. This is so called because of its similarity to the heart. Another case worth trying is that of focus = 0.0. This produces a set of circles of all the same radius, and looks reasonably attractive. My sister said it would be good to colour in (she's 19!)... Those who remember the interference generator on the beeb welcome tape (you know, the one where you pressed a couple of function keys and it drew a Persian carpet) might like to try limacons with a few hundred circles. I believe the limacon is the shape you may have seen when holding a mug or cup under a light, but so far I haven't been able to verify this. The shape is seen as a bright line across the bottom and sides of the cup. The reason for its appearance is to do with reflection of light from the circular sides of the cup. Varying the angle of the sides (thus varying the shape of the ellipse presented to the light source) changes the path of the line in a way that represents a change in the position of the focus in this program. Technical Bits ============== There isn't really much to say. The program was written in C, and compiled using GNU C and Desklib. This is the first program I have written to work in the desktop and I don't have the benefit of the PRM. That I got anywhere is due to the comprehensive Desklib and SWI StrongHelp manuals and guesswork. As a result, I still can't get the RamTransfer thingy to work. It works with Zap, but not Draw. Nevermind. The file produced is a Draw Selection. I used this format for two reasons, firstly the selection file format is shorter and therefore easier to work out than the entire file (I don't have the PRM, and only AFTERWARDS did I discover the file format was in StrongHelp). Secondly, providing you get the left and bottom edges of the pattern on the page, Draw will select the best page size and orientation to get the rest of the pattern on, no matter what size it is: My program does not need to worry about it. I have fixed it so that the bottom and left edges of the pattern are always 2cm each from the bottom and left edges of the page. This seems to always avoid the print margin (at least with my printer), no matter what the page orientation. The files can then be printed out immediately, although please note that you cannot drag the icon directly to the printer driver icon; you must first transfer the file to Draw. The entire pattern is defined as a single object, not a group. This allows it to be drawn more rapidly. In the future (if I actually do any more to this program) I should like to find out why my RamTransfer protocol was failing with Draw and fix it, and also allow dragging directly to the printer driver, or (preferably) add a Print option within the program window. Copyright notice ================ The application '!Patterns' is copyright Michael Windsor 1996. I offer no guarantees as to the reliability/stability of it or any of its functions. You may copy the program freely provided that the whole application remains unaltered and all help text is included. You may not sell the program without my written permission. However, Public Domain libraries may distribute the program provided they charge at most 3 pounds sterling per disc. If anyone else would like to distribute Patterns then please write to me first to get my permission. Acknowledgments =============== I'd like to give my thanks to Dominic Symes for Zap, which is excellent and Martin Ebourne who wrote the C mode for Zap, also extremely useful. As I mentioned earlier, StrongHelp has been invaluable, so thank you Guttorm Vik. I'd also like to thank Julian Smith and those who have contributed to Desklib, Peter Burwood, Simon Callan, and Nick Burret (and anyone else) for the RiscOS port of GCC and UnixLib. A free C compiler with libraries is almost too good to believe. Also, my Dad, Brian Windsor, who wrote the original programs about ten years ago. I hope I have written the program so that it won't crash, no matter what you do to it, but if it does please let me know how and (preferably) why. It has been tested on a Risc PC (OS 3.6 & 3.7) with both a StrongARM and 710 and an A310 (OS 3.1).
