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StarInfo/Lurcock/!SpiroLat/!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 » Recent acquisitions » Acorn ADFS disks » adfs_AcornUser_199609.adf » Regulars
Filename: StarInfo/Lurcock/!SpiroLat/!Help
Read OK:
File size: 0C60 bytes
Load address: 0000
Exec address: 0000
File contents
SpiroLateral 1.01               � 1996 Pontus Lurcock           10.04.1996
============================================================================


What is a Spirolateral?
-----------------------

A Spirolateral might bear a passing resemblance to a Spirograph picture at
first but in fact it's more like a subset of Logo. Basically the procedure
for drawing one is:

  Repeat
    For Length = 1 to n
      Go forward (drawing a line) for Length units
      Turn through A degrees, either to the left or to the right
    Next
  Until you reach your starting point again

A is from 0 to 180 (exclusive), and the sequence of left and right turns is
predetermined by the user.


How to use the program
----------------------

!SpiroLat requires Acorn's toolbox modules, and the DrawFile module for
redrawing. Interactive help is supported.

The things you can change in the toolbar are: the order of the spirolateral
(n in the pseudocode above; the maximum line length), the angle of the turns,
and the direction of each turn. The directions are specified using a sequence
of letters: "L", "l" or "<" for left and "R", "r" or ">" for right.

Some spirolaterals will not close; they never return to their starting point,
preferring to scoot off to infinity (all even-ordered spirolaterals with an
equal number of left and right turns do this). When given an infinite
spirolateral, !SpiroLat will draw one iteration only, in red.

Clicking Menu will bring up a save box from which you can save to file or to
another application.

The Scale factor only affects the saved drawfile; the file displayed by
!SpiroLat is always scaled to fill the window.

If the number of letters in the 'Turns' icon is less than the order, the
unspecified turns will default to right.

A huge variety of different spirolaterals is possible, including some
disgustingly large ones which take ages to redraw and don't look very good.
In general, the more common factors a spirolateral's angle has with 360, the
more simple it will be. This means, for example,  that angles which are prime
numbers will tend to produce larger, denser patterns.

Once you have produced a nice-looking spirolateral, it can be further
beautified by some judicious tinkering in !Draw. Most spirolaterals look good
if you change the line colour to none, change the fill colour to something
pleasant, and make sure the winding rule is even-odd. A few examples can be
found in the file 'Examples' within the !SpiroLat directory - though note
that they represent only a tiny sample of what is possible :-)


Acknowledgements and Stuff
--------------------------

I came across spirolaterals in a book by Martin Gardner. I think it was
called 'Knotted Doughnuts' - it was a collection of Gardner's Scientific
American articles... I'd also like to acknowledge the person who invented the
cunning algorithm for finding the length of a spirolateral, but I can't
remember his name :-(

Thanks also to Jonathan Coxhead for the excellent OSLib, and of course
everyone on Arcade...


My address, for bug reports, comments, and all the usual stuff:

