Home » Archimedes archive » Acorn User » AU 1995-03.adf » !StarInfo_StarInfo » Harvey/!Chaosymm/!Help

Harvey/!Chaosymm/!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 1995-03.adf » !StarInfo_StarInfo
Filename: Harvey/!Chaosymm/!Help
Read OK:
File size: 0C85 bytes
Load address: 0000
Exec address: 0000
File contents
!Chaosymm    � 1994 James Harvey 

This file last updated on 24/10/94


This program draws chaotic symmetric icons and fractals. Given a series of values for various constants, it draws repeated iterations of a point. 


For the icons, the screen is representing an Argand diagram of the complex plane. The iterations are as follows :

               _         n          n-1
 z' = (a + b.z.z + c.Re(z )).z + d.z    + e.zi
 
 
The fractals show the screen as an x-y plane. The iterations are repeated transformations : 

(x',y') = (x,y)( a11, a12 ) + (b1)    of a symmetry group either D(n) or Z(n)
               ( a21, a22 )   (b2)
               

Upon loading and clicking on the icon bar icon, a window appears in the screen. 
  To start with, you can load some of the example patterns from the disc. Drag the FracDef files to the main window, and the disc should indicate activity. Once you have done this, you can press the icon labelled "Plot the fractal" and the screen should change to black and start plotting points. Once the fractal has progressed sufficiently on screen you can press SPACE and the screen will revert back to the desktop. You can now bring up a menu to save the sprite with a standard RISC OS save window. 
  Once you have done this, and are happy with the operation of the program, then you can start experimenting with the parameters. Press "View the variables" to bring up another window into which you can see the parameters for the current fractal displayed. You can now alter these, by inputting new variables into the writable icons. When you want to redisplay the fractal, press "Test the fractal", which will iterate the fractal a few times and check that it remains convergent, and also auto-scale it (if you want your own scale input a new value in the main window). You can then calculate the fractal. To show this in a window in a desktop (non-multi-tasking, so only after it has finished), click on the first menu item (not into the submenu). The submenu is for changing the size of the sprite.
  
I wrote this program after reading "Symmetry and Chaos", which is very interesting if you are into that kind of thing. It is expandable, so if anyone knows of any more iterative functions, then write to me at the address below. 

My address is :
  James Harvey,
    1, Woodlands Drive,
      Harrogate,
        N. Yorks,
          HG2 7AT
   Please write if you like the program, enclosing hellos, comments, bug reports, money (I wish!), ideas for new applications, PD software etc. I cannot guarantee replies because I have exams. this winter but I will bear any comments in mind for future versions or programs. I am willing to swap PD software (especially Trackers) - I am trying to build up a decent collection, so if anyone wants to swap some software then please write. Also if anyone has any hints or tips that might be useful to other people then please write and I will compile them all and hopefully release them all on one disc. Also if anyone has any manuals that they don't want then please send them to a poor impoverished young programmer (yours truly) who can't afford to shell out �100 for new ones.
 
Thanks for reading.