00000000 09 09 09 21 50 61 74 74 65 72 6e 73 20 20 2d 20 |...!Patterns - | 00000010 56 65 72 73 69 6f 6e 20 31 2e 30 30 0a 09 09 09 |Version 1.00....| 00000020 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d |================| 00000030 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 0a 21 50 61 74 74 |=========..!Patt| 00000040 65 72 6e 73 20 77 61 73 20 77 72 69 74 74 65 6e |erns was written| 00000050 20 73 69 6d 70 6c 79 20 61 73 20 61 6e 20 65 78 | simply as an ex| 00000060 65 72 63 69 73 65 20 69 6e 20 64 65 73 6b 74 6f |ercise in deskto| 00000070 70 20 70 72 6f 67 72 61 6d 6d 69 6e 67 2e 20 49 |p programming. I| 00000080 74 20 69 73 6e 27 74 0a 70 61 72 74 69 63 75 6c |t isn't.particul| 00000090 61 72 6c 79 20 75 73 65 66 75 6c 2c 20 61 73 20 |arly useful, as | 000000a0 66 61 72 20 61 73 20 49 20 63 61 6e 20 73 65 65 |far as I can see| 000000b0 2c 20 75 6e 6c 65 73 73 20 79 6f 75 20 6e 65 65 |, unless you nee| 000000c0 64 20 72 65 67 75 6c 61 72 20 70 6f 6c 79 67 6f |d regular polygo| 000000d0 6e 73 0a 70 72 6f 64 75 63 69 6e 67 20 69 6e 20 |ns.producing in | 000000e0 44 72 61 77 46 69 6c 65 20 66 6f 72 6d 61 74 2e |DrawFile format.| 000000f0 20 54 68 65 20 61 6c 67 6f 72 69 74 68 6d 73 20 | The algorithms | 00000100 66 6f 72 20 74 68 65 20 27 52 6f 73 65 27 20 61 |for the 'Rose' a| 00000110 6e 64 20 27 45 70 69 63 79 63 6c 6f 69 64 27 0a |nd 'Epicycloid'.| 00000120 73 65 63 74 69 6f 6e 20 77 65 72 65 20 61 64 61 |section were ada| 00000130 70 74 65 64 20 66 72 6f 6d 20 73 6f 6d 65 20 70 |pted from some p| 00000140 72 6f 67 72 61 6d 73 20 77 72 69 74 74 65 6e 20 |rograms written | 00000150 62 79 20 6d 79 20 44 61 64 2c 20 42 72 69 61 6e |by my Dad, Brian| 00000160 20 57 69 6e 64 73 6f 72 2c 0a 73 6f 6d 65 20 79 | Windsor,.some y| 00000170 65 61 72 73 20 61 67 6f 20 69 6e 20 42 41 53 49 |ears ago in BASI| 00000180 43 20 6f 6e 20 74 68 65 20 62 65 65 62 2c 20 66 |C on the beeb, f| 00000190 6f 72 20 63 6c 61 73 73 20 64 65 6d 6f 6e 73 74 |or class demonst| 000001a0 72 61 74 69 6f 6e 73 2e 20 49 20 64 65 63 69 64 |rations. I decid| 000001b0 65 64 20 74 6f 0a 6d 6f 64 65 72 6e 69 73 65 20 |ed to.modernise | 000001c0 74 68 65 6d 2e 2e 2e 20 54 68 65 20 69 64 65 61 |them... The idea| 000001d0 20 66 6f 72 20 74 68 65 20 27 4c 69 6d 61 63 6f | for the 'Limaco| 000001e0 6e 27 20 73 65 63 74 69 6f 6e 20 77 61 73 20 61 |n' section was a| 000001f0 6c 73 6f 20 64 65 72 69 76 65 64 20 66 72 6f 6d |lso derived from| 00000200 0a 6f 6e 65 20 6f 66 20 68 69 73 20 70 72 6f 67 |.one of his prog| 00000210 72 61 6d 73 2c 20 61 6c 74 68 6f 75 67 68 20 74 |rams, although t| 00000220 68 61 74 20 6f 6e 6c 79 20 64 72 65 77 20 74 68 |hat only drew th| 00000230 65 20 65 6e 76 65 6c 6f 70 65 20 28 74 68 65 20 |e envelope (the | 00000240 6f 75 74 6c 69 6e 65 29 2e 0a 0a 54 68 65 20 70 |outline)...The p| 00000250 72 6f 67 72 61 6d 20 70 72 6f 64 75 63 65 73 20 |rogram produces | 00000260 66 6f 75 72 20 74 79 70 65 73 20 6f 66 20 70 61 |four types of pa| 00000270 74 74 65 72 6e 73 20 69 6e 20 74 68 65 20 44 72 |tterns in the Dr| 00000280 61 77 20 66 6f 72 6d 61 74 2e 20 46 69 6c 65 73 |aw format. Files| 00000290 20 63 61 6e 20 62 65 0a 73 61 76 65 64 20 74 6f | can be.saved to| 000002a0 20 64 69 73 6b 2c 20 6f 72 20 64 72 61 67 67 65 | disk, or dragge| 000002b0 64 20 73 74 72 61 69 67 68 74 20 69 6e 74 6f 20 |d straight into | 000002c0 44 72 61 77 2e 20 54 68 65 20 66 6f 75 72 20 6f |Draw. The four o| 000002d0 62 6a 65 63 74 20 74 79 70 65 73 20 68 61 76 65 |bject types have| 000002e0 20 62 65 65 6e 0a 6e 61 6d 65 64 20 61 73 20 66 | been.named as f| 000002f0 6f 6c 6c 6f 77 73 3a 0a 0a 0a 31 2e 50 6f 6c 79 |ollows:...1.Poly| 00000300 67 6f 6e 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 0a 54 |gon.=========..T| 00000310 68 69 73 20 71 75 69 74 65 20 73 69 6d 70 6c 79 |his quite simply| 00000320 20 70 72 6f 64 75 63 65 73 20 61 20 72 65 67 75 | produces a regu| 00000330 6c 61 72 20 70 6f 6c 79 67 6f 6e 20 74 68 61 74 |lar polygon that| 00000340 20 66 69 74 73 20 69 6e 20 61 20 63 69 72 63 6c | fits in a circl| 00000350 65 20 6f 66 20 74 68 65 0a 67 69 76 65 6e 20 72 |e of the.given r| 00000360 61 64 69 75 73 2e 20 49 66 20 79 6f 75 20 77 61 |adius. If you wa| 00000370 6e 74 20 61 20 73 70 65 63 69 66 69 63 20 6c 65 |nt a specific le| 00000380 6e 67 74 68 20 6f 66 20 73 69 64 65 2c 20 49 20 |ngth of side, I | 00000390 61 6d 20 61 66 72 61 69 64 20 79 6f 75 20 77 69 |am afraid you wi| 000003a0 6c 6c 0a 68 61 76 65 20 74 6f 20 77 6f 72 6b 20 |ll.have to work | 000003b0 6f 75 74 20 74 68 65 20 72 61 64 69 75 73 20 6f |out the radius o| 000003c0 66 20 74 68 65 20 63 69 72 63 6c 65 20 6e 65 65 |f the circle nee| 000003d0 64 65 64 3a 20 49 20 68 61 76 65 20 74 72 69 65 |ded: I have trie| 000003e0 64 20 74 6f 20 6b 65 65 70 20 74 68 65 0a 6f 70 |d to keep the.op| 000003f0 74 69 6f 6e 73 20 61 73 20 73 69 6d 70 6c 65 20 |tions as simple | 00000400 61 73 20 70 6f 73 73 69 62 6c 65 2e 0a 0a 0a 32 |as possible....2| 00000410 2e 4d 79 73 74 69 63 20 52 6f 73 65 0a 3d 3d 3d |.Mystic Rose.