        pontus@arcade.demon.co.uk
or      9 Monmouth Road, Oxford OX1 4TD

00000000  53 70 69 72 6f 4c 61 74  65 72 61 6c 20 31 2e 30  |SpiroLateral 1.0|
00000010  31 20 20 20 20 20 20 20  20 20 20 20 20 20 20 20  |1               |
00000020  a9 20 31 39 39 36 20 50  6f 6e 74 75 73 20 4c 75  |. 1996 Pontus Lu|
00000030  72 63 6f 63 6b 20 20 20  20 20 20 20 20 20 20 20  |rcock           |
00000040  31 30 2e 30 34 2e 31 39  39 36 0a 3d 3d 3d 3d 3d  |10.04.1996.=====|
00000050  3d 3d 3d 3d 3d 3d 3d 3d  3d 3d 3d 3d 3d 3d 3d 3d  |================|
*
00000090  3d 3d 3d 3d 3d 3d 3d 0a  0a 0a 57 68 61 74 20 69  |=======...What i|
000000a0  73 20 61 20 53 70 69 72  6f 6c 61 74 65 72 61 6c  |s a Spirolateral|
000000b0  3f 0a 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |?.--------------|
000000c0  2d 2d 2d 2d 2d 2d 2d 2d  2d 0a 0a 41 20 53 70 69  |---------..A Spi|
000000d0  72 6f 6c 61 74 65 72 61  6c 20 6d 69 67 68 74 20  |rolateral might |
000000e0  62 65 61 72 20 61 20 70  61 73 73 69 6e 67 20 72  |bear a passing r|
000000f0  65 73 65 6d 62 6c 61 6e  63 65 20 74 6f 20 61 20  |esemblance to a |
00000100  53 70 69 72 6f 67 72 61  70 68 20 70 69 63 74 75  |Spirograph pictu|
00000110  72 65 20 61 74 0a 66 69  72 73 74 20 62 75 74 20  |re at.first but |
00000120  69 6e 20 66 61 63 74 20  69 74 27 73 20 6d 6f 72  |in fact it's mor|
00000130  65 20 6c 69 6b 65 20 61  20 73 75 62 73 65 74 20  |e like a subset |
00000140  6f 66 20 4c 6f 67 6f 2e  20 42 61 73 69 63 61 6c  |of Logo. Basical|
00000150  6c 79 20 74 68 65 20 70  72 6f 63 65 64 75 72 65  |ly the procedure|
00000160  0a 66 6f 72 20 64 72 61  77 69 6e 67 20 6f 6e 65  |.for drawing one|
00000170  20 69 73 3a 0a 0a 20 20  52 65 70 65 61 74 0a 20  | is:..  Repeat. |
00000180  20 20 20 46 6f 72 20 4c  65 6e 67 74 68 20 3d 20  |   For Length = |
00000190  31 20 74 6f 20 6e 0a 20  20 20 20 20 20 47 6f 20  |1 to n.      Go |
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000001c0  67 74 68 20 75 6e 69 74  73 0a 20 20 20 20 20 20  |gth units.      |
000001d0  54 75 72 6e 20 74 68 72  6f 75 67 68 20 41 20 64  |Turn through A d|
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00000200  20 74 68 65 20 72 69 67  68 74 0a 20 20 20 20 4e  | the right.    N|
00000210  65 78 74 0a 20 20 55 6e  74 69 6c 20 79 6f 75 20  |ext.  Until you |
00000220  72 65 61 63 68 20 79 6f  75 72 20 73 74 61 72 74  |reach your start|
00000230  69 6e 67 20 70 6f 69 6e  74 20 61 67 61 69 6e 0a  |ing point again.|
00000240  0a 41 20 69 73 20 66 72  6f 6d 20 30 20 74 6f 20  |.A is from 0 to |
00000250  31 38 30 20 28 65 78 63  6c 75 73 69 76 65 29 2c  |180 (exclusive),|
00000260  20 61 6e 64 20 74 68 65  20 73 65 71 75 65 6e 63  | and the sequenc|
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000002c0  0a 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |.---------------|
000002d0  2d 2d 2d 2d 2d 2d 2d 0a  0a 21 53 70 69 72 6f 4c  |-------..!SpiroL|
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00000560  74 65 72 61 6c 2c 20 21  53 70 69 72 6f 4c 61 74  |teral, !SpiroLat|
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000005e0  72 20 74 6f 0a 61 6e 6f  74 68 65 72 20 61 70 70  |r to.another app|
000005f0  6c 69 63 61 74 69 6f 6e  2e 0a 0a 54 68 65 20 53  |lication...The S|
00000600  63 61 6c 65 20 66 61 63  74 6f 72 20 6f 6e 6c 79  |cale factor only|
00000610  20 61 66 66 65 63 74 73  20 74 68 65 20 73 61 76  | affects the sav|
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00000660  20 66 69 6c 6c 20 74 68  65 20 77 69 6e 64 6f 77  | fill the window|
00000670  2e 0a 0a 49 66 20 74 68  65 20 6e 75 6d 62 65 72  |...If the number|
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000007e0  73 20 6d 65 61 6e 73 2c  20 66 6f 72 20 65 78 61  |s means, for exa|
000007f0  6d 70 6c 65 2c 20 20 74  68 61 74 20 61 6e 67 6c  |mple,  that angl|
00000800  65 73 20 77 68 69 63 68  20 61 72 65 20 70 72 69  |es which are pri|
00000810  6d 65 0a 6e 75 6d 62 65  72 73 20 77 69 6c 6c 20  |me.numbers will |
00000820  74 65 6e 64 20 74 6f 20  70 72 6f 64 75 63 65 20  |tend to produce |
00000830  6c 61 72 67 65 72 2c 20  64 65 6e 73 65 72 20 70  |larger, denser p|
00000840  61 74 74 65 72 6e 73 2e  0a 0a 4f 6e 63 65 20 79  |atterns...Once y|
00000850  6f 75 20 68 61 76 65 20  70 72 6f 64 75 63 65 64  |ou have produced|
00000860  20 61 20 6e 69 63 65 2d  6c 6f 6f 6b 69 6e 67 20  | a nice-looking |
00000870  73 70 69 72 6f 6c 61 74  65 72 61 6c 2c 20 69 74  |spirolateral, it|
00000880  20 63 61 6e 20 62 65 20  66 75 72 74 68 65 72 0a  | can be further.|
00000890  62 65 61 75 74 69 66 69  65 64 20 62 79 20 73 6f  |beautified by so|
000008a0  6d 65 20 6a 75 64 69 63  69 6f 75 73 20 74 69 6e  |me judicious tin|
000008b0  6b 65 72 69 6e 67 20 69  6e 20 21 44 72 61 77 2e  |kering in !Draw.|
000008c0  20 4d 6f 73 74 20 73 70  69 72 6f 6c 61 74 65 72  | Most spirolater|
000008d0  61 6c 73 20 6c 6f 6f 6b  20 67 6f 6f 64 0a 69 66  |als look good.if|
000008e0  20 79 6f 75 20 63 68 61  6e 67 65 20 74 68 65 20  | you change the |
000008f0  6c 69 6e 65 20 63 6f 6c  6f 75 72 20 74 6f 20 6e  |line colour to n|
00000900  6f 6e 65 2c 20 63 68 61  6e 67 65 20 74 68 65 20  |one, change the |
00000910  66 69 6c 6c 20 63 6f 6c  6f 75 72 20 74 6f 20 73  |fill colour to s|
00000920  6f 6d 65 74 68 69 6e 67  0a 70 6c 65 61 73 61 6e  |omething.pleasan|
00000930  74 2c 20 61 6e 64 20 6d  61 6b 65 20 73 75 72 65  |t, and make sure|
00000940  20 74 68 65 20 77 69 6e  64 69 6e 67 20 72 75 6c  | the winding rul|
00000950  65 20 69 73 20 65 76 65  6e 2d 6f 64 64 2e 20 41  |e is even-odd. A|
00000960  20 66 65 77 20 65 78 61  6d 70 6c 65 73 20 63 61  | few examples ca|
00000970  6e 20 62 65 0a 66 6f 75  6e 64 20 69 6e 20 74 68  |n be.found in th|
00000980  65 20 66 69 6c 65 20 27  45 78 61 6d 70 6c 65 73  |e file 'Examples|
00000990  27 20 77 69 74 68 69 6e  20 74 68 65 20 21 53 70  |' within the !Sp|
000009a0  69 72 6f 4c 61 74 20 64  69 72 65 63 74 6f 72 79  |iroLat directory|
000009b0  20 2d 20 74 68 6f 75 67  68 20 6e 6f 74 65 0a 74  | - though note.t|
000009c0  68 61 74 20 74 68 65 79  20 72 65 70 72 65 73 65  |hat they represe|
000009d0  6e 74 20 6f 6e 6c 79 20  61 20 74 69 6e 79 20 73  |nt only a tiny s|