===| 00000420 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a 0a 54 68 69 73 |==========..This| 00000430 20 69 73 20 73 69 6d 69 6c 61 72 20 74 6f 20 74 | is similar to t| 00000440 68 65 20 70 6f 6c 79 67 6f 6e 20 6f 70 74 69 6f |he polygon optio| 00000450 6e 2c 20 69 6e 20 74 68 61 74 20 74 68 65 20 70 |n, in that the p| 00000460 61 74 74 65 72 6e 20 69 73 20 70 72 6f 64 75 63 |attern is produc| 00000470 65 64 20 66 72 6f 6d 20 61 0a 70 6f 6c 79 67 6f |ed from a.polygo| 00000480 6e 20 6f 66 20 74 68 65 20 67 69 76 65 6e 20 6e |n of the given n| 00000490 75 6d 62 65 72 20 6f 66 20 76 65 72 74 69 63 65 |umber of vertice| 000004a0 73 2e 20 41 67 61 69 6e 2c 20 74 68 69 73 20 66 |s. Again, this f| 000004b0 69 74 73 20 69 6e 20 74 68 65 20 63 69 72 63 6c |its in the circl| 000004c0 65 20 6f 66 0a 74 68 65 20 72 61 64 69 75 73 20 |e of.the radius | 000004d0 73 70 65 63 69 66 69 65 64 2e 20 54 68 65 20 64 |specified. The d| 000004e0 69 66 66 65 72 65 6e 63 65 20 69 73 20 74 68 61 |ifference is tha| 000004f0 74 20 66 6f 72 20 61 20 70 6f 6c 79 67 6f 6e 2c |t for a polygon,| 00000500 20 6f 6e 6c 79 20 61 64 6a 61 63 65 6e 74 0a 70 | only adjacent.p| 00000510 6f 69 6e 74 73 20 61 72 65 20 63 6f 6e 6e 65 63 |oints are connec| 00000520 74 65 64 2c 20 73 68 6f 77 69 6e 67 20 74 68 65 |ted, showing the| 00000530 20 73 69 64 65 73 2c 20 77 68 69 6c 65 20 74 68 | sides, while th| 00000540 65 20 70 61 74 74 65 72 6e 20 70 72 6f 64 75 63 |e pattern produc| 00000550 65 64 20 68 65 72 65 20 69 73 0a 67 65 6e 65 72 |ed here is.gener| 00000560 61 74 65 64 20 62 79 20 63 6f 6e 6e 65 63 74 69 |ated by connecti| 00000570 6e 67 20 65 76 65 72 79 20 70 6f 69 6e 74 20 74 |ng every point t| 00000580 6f 20 65 76 65 72 79 20 6f 74 68 65 72 20 61 72 |o every other ar| 00000590 6f 75 6e 64 20 74 68 65 20 63 69 72 63 75 6d 66 |ound the circumf| 000005a0 65 72 65 6e 63 65 2e 0a 0a 0a 33 2e 45 70 69 63 |erence....3.Epic| 000005b0 79 63 6c 6f 69 64 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d |ycloid.=========| 000005c0 3d 3d 3d 0a 0a 41 74 20 74 68 69 73 20 70 6f 69 |===..At this poi| 000005d0 6e 74 2c 20 74 68 69 6e 67 73 20 62 65 63 6f 6d |nt, things becom| 000005e0 65 20 61 20 6c 69 74 74 6c 65 20 6d 6f 72 65 20 |e a little more | 000005f0 63 6f 6d 70 6c 69 63 61 74 65 64 2e 20 4c 69 6b |complicated. Lik| 00000600 65 20 74 68 65 20 66 69 72 73 74 20 74 77 6f 0a |e the first two.| 00000610 70 61 74 74 65 72 6e 20 74 79 70 65 73 2c 20 74 |pattern types, t| 00000620 68 69 73 20 70 61 74 74 65 72 6e 20 69 73 20 70 |his pattern is p| 00000630 72 6f 64 75 63 65 64 20 62 79 20 64 72 61 77 69 |roduced by drawi| 00000640 6e 67 20 6c 69 6e 65 73 20 62 65 74 77 65 65 6e |ng lines between| 00000650 20 72 65 67 75 6c 61 72 6c 79 0a 73 70 61 63 65 | regularly.space| 00000660 64 20 70 6f 69 6e 74 73 20 6f 6e 20 61 20 63 69 |d points on a ci| 00000670 72 63 6c 65 27 73 20 63 69 72 63 75 6d 66 65 72 |rcle's circumfer| 00000680 65 6e 63 65 2e 20 49 74 20 69 73 20 74 68 65 20 |ence. It is the | 00000690 6f 6e 6c 79 20 6f 6e 65 20 69 6e 20 77 68 69 63 |only one in whic| 000006a0 68 20 74 68 65 0a 62 6f 75 6e 64 69 6e 67 20 63 |h the.bounding c| 000006b0 69 72 63 6c 65 20 69 73 20 64 72 61 77 6e 2e 20 |ircle is drawn. | 000006c0 49 66 20 77 65 20 6e 75 6d 62 65 72 20 65 61 63 |If we number eac| 000006d0 68 20 70 6f 69 6e 74 20 61 72 6f 75 6e 64 20 74 |h point around t| 000006e0 68 65 20 63 69 72 63 6c 65 2c 20 70 6f 69 6e 74 |he circle, point| 000006f0 20 6e 0a 69 73 20 63 6f 6e 6e 65 63 74 65 64 20 | n.is connected | 00000700 74 6f 20 74 68 65 20 70 6f 69 6e 74 20 28 6c 6f |to the point (lo| 00000710 6f 70 73 20 2b 20 31 29 20 2a 20 6e 2e 20 53 6f |ops + 1) * n. So| 00000720 2c 20 69 66 20 6c 6f 6f 70 73 20 3d 20 31 2c 20 |, if loops = 1, | 00000730 70 6f 69 6e 74 20 31 20 69 73 0a 63 6f 6e 6e 65 |point 1 is.conne| 00000740 63 74 65 64 20 74 6f 20 70 6f 69 6e 74 20 32 2c |cted to point 2,| 00000750 20 70 6f 69 6e 74 20 32 20 74 6f 20 70 6f 69 6e | point 2 to poin| 00000760 74 20 34 2c 20 70 6f 69 6e 74 20 33 20 74 6f 20 |t 4, point 3 to | 00000770 70 6f 69 6e 74 20 36 2c 20 65 74 63 2e 20 50 6f |point 6, etc. Po| 00000780 73 69 74 69 6f 6e 0a 6e 75 6d 62 65 72 73 20 68 |sition.numbers h| 00000790 69 67 68 65 72 20 74 68 61 6e 20 74 68 65 20 74 |igher than the t| 000007a0 6f 74 61 6c 20 6e 75 6d 62 65 72 20 6f 66 20 70 |otal number of p| 000007b0 6f 69 6e 74 73 20 61 72 65 20 6d 61 70 70 65 64 |oints are mapped| 000007c0 20 6f 6e 74 6f 20 74 68 65 20 65 78 69 73 74 69 | onto the existi| 000007d0 6e 67 0a 70 6f 73 69 74 69 6f 6e 73 2c 20 73 74 |ng.positions, st| 000007e0 61 72 74 69 6e 67 20 61 67 61 69 6e 20 66 72 6f |arting again fro| 000007f0 6d 20 70 6f 69 6e 74 20 7a 65 72 6f 2e 20 57 69 |m point zero. Wi| 00000800 74 68 69 6e 20 74 68 65 20 66 69 67 75 72 65 2c |thin the figure,| 00000810 20 61 20 64 65 66 69 6e 69 74 65 20 70 61 74 68 | a definite path| 00000820 0a 63 61 6e 20 62 65 20 74 72 61 63 65 64 20 6f |.can be traced o| 00000830 75 74 20 77 68 69 63 68 20 6c 6f 6f 70 73 20 61 |ut which loops a| 00000840 72 6f 75 6e 64 20 61 20 6e 75 6d 62 65 72 20 6f |round a number o| 00000850 66 20 74 69 6d 65 73 2e 20 54 68 69 73 20 6e 75 |f times. This nu| 00000860 6d 62 65 72 20 69 73 20 74 68 65 0a 76 61 6c 75 |mber is the.valu| 00000870 65 20 63 6f 6e 74 61 69 6e 65 64 20 69 6e 20 74 |e contained in t| 00000880 68 65 20 22 6c 6f 6f 70 73 22 20 62 6f 78 2e 0a |he "loops" box..| 00000890 0a 54 6f 20 6d 61 6b 65 20 74 68 69 73 20 70 61 |.To make this pa| 000008a0 74 74 65 72 6e 20 6d 6f 72 65 20 67 65 6e 65 72 |ttern more gener| 000008b0 61 6c 2c 20 49 20 68 61 76 65 20 61 6c 6c 6f 77 |al, I have allow| 000008c0 65 64 20 6e 6f 6e 20 69 6e 74 65 67 65 72 20 76 |ed non integer v| 000008d0 61 6c 75 65 73 20 6f 66 0a 27 6c 6f 6f 70 73 27 |alues of.'loops'| 000008e0 2c 20 62 75 74 20 74 68 69 73 20 73 68 6f 75 6c |, but this shoul| 000008f0 64 20 62 65 20 75 73 65 64 20 77 69 74 68 20 63 |d be used with c| 00000900 61 72 65 2e 20 54 68 65 20 70 72 6f 67 72 61 6d |are. The program| 00000910 20 63 6f 6e 74 69 6e 75 65 73 20 74 6f 20 74 72 | continues to tr| 00000920 61 76 65 72 73 65 0a 74 68 65 20 62 61 73 69 63 |averse.the basic| 00000930 20 63 69 72 63 6c 65 20 63 69 72 63 75 6d 66 65 | circle circumfe| 00000940 72 65 6e 63 65 20 75 6e 74 69 6c 20 69 74 20 68 |rence until it h| 00000950 61 73 20 6d 61 64 65 20 61 20 6e 75 6d 62 65 72 |as made a number| 00000960 20 6f 66 20 72 65 76 6f 6c 75 74 69 6f 6e 73 0a | of revolutions.| 00000970 65 71 75 61 6c 20 74 6f 20 74 68 65 20 72 65 63 |equal to the rec| 00000980 69 70 72 6f 63 61 6c 20 6f 66 20 74 68 65 20 66 |iprocal of the f| 00000990 72 61 63 74 69 6f 6e 61 6c 20 70 61 72 74 20 6f |ractional part o| 000009a0 66 20 27 6c 6f 6f 70 73 27 2e 20 46 6f 72 20 74 |f 'loops'. For t| 000009b0 68 69 73 20 72 65 61 73 6f 6e 2c 0a 73 65 6c 65 |his reason,.sele| 000009c0 63 74 69 6e 67 20 61 20 66 72 61 63 74 69 6f 6e |cting a fraction| 000009d0 61 6c 20 70 61 72 74 20 77 68 69 63 68 20 68 61 |al part which ha| 000009e0 73 20 61 20 76 65 72 79 20 68 69 67 68 20 72 65 |s a very high re| 000009f0 63 69 70 72 6f 63 61 6c 20 77 69 6c 6c 20 6c 65 |ciprocal will le| 00000a00 61 64 20 74 6f 20 61 0a 68 69 67 68 20 6e 75 6d |ad to a.high num| 00000a10 62 65 72 20 6f 66 20 72 65 76 6f 6c 75 74 69 6f |ber of revolutio| 00000a20 6e 73 20 61 6e 64 20 61 20 6c 6f 74 20 6f 66 20 |ns and a lot of | 00000a30 6c 69 6e 65 73 2e 20 41 73 20 61 20 67 65 6e 65 |lines. As a gene| 00000a40 72 61 6c 20 72 75 6c 65 20 6f 66 20 74 68 75 6d |ral rule of thum| 00000a50 62 2c 0a 76 61 6c 75 65 73 20 73 75 63 68 20 61 |b,.values such a| 00000a60 73 20 22 78 2e 35 22 20 6f 72 20 22 78 2e 32 35 |s "x.5" or "x.25| 00000a70 22 20 70 72 6f 64 75 63 65 20 61 63 63 65 70 74 |" produce accept| 00000a80 61 62 6c 65 20 72 65 73 75 6c 74 73 2e 20 41 6c |able results. Al| 00000a90 73 6f 20 77 6f 72 74 68 20 6e 6f 74 69 6e 67 0a |so worth noting.| 00000aa0 69 73 20 74 68 65 20 66 61 63 74 20 74 68 61 74 |is the fact that| 00000ab0 20 61 20 66 72 61 63 74 69 6f 6e 61 6c 20 76 61 | a fractional va| 00000ac0 6c 75 65 20 77 69 74 68 20 61 20 6e 6f 6e 2d 69 |lue with a non-i| 00000ad0 6e 74 65 67 65 72 20 72 65 63 69 70 72 6f 63 61 |nteger reciproca| 00000ae0 6c 20 77 69 6c 6c 0a 70 72 6f 64 75 63 65 20 61 |l will.produce a| 00000af0 20 70 61 74 74 65 72 6e 20 74 68 61 74 20 64 6f | pattern that do| 00000b00 65 73 6e 27 74 20 66 69 6e 69 73 68 20 61 74 20 |esn't finish at | 00000b10 74 68 65 20 70 6f 69 6e 74 20 61 74 20 77 68 69 |the point at whi| 00000b20 63 68 20 69 74 20 73 74 61 72 74 65 64 2e 0a 0a |ch it started...| 00000b30 54 65 63 68 6e 69 63 61 6c 6c 79 20 73 70 65 61 |Technically spea| 00000b40 6b 69 6e 67 2c 20 61 6e 20 65 70 69 63 79 63 6c |king, an epicycl| 00000b50 6f 69 64 20 69 73 20 74 68 65 20 70 61 74 74 65 |oid is the patte| 00000b60 72 6e 20 70 72 6f 64 75 63 65 64 20 62 79 20 66 |rn produced by f| 00000b70 6f 6c 6c 6f 77 69 6e 67 20 61 0a 70 6f 69 6e 74 |ollowing a.point| 00000b80 20 6f 6e 20 74 68 65 20 65 64 67 65 20 6f 66 20 | on the edge of | 00000b90 61 20 63 69 72 63 6c 65 20 72 6f 6c 6c 69 6e 67 |a circle rolling| 00000ba0 20 61 72 6f 75 6e 64 20 74 68 65 20 63 69 72 63 | around the circ| 00000bb0 75 6d 66 65 72 65 6e 63 65 20 6f 66 20 61 6e 6f |umference of ano| 00000bc0 74 68 65 72 0a 63 69 72 63 6c 65 2c 20 69 6e 20 |ther.circle, in | 00000bd0 6d 75 63 68 20 74 68 65 20 73 61 6d 65 20 77 61 |much the same wa| 00000be0 79 20 61 73 20 61 20 73 70 69 72 6f 67 72 61 70 |y as a spirograp| 00000bf0 68 20 77 6f 72 6b 73 2e 20 49 74 20 69 73 20 74 |h works. It is t| 00000c00 68 65 20 65 6e 76 65 6c 6f 70 65 2c 20 6f 72 0a |he envelope, or.