000009e0  61 6d 70 6c 65 20 6f 66  20 77 68 61 74 20 69 73  |ample of what is|
000009f0  20 70 6f 73 73 69 62 6c  65 20 3a 2d 29 0a 0a 0a  | possible :-)...|
00000a00  41 63 6b 6e 6f 77 6c 65  64 67 65 6d 65 6e 74 73  |Acknowledgements|
00000a10  20 61 6e 64 20 53 74 75  66 66 0a 2d 2d 2d 2d 2d  | and Stuff.-----|
00000a20  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
00000a30  2d 2d 2d 2d 2d 0a 0a 49  20 63 61 6d 65 20 61 63  |-----..I came ac|
00000a40  72 6f 73 73 20 73 70 69  72 6f 6c 61 74 65 72 61  |ross spirolatera|
00000a50  6c 73 20 69 6e 20 61 20  62 6f 6f 6b 20 62 79 20  |ls in a book by |
00000a60  4d 61 72 74 69 6e 20 47  61 72 64 6e 65 72 2e 20  |Martin Gardner. |
00000a70  49 20 74 68 69 6e 6b 20  69 74 20 77 61 73 0a 63  |I think it was.c|
00000a80  61 6c 6c 65 64 20 27 4b  6e 6f 74 74 65 64 20 44  |alled 'Knotted D|
00000a90  6f 75 67 68 6e 75 74 73  27 20 2d 20 69 74 20 77  |oughnuts' - it w|
00000aa0  61 73 20 61 20 63 6f 6c  6c 65 63 74 69 6f 6e 20  |as a collection |
00000ab0  6f 66 20 47 61 72 64 6e  65 72 27 73 20 53 63 69  |of Gardner's Sci|
00000ac0  65 6e 74 69 66 69 63 0a  41 6d 65 72 69 63 61 6e  |entific.American|
00000ad0  20 61 72 74 69 63 6c 65  73 2e 2e 2e 20 49 27 64  | articles... I'd|
00000ae0  20 61 6c 73 6f 20 6c 69  6b 65 20 74 6f 20 61 63  | also like to ac|
00000af0  6b 6e 6f 77 6c 65 64 67  65 20 74 68 65 20 70 65  |knowledge the pe|
00000b00  72 73 6f 6e 20 77 68 6f  20 69 6e 76 65 6e 74 65  |rson who invente|
00000b10  64 20 74 68 65 0a 63 75  6e 6e 69 6e 67 20 61 6c  |d the.cunning al|
00000b20  67 6f 72 69 74 68 6d 20  66 6f 72 20 66 69 6e 64  |gorithm for find|
00000b30  69 6e 67 20 74 68 65 20  6c 65 6e 67 74 68 20 6f  |ing the length o|
00000b40  66 20 61 20 73 70 69 72  6f 6c 61 74 65 72 61 6c  |f a spirolateral|
00000b50  2c 20 62 75 74 20 49 20  63 61 6e 27 74 0a 72 65  |, but I can't.re|
00000b60  6d 65 6d 62 65 72 20 68  69 73 20 6e 61 6d 65 20  |member his name |
00000b70  3a 2d 28 0a 0a 54 68 61  6e 6b 73 20 61 6c 73 6f  |:-(..Thanks also|
00000b80  20 74 6f 20 4a 6f 6e 61  74 68 61 6e 20 43 6f 78  | to Jonathan Cox|
00000b90  68 65 61 64 20 66 6f 72  20 74 68 65 20 65 78 63  |head for the exc|
00000ba0  65 6c 6c 65 6e 74 20 4f  53 4c 69 62 2c 20 61 6e  |ellent OSLib, an|
00000bb0  64 20 6f 66 20 63 6f 75  72 73 65 0a 65 76 65 72  |d of course.ever|
00000bc0  79 6f 6e 65 20 6f 6e 20  41 72 63 61 64 65 2e 2e  |yone on Arcade..|
00000bd0  2e 0a 0a 0a 4d 79 20 61  64 64 72 65 73 73 2c 20  |....My address, |
00000be0  66 6f 72 20 62 75 67 20  72 65 70 6f 72 74 73 2c  |for bug reports,|
00000bf0  20 63 6f 6d 6d 65 6e 74  73 2c 20 61 6e 64 20 61  | comments, and a|
00000c00  6c 6c 20 74 68 65 20 75  73 75 61 6c 20 73 74 75  |ll the usual stu|
00000c10  66 66 3a 0a 0a 20 20 20  20 20 20 20 20 70 6f 6e  |ff:..        pon|
00000c20  74 75 73 40 61 72 63 61  64 65 2e 64 65 6d 6f 6e  |tus@arcade.demon|
00000c30  2e 63 6f 2e 75 6b 0a 6f  72 20 20 20 20 20 20 39  |.co.uk.or      9|
00000c40  20 4d 6f 6e 6d 6f 75 74  68 20 52 6f 61 64 2c 20  | Monmouth Road, |
00000c50  4f 78 66 6f 72 64 20 4f  58 31 20 34 54 44 0a 0a  |Oxford OX1 4TD..|
00000c60