| 00000c10 62 6f 75 6e 64 69 6e 67 20 70 61 74 68 2c 20 6f |bounding path, o| 00000c20 66 20 74 68 65 20 70 61 74 74 65 72 6e 20 70 72 |f the pattern pr| 00000c30 6f 64 75 63 65 64 20 68 65 72 65 2e 20 54 68 65 |oduced here. The| 00000c40 20 6e 75 6d 62 65 72 20 6f 66 20 6c 6f 6f 70 73 | number of loops| 00000c50 20 70 72 6f 64 75 63 65 64 20 69 73 0a 74 68 65 | produced is.the| 00000c60 72 65 66 6f 72 65 20 64 65 70 65 6e 64 65 6e 74 |refore dependent| 00000c70 20 6f 6e 20 74 68 65 20 72 61 74 69 6f 20 6f 66 | on the ratio of| 00000c80 20 74 68 65 20 73 69 7a 65 73 20 6f 66 20 74 68 | the sizes of th| 00000c90 65 20 74 77 6f 20 63 69 72 63 6c 65 73 3a 20 43 |e two circles: C| 00000ca0 69 72 63 6c 65 73 20 74 68 65 0a 73 61 6d 65 20 |ircles the.same | 00000cb0 73 69 7a 65 20 77 69 6c 6c 20 70 72 6f 64 75 63 |size will produc| 00000cc0 65 20 61 20 73 69 6e 67 6c 65 20 6c 6f 6f 70 20 |e a single loop | 00000cd0 28 74 68 65 20 63 61 72 64 69 6f 69 64 2c 20 73 |(the cardioid, s| 00000ce0 65 65 20 62 65 6c 6f 77 29 2c 20 74 77 6f 20 6c |ee below), two l| 00000cf0 6f 6f 70 73 20 63 61 6e 0a 62 65 20 70 72 6f 64 |oops can.be prod| 00000d00 75 63 65 64 20 62 79 20 75 73 69 6e 67 20 61 20 |uced by using a | 00000d10 72 6f 6c 6c 69 6e 67 20 63 69 72 63 6c 65 20 6f |rolling circle o| 00000d20 66 20 68 61 6c 66 20 74 68 65 20 72 61 64 69 75 |f half the radiu| 00000d30 73 20 6f 66 20 74 68 65 20 66 69 78 65 64 20 6f |s of the fixed o| 00000d40 6e 65 2c 0a 61 6e 64 20 73 6f 20 6f 6e 2e 20 54 |ne,.and so on. 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T| 00000f20 72 79 20 31 35 20 6c 6f 6f 70 73 2c 20 66 6f 72 |ry 15 loops, for| 00000f30 20 69 6e 73 74 61 6e 63 65 2c 20 6f 72 20 36 30 | instance, or 60| 00000f40 2c 20 36 31 20 61 6e 64 0a 38 39 2e 0a 0a 0a 34 |, 61 and.89....4| 00000f50 2e 4c 69 6d 61 63 6f 6e 0a 3d 3d 3d 3d 3d 3d 3d |.Limacon.=======| 00000f60 3d 3d 0a 0a 41 73 20 77 69 74 68 20 74 68 65 20 |==..As with the | 00000f70 65 70 69 63 79 63 6c 6f 69 64 2c 20 74 68 65 20 |epicycloid, the | 00000f80 6c 69 6d 61 63 6f 6e 20 69 73 20 61 63 74 75 61 |limacon is actua| 00000f90 6c 6c 79 20 74 68 65 20 73 68 61 70 65 20 6f 66 |lly the shape of| 00000fa0 20 74 68 65 20 65 6e 76 65 6c 6f 70 65 0a 61 72 | the envelope.ar| 00000fb0 6f 75 6e 64 20 74 68 65 20 70 61 74 74 65 72 6e |ound the pattern| 00000fc0 20 6f 66 20 63 69 72 63 6c 65 73 20 73 65 65 6e | of circles seen| 00000fd0 20 68 65 72 65 2e 20 54 68 65 20 70 61 74 74 65 | here. 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If 'Basic Ci| 000012c0 72 63 6c 65 27 20 69 73 20 73 65 6c 65 63 74 65 |rcle' is selecte| 000012d0 64 2c 20 74 68 65 20 62 61 73 69 63 20 63 69 72 |d, the basic cir| 000012e0 63 6c 65 0a 77 69 6c 6c 20 62 65 20 64 72 61 77 |cle.will be draw| 000012f0 6e 20 6f 6e 20 74 68 65 20 72 65 73 75 6c 74 69 |n on the resulti| 00001300 6e 67 20 64 69 61 67 72 61 6d 2c 20 6f 74 68 65 |ng diagram, othe| 00001310 72 77 69 73 65 20 69 74 20 69 73 20 6c 65 66 74 |rwise it is left| 00001320 20 6f 66 66 2e 0a 0a 54 68 65 20 6d 65 6d 62 65 | off...The membe| 00001330 72 20 6f 66 20 74 68 65 20 6c 69 6d 61 63 6f 6e |r of the limacon| 00001340 20 66 61 6d 69 6c 79 20 70 72 6f 64 75 63 65 64 | family produced| 00001350 20 77 68 65 6e 20 74 68 65 20 66 6f 63 75 73 20 | when the focus | 00001360 69 73 20 6f 6e 20 74 68 65 20 62 61 73 69 63 0a |is on the basic.| 00001370 63 69 72 63 6c 65 20 63 69 72 63 75 6d 66 65 72 |circle circumfer| 00001380 65 6e 63 65 20 28 69 2e 65 2e 20 66 6f 63 75 73 |ence (i.e. focus| 00001390 20 3d 20 31 2e 30 29 20 69 73 20 63 61 6c 6c 65 | = 1.0) is calle| 000013a0 64 20 61 20 63 61 72 64 69 6f 69 64 2c 20 74 68 |d a cardioid, th| 000013b0 65 20 73 68 61 70 65 0a 6d 65 6e 74 69 6f 6e 65 |e shape.mentione| 000013c0 64 20 61 62 6f 76 65 2e 20 54 68 69 73 20 69 73 |d above. This is| 000013d0 20 73 6f 20 63 61 6c 6c 65 64 20 62 65 63 61 75 | so called becau| 000013e0 73 65 20 6f 66 20 69 74 73 20 73 69 6d 69 6c 61 |se of its simila| 000013f0 72 69 74 79 20 74 6f 20 74 68 65 20 68 65 61 72 |rity to the hear| 00001400 74 2e 0a 41 6e 6f 74 68 65 72 20 63 61 73 65 20 |t..Another case | 00001410 77 6f 72 74 68 20 74 72 79 69 6e 67 20 69 73 20 |worth trying is | 00001420 74 68 61 74 20 6f 66 20 66 6f 63 75 73 20 3d 20 |that of focus = | 00001430 30 2e 30 2e 20 54 68 69 73 20 70 72 6f 64 75 63 |0.0. This produc| 00001440 65 73 20 61 20 73 65 74 20 6f 66 0a 63 69 72 63 |es a set of.circ| 00001450 6c 65 73 20 6f 66 20 61 6c 6c 20 74 68 65 20 73 |les of all the s| 00001460 61 6d 65 20 72 61 64 69 75 73 2c 20 61 6e 64 20 |ame radius, and | 00001470 6c 6f 6f 6b 73 20 72 65 61 73 6f 6e 61 62 6c 79 |looks reasonably| 00001480 20 61 74 74 72 61 63 74 69 76 65 2e 20 4d 79 20 | attractive. 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Those w| 000014d0 68 6f 20 72 65 6d 65 6d 62 65 72 20 74 68 65 0a |ho remember the.| 000014e0 69 6e 74 65 72 66 65 72 65 6e 63 65 20 67 65 6e |interference gen| 000014f0 65 72 61 74 6f 72 20 6f 6e 20 74 68 65 20 62 65 |erator on the be| 00001500 65 62 20 77 65 6c 63 6f 6d 65 20 74 61 70 65 20 |eb welcome tape | 00001510 28 79 6f 75 20 6b 6e 6f 77 2c 20 74 68 65 20 6f |(you know, the o| 00001520 6e 65 20 77 68 65 72 65 0a 79 6f 75 20 70 72 65 |ne where.you pre| 00001530 73 73 65 64 20 61 20 63 6f 75 70 6c 65 20 6f 66 |ssed a couple of| 00001540 20 66 75 6e 63 74 69 6f 6e 20 6b 65 79 73 20 61 | function keys a| 00001550 6e 64 20 69 74 20 64 72 65 77 20 61 20 50 65 72 |nd it drew a Per| 00001560 73 69 61 6e 20 63 61 72 70 65 74 29 20 6d 69 67 |sian carpet) mig| 00001570 68 74 0a 6c 69 6b 65 20 74 6f 20 74 72 79 20 6c |ht.like to try l| 00001580 69 6d 61 63 6f 6e 73 20 77 69 74 68 20 61 20 66 |imacons with a f| 00001590 65 77 20 68 75 6e 64 72 65 64 20 63 69 72 63 6c |ew hundred circl| 000015a0 65 73 2e 0a 0a 49 20 62 65 6c 69 65 76 65 20 74 |es...I believe t| 000015b0 68 65 20 6c 69 6d 61 63 6f 6e 20 69 73 20 74 68 |he limacon is th| 000015c0 65 20 73 68 61 70 65 20 79 6f 75 20 6d 61 79 20 |e shape you may | 000015d0 68 61 76 65 20 73 65 65 6e 20 77 68 65 6e 20 68 |have seen when h| 000015e0 6f 6c 64 69 6e 67 20 61 20 6d 75 67 20 6f 72 0a |olding a mug or.| 000015f0 63 75 70 20 75 6e 64 65 72 20 61 20 6c 69 67 68 |cup under a ligh| 00001600 74 2c 20 62 75 74 20 73 6f 20 66 61 72 20 49 20 |t, but so far I | 00001610 68 61 76 65 6e 27 74 20 62 65 65 6e 20 61 62 6c |haven't been abl| 00001620 65 20 74 6f 20 76 65 72 69 66 79 20 74 68 69 73 |e to verify this| 00001630 2e 20 54 68 65 20 73 68 61 70 65 0a 69 73 20 73 |. The shape.is s| 00001640 65 65 6e 20 61 73 20 61 20 62 72 69 67 68 74 20 |een as a bright | 00001650 6c 69 6e 65 20 61 63 72 6f 73 73 20 74 68 65 20 |line across the | 00001660 62 6f 74 74 6f 6d 20 61 6e 64 20 73 69 64 65 73 |bottom and sides| 00001670 20 6f 66 20 74 68 65 20 63 75 70 2e 20 54 68 65 | of the cup. 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The program | 00001800 77 61 73 20 77 72 69 74 74 65 6e 20 69 6e 20 43 |was written in C| 00001810 2c 20 61 6e 64 20 63 6f 6d 70 69 6c 65 64 0a 75 |, and compiled.u| 00001820 73 69 6e 67 20 47 4e 55 20 43 20 61 6e 64 20 44 |sing GNU C and D| 00001830 65 73 6b 6c 69 62 2e 20 54 68 69 73 20 69 73 20 |esklib. 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I used thi| 000019a0 73 20 66 6f 72 6d 61 74 20 66 6f 72 20 74 77 6f |s format for two| 000019b0 20 72 65 61 73 6f 6e 73 2c 0a 66 69 72 73 74 6c | reasons,.firstl| 000019c0 79 20 74 68 65 20 73 65 6c 65 63 74 69 6f 6e 20 |y the selection | 000019d0 66 69 6c 65 20 66 6f 72 6d 61 74 20 69 73 20 73 |file format is s| 000019e0 68 6f 72 74 65 72 20 61 6e 64 20 74 68 65 72 65 |horter and there| 000019f0 66 6f 72 65 20 65 61 73 69 65 72 20 74 6f 20 77 |fore easier to w| 00001a00 6f 72 6b 20 6f 75 74 0a 74 68 61 6e 20 74 68 65 |ork out.than the| 00001a10 20 65 6e 74 69 72 65 20 66 69 6c 65 20 28 49 20 | entire file (I | 00001a20 64 6f 6e 27 74 20 68 61 76 65 20 74 68 65 20 50 |don't have the P| 00001a30 52 4d 2c 20 61 6e 64 20 6f 6e 6c 79 20 41 46 54 |RM, and only AFT| 00001a40 45 52 57 41 52 44 53 20 64 69 64 20 49 0a 64 69 |ERWARDS did I.di| 00001a50 73 63 6f 76 65 72 20 74 68 65 20 66 69 6c 65 20 |scover the file | 00001a60 66 6f 72 6d 61 74 20 77 61 73 20 69 6e 20 53 74 |format was in St| 00001a70 72 6f 6e 67 48 65 6c 70 29 2e 20 53 65 63 6f 6e |rongHelp). 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I hav| 00001b70 65 20 66 69 78 65 64 20 69 74 20 73 6f 0a 74 68 |e fixed it so.th| 00001b80 61 74 20 74 68 65 20 62 6f 74 74 6f 6d 20 61 6e |at the bottom an| 00001b90 64 20 6c 65 66 74 20 65 64 67 65 73 20 6f 66 20 |d left edges of | 00001ba0 74 68 65 20 70 61 74 74 65 72 6e 20 61 72 65 20 |the pattern are | 00001bb0 61 6c 77 61 79 73 20 32 63 6d 20 65 61 63 68 20 |always 2cm each | 00001bc0 66 72 6f 6d 20 74 68 65 0a 62 6f 74 74 6f 6d 20 |from the.bottom | 00001bd0 61 6e 64 20 6c 65 66 74 20 65 64 67 65 73 20 6f |and left edges o| 00001be0 66 20 74 68 65 20 70 61 67 65 2e 20 54 68 69 73 |f the page. This| 00001bf0 20 73 65 65 6d 73 20 74 6f 20 61 6c 77 61 79 73 | seems to always| 00001c00 20 61 76 6f 69 64 20 74 68 65 20 70 72 69 6e 74 | avoid the print| 00001c10 0a 6d 61 72 67 69 6e 20 28 61 74 20 6c 65 61 73 |.margin (at leas| 00001c20 74 20 77 69 74 68 20 6d 79 20 70 72 69 6e 74 65 |t with my printe| 00001c30 72 29 2c 20 6e 6f 20 6d 61 74 74 65 72 20 77 68 |r), no matter wh| 00001c40 61 74 20 74 68 65 20 70 61 67 65 20 6f 72 69 65 |at the page orie| 00001c50 6e 74 61 74 69 6f 6e 2e 20 54 68 65 0a 66 69 6c |ntation. The.fil| 00001c60 65 73 20 63 61 6e 20 74 68 65 6e 20 62 65 20 70 |es can then be p| 00001c70 72 69 6e 74 65 64 20 6f 75 74 20 69 6d 6d 65 64 |rinted out immed| 00001c80 69 61 74 65 6c 79 2c 20 61 6c 74 68 6f 75 67 68 |iately, although| 00001c90 20 70 6c 65 61 73 65 20 6e 6f 74 65 20 74 68 61 | please note tha| 00001ca0 74 20 79 6f 75 0a 63 61 6e 6e 6f 74 20 64 72 61 |t you.cannot dra| 00001cb0 67 20 74 68 65 20 69 63 6f 6e 20 64 69 72 65 63 |g the icon direc| 00001cc0 74 6c 79 20 74 6f 20 74 68 65 20 70 72 69 6e 74 |tly to the print| 00001cd0 65 72 20 64 72 69 76 65 72 20 69 63 6f 6e 3b 20 |er driver icon; | 00001ce0 79 6f 75 20 6d 75 73 74 20 66 69 72 73 74 0a 74 |you must first.t| 00001cf0 72 61 6e 73 66 65 72 20 74 68 65 20 66 69 6c 65 |ransfer the file| 00001d00 20 74 6f 20 44 72 61 77 2e 0a 0a 54 68 65 20 65 | to Draw...The e| 00001d10 6e 74 69 72 65 20 70 61 74 74 65 72 6e 20 69 73 |ntire pattern is| 00001d20 20 64 65 66 69 6e 65 64 20 61 73 20 61 20 73 69 | defined as a si| 00001d30 6e 67 6c 65 20 6f 62 6a 65 63 74 2c 20 6e 6f 74 |ngle object, not| 00001d40 20 61 20 67 72 6f 75 70 2e 20 54 68 69 73 20 61 | a group. This a| 00001d50 6c 6c 6f 77 73 20 69 74 0a 74 6f 20 62 65 20 64 |llows it.to be d| 00001d60 72 61 77 6e 20 6d 6f 72 65 20 72 61 70 69 64 6c |rawn more rapidl| 00001d70 79 2e 0a 0a 49 6e 20 74 68 65 20 66 75 74 75 72 |y...In the futur| 00001d80 65 20 28 69 66 20 49 20 61 63 74 75 61 6c 6c 79 |e (if I actually| 00001d90 20 64 6f 20 61 6e 79 20 6d 6f 72 65 20 74 6f 20 | do any more to | 00001da0 74 68 69 73 20 70 72 6f 67 72 61 6d 29 20 49 20 |this program) I | 00001db0 73 68 6f 75 6c 64 20 6c 69 6b 65 20 74 6f 0a 66 |should like to.f| 00001dc0 69 6e 64 20 6f 75 74 20 77 68 79 20 6d 79 20 52 |ind out why my R| 00001dd0 61 6d 54 72 61 6e 73 66 65 72 20 70 72 6f 74 6f |amTransfer proto| 00001de0 63 6f 6c 20 77 61 73 20 66 61 69 6c 69 6e 67 20 |col was failing | 00001df0 77 69 74 68 20 44 72 61 77 20 61 6e 64 20 66 69 |with Draw and fi| 00001e00 78 20 69 74 2c 20 61 6e 64 0a 61 6c 73 6f 20 61 |x it, and.also a| 00001e10 6c 6c 6f 77 20 64 72 61 67 67 69 6e 67 20 64 69 |llow dragging di| 00001e20 72 65 63 74 6c 79 20 74 6f 20 74 68 65 20 70 72 |rectly to the pr| 00001e30 69 6e 74 65 72 20 64 72 69 76 65 72 2c 20 6f 72 |inter driver, or| 00001e40 20 28 70 72 65 66 65 72 61 62 6c 79 29 20 61 64 | (preferably) ad| 00001e50 64 20 61 0a 50 72 69 6e 74 20 6f 70 74 69 6f 6e |d a.Print option| 00001e60 20 77 69 74 68 69 6e 20 74 68 65 20 70 72 6f 67 | within the prog| 00001e70 72 61 6d 20 77 69 6e 64 6f 77 2e 0a 0a 0a 43 6f |ram window....Co| 00001e80 70 79 72 69 67 68 74 20 6e 6f 74 69 63 65 0a 3d |pyright notice.=| 00001e90 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 0a |===============.| 00001ea0 0a 54 68 65 20 61 70 70 6c 69 63 61 74 69 6f 6e |.The application| 00001eb0 20 27 21 50 61 74 74 65 72 6e 73 27 20 69 73 20 | '!Patterns' is | 00001ec0 63 6f 70 79 72 69 67 68 74 20 4d 69 63 68 61 65 |copyright Michae| 00001ed0 6c 20 57 69 6e 64 73 6f 72 20 31 39 39 36 2e 20 |l Windsor 1996. | 00001ee0 49 20 6f 66 66 65 72 20 6e 6f 0a 67 75 61 72 61 |I offer no.guara| 00001ef0 6e 74 65 65 73 20 61 73 20 74 6f 20 74 68 65 20 |ntees as to the | 00001f00 72 65 6c 69 61 62 69 6c 69 74 79 2f 73 74 61 62 |reliability/stab| 00001f10 69 6c 69 74 79 20 6f 66 20 69 74 20 6f 72 20 61 |ility of it or a| 00001f20 6e 79 20 6f 66 20 69 74 73 20 66 75 6e 63 74 69 |ny of its functi| 00001f30 6f 6e 73 2e 0a 0a 59 6f 75 20 6d 61 79 20 63 6f |ons...You may co| 00001f40 70 79 20 74 68 65 20 70 72 6f 67 72 61 6d 20 66 |py the program f| 00001f50 72 65 65 6c 79 20 70 72 6f 76 69 64 65 64 20 74 |reely provided t| 00001f60 68 61 74 20 74 68 65 20 77 68 6f 6c 65 20 61 70 |hat the whole ap| 00001f70 70 6c 69 63 61 74 69 6f 6e 20 72 65 6d 61 69 6e |plication remain| 00001f80 73 0a 75 6e 61 6c 74 65 72 65 64 20 61 6e 64 20 |s.unaltered and | 00001f90 61 6c 6c 20 68 65 6c 70 20 74 65 78 74 20 69 73 |all help text is| 00001fa0 20 69 6e 63 6c 75 64 65 64 2e 0a 0a 59 6f 75 20 | included...You | 00001fb0 6d 61 79 20 6e 6f 74 20 73 65 6c 6c 20 74 68 65 |may not sell the| 00001fc0 20 70 72 6f 67 72 61 6d 20 77 69 74 68 6f 75 74 | program without| 00001fd0 20 6d 79 20 77 72 69 74 74 65 6e 20 70 65 72 6d | my written perm| 00001fe0 69 73 73 69 6f 6e 2e 20 48 6f 77 65 76 65 72 2c |ission. However,| 00001ff0 20 50 75 62 6c 69 63 0a 44 6f 6d 61 69 6e 20 6c | Public.Domain l| 00002000 69 62 72 61 72 69 65 73 20 6d 61 79 20 64 69 73 |ibraries may dis| 00002010 74 72 69 62 75 74 65 20 74 68 65 20 70 72 6f 67 |tribute the prog| 00002020 72 61 6d 20 70 72 6f 76 69 64 65 64 20 74 68 65 |ram provided the| 00002030 79 20 63 68 61 72 67 65 20 61 74 20 6d 6f 73 74 |y charge at most| 00002040 20 33 0a 70 6f 75 6e 64 73 20 73 74 65 72 6c 69 | 3.pounds sterli| 00002050 6e 67 20 70 65 72 20 64 69 73 63 2e 20 49 66 20 |ng per disc. If | 00002060 61 6e 79 6f 6e 65 20 65 6c 73 65 20 77 6f 75 6c |anyone else woul| 00002070 64 20 6c 69 6b 65 20 74 6f 20 64 69 73 74 72 69 |d like to distri| 00002080 62 75 74 65 20 50 61 74 74 65 72 6e 73 0a 74 68 |bute Patterns.th| 00002090 65 6e 20 70 6c 65 61 73 65 20 77 72 69 74 65 20 |en please write | 000020a0 74 6f 20 6d 65 20 66 69 72 73 74 20 74 6f 20 67 |to me first to g| 000020b0 65 74 20 6d 79 20 70 65 72 6d 69 73 73 69 6f 6e |et my permission| 000020c0 2e 0a 0a 0a 41 63 6b 6e 6f 77 6c 65 64 67 6d 65 |....Acknowledgme| 000020d0 6e 74 73 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d |nts.============| 000020e0 3d 3d 3d 0a 0a 49 27 64 20 6c 69 6b 65 20 74 6f |===..I'd like to| 000020f0 20 67 69 76 65 20 6d 79 20 74 68 61 6e 6b 73 20 | give my thanks | 00002100 74 6f 20 44 6f 6d 69 6e 69 63 20 53 79 6d 65 73 |to Dominic Symes| 00002110 20 66 6f 72 20 5a 61 70 2c 20 77 68 69 63 68 20 | for Zap, which | 00002120 69 73 20 65 78 63 65 6c 6c 65 6e 74 20 61 6e 64 |is excellent and| 00002130 0a 4d 61 72 74 69 6e 20 45 62 6f 75 72 6e 65 20 |.Martin Ebourne | 00002140 77 68 6f 20 77 72 6f 74 65 20 74 68 65 20 43 20 |who wrote the C | 00002150 6d 6f 64 65 20 66 6f 72 20 5a 61 70 2c 20 61 6c |mode for Zap, al| 00002160 73 6f 20 65 78 74 72 65 6d 65 6c 79 20 75 73 65 |so extremely use| 00002170 66 75 6c 2e 20 41 73 20 49 0a 6d 65 6e 74 69 6f |ful. As I.mentio| 00002180 6e 65 64 20 65 61 72 6c 69 65 72 2c 20 53 74 72 |ned earlier, Str| 00002190 6f 6e 67 48 65 6c 70 20 68 61 73 20 62 65 65 6e |ongHelp has been| 000021a0 20 69 6e 76 61 6c 75 61 62 6c 65 2c 20 73 6f 20 | invaluable, so | 000021b0 74 68 61 6e 6b 20 79 6f 75 20 47 75 74 74 6f 72 |thank you Guttor| 000021c0 6d 20 56 69 6b 2e 0a 0a 49 27 64 20 61 6c 73 6f |m Vik...I'd also| 000021d0 20 6c 69 6b 65 20 74 6f 20 74 68 61 6e 6b 20 4a | like to thank J| 000021e0 75 6c 69 61 6e 20 53 6d 69 74 68 20 61 6e 64 20 |ulian Smith and | 000021f0 74 68 6f 73 65 20 77 68 6f 20 68 61 76 65 20 63 |those who have c| 00002200 6f 6e 74 72 69 62 75 74 65 64 20 74 6f 0a 44 65 |ontributed to.De| 00002210 73 6b 6c 69 62 2c 20 50 65 74 65 72 20 42 75 72 |sklib, Peter Bur| 00002220 77 6f 6f 64 2c 20 53 69 6d 6f 6e 20 43 61 6c 6c |wood, Simon Call| 00002230 61 6e 2c 20 61 6e 64 20 4e 69 63 6b 20 42 75 72 |an, and Nick Bur| 00002240 72 65 74 20 28 61 6e 64 20 61 6e 79 6f 6e 65 20 |ret (and anyone | 00002250 65 6c 73 65 29 20 66 6f 72 0a 74 68 65 20 52 69 |else) for.the Ri| 00002260 73 63 4f 53 20 70 6f 72 74 20 6f 66 20 47 43 43 |scOS port of GCC| 00002270 20 61 6e 64 20 55 6e 69 78 4c 69 62 2e 20 41 20 | and UnixLib. A | 00002280 66 72 65 65 20 43 20 63 6f 6d 70 69 6c 65 72 20 |free C compiler | 00002290 77 69 74 68 20 6c 69 62 72 61 72 69 65 73 20 69 |with libraries i| 000022a0 73 20 61 6c 6d 6f 73 74 0a 74 6f 6f 20 67 6f 6f |s almost.too goo| 000022b0 64 20 74 6f 20 62 65 6c 69 65 76 65 2e 0a 0a 41 |d to believe...A| 000022c0 6c 73 6f 2c 20 6d 79 20 44 61 64 2c 20 42 72 69 |lso, my Dad, Bri| 000022d0 61 6e 20 57 69 6e 64 73 6f 72 2c 20 77 68 6f 20 |an Windsor, who | 000022e0 77 72 6f 74 65 20 74 68 65 20 6f 72 69 67 69 6e |wrote the origin| 000022f0 61 6c 20 70 72 6f 67 72 61 6d 73 20 61 62 6f 75 |al programs abou| 00002300 74 20 74 65 6e 20 79 65 61 72 73 0a 61 67 6f 2e |t ten years.ago.| 00002310 0a 0a 0a 49 20 68 6f 70 65 20 49 20 68 61 76 65 |...I hope I have| 00002320 20 77 72 69 74 74 65 6e 20 74 68 65 20 70 72 6f | written the pro| 00002330 67 72 61 6d 20 73 6f 20 74 68 61 74 20 69 74 20 |gram so that it | 00002340 77 6f 6e 27 74 20 63 72 61 73 68 2c 20 6e 6f 20 |won't crash, no | 00002350 6d 61 74 74 65 72 20 77 68 61 74 20 79 6f 75 0a |matter what you.| 00002360 64 6f 20 74 6f 20 69 74 2c 20 62 75 74 20 69 66 |do to it, but if| 00002370 20 69 74 20 64 6f 65 73 20 70 6c 65 61 73 65 20 | it does please | 00002380 6c 65 74 20 6d 65 20 6b 6e 6f 77 20 68 6f 77 20 |let me know how | 00002390 61 6e 64 20 28 70 72 65 66 65 72 61 62 6c 79 29 |and (preferably)| 000023a0 20 77 68 79 2e 20 49 74 20 68 61 73 0a 62 65 65 | why. It has.bee| 000023b0 6e 20 74 65 73 74 65 64 20 6f 6e 20 61 20 52 69 |n tested on a Ri| 000023c0 73 63 20 50 43 20 28 4f 53 20 33 2e 36 20 26 20 |sc PC (OS 3.6 & | 000023d0 33 2e 37 29 20 77 69 74 68 20 62 6f 74 68 20 61 |3.7) with both a| 000023e0 20 53 74 72 6f 6e 67 41 52 4d 20 61 6e 64 20 37 | StrongARM and 7| 000023f0 31 30 20 61 6e 64 20 61 6e 0a 41 33 31 30 20 28 |10 and an.A310 (| 00002400 4f 53 20 33 2e 31 29 2e 0a 0a |OS 3.1)...| 0000240a
.