JRH '94 
   

         
00000000  21 43 68 61 6f 73 79 6d  6d 20 20 20 20 a9 20 31  |!Chaosymm    . 1|
00000010  39 39 34 20 4a 61 6d 65  73 20 48 61 72 76 65 79  |994 James Harvey|
00000020  20 0a 0a 54 68 69 73 20  66 69 6c 65 20 6c 61 73  | ..This file las|
00000030  74 20 75 70 64 61 74 65  64 20 6f 6e 20 32 34 2f  |t updated on 24/|
00000040  31 30 2f 39 34 0a 0a 0a  54 68 69 73 20 70 72 6f  |10/94...This pro|
00000050  67 72 61 6d 20 64 72 61  77 73 20 63 68 61 6f 74  |gram draws chaot|
00000060  69 63 20 73 79 6d 6d 65  74 72 69 63 20 69 63 6f  |ic symmetric ico|
00000070  6e 73 20 61 6e 64 20 66  72 61 63 74 61 6c 73 2e  |ns and fractals.|
00000080  20 47 69 76 65 6e 20 61  20 73 65 72 69 65 73 20  | Given a series |
00000090  6f 66 20 76 61 6c 75 65  73 20 66 6f 72 20 76 61  |of values for va|
000000a0  72 69 6f 75 73 20 63 6f  6e 73 74 61 6e 74 73 2c  |rious constants,|
000000b0  20 69 74 20 64 72 61 77  73 20 72 65 70 65 61 74  | it draws repeat|
000000c0  65 64 20 69 74 65 72 61  74 69 6f 6e 73 20 6f 66  |ed iterations of|
000000d0  20 61 20 70 6f 69 6e 74  2e 20 0a 0a 0a 46 6f 72  | a point. ...For|
000000e0  20 74 68 65 20 69 63 6f  6e 73 2c 20 74 68 65 20  | the icons, the |
000000f0  73 63 72 65 65 6e 20 69  73 20 72 65 70 72 65 73  |screen is repres|
00000100  65 6e 74 69 6e 67 20 61  6e 20 41 72 67 61 6e 64  |enting an Argand|
00000110  20 64 69 61 67 72 61 6d  20 6f 66 20 74 68 65 20  | diagram of the |
00000120  63 6f 6d 70 6c 65 78 20  70 6c 61 6e 65 2e 20 54  |complex plane. T|
00000130  68 65 20 69 74 65 72 61  74 69 6f 6e 73 20 61 72  |he iterations ar|
00000140  65 20 61 73 20 66 6f 6c  6c 6f 77 73 20 3a 0a 0a  |e as follows :..|
00000150  20 20 20 20 20 20 20 20  20 20 20 20 20 20 20 5f  |               _|
00000160  20 20 20 20 20 20 20 20  20 6e 20 20 20 20 20 20  |         n      |
00000170  20 20 20 20 6e 2d 31 0a  20 7a 27 20 3d 20 28 61  |    n-1. z' = (a|
00000180  20 2b 20 62 2e 7a 2e 7a  20 2b 20 63 2e 52 65 28  | + b.z.z + c.Re(|
00000190  7a 20 29 29 2e 7a 20 2b  20 64 2e 7a 20 20 20 20  |z )).z + d.z    |
000001a0  2b 20 65 2e 7a 69 0a 20  0a 20 0a 54 68 65 20 66  |+ e.zi. . .The f|
000001b0  72 61 63 74 61 6c 73 20  73 68 6f 77 20 74 68 65  |ractals show the|
000001c0  20 73 63 72 65 65 6e 20  61 73 20 61 6e 20 78 2d  | screen as an x-|
000001d0  79 20 70 6c 61 6e 65 2e  20 54 68 65 20 69 74 65  |y plane. The ite|
000001e0  72 61 74 69 6f 6e 73 20  61 72 65 20 72 65 70 65  |rations are repe|
000001f0  61 74 65 64 20 74 72 61  6e 73 66 6f 72 6d 61 74  |ated transformat|
00000200  69 6f 6e 73 20 3a 20 0a  0a 28 78 27 2c 79 27 29  |ions : ..(x',y')|
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00000220  31 32 20 29 20 2b 20 28  62 31 29 20 20 20 20 6f  |12 ) + (b1)    o|
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00000300  66 20 74 68 65 20 65 78  61 6d 70 6c 65 20 70 61  |f the example pa|
00000310  74 74 65 72 6e 73 20 66  72 6f 6d 20 74 68 65 20  |tterns from the |
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00000360  6f 75 6c 64 20 69 6e 64  69 63 61 74 65 20 61 63  |ould indicate ac|
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000003a0  68 65 20 69 63 6f 6e 20  6c 61 62 65 6c 6c 65 64  |he icon labelled|
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000003d0  65 6e 20 73 68 6f 75 6c  64 20 63 68 61 6e 67 65  |en should change|
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00000440  63 61 6e 20 70 72 65 73  73 20 53 50 41 43 45 20  |can press SPACE |
00000450  61 6e 64 20 74 68 65 20  73 63 72 65 65 6e 20 77  |and the screen w|
00000460  69 6c 6c 20 72 65 76 65  72 74 20 62 61 63 6b 20  |ill revert back |
00000470  74 6f 20 74 68 65 20 64  65 73 6b 74 6f 70 2e 20  |to the desktop. |
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00000570  22 20 74 6f 20 62 72 69  6e 67 20 75 70 20 61 6e  |" to bring up an|
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000007f0  70 72 69 74 65 2e 0a 20  20 0a 49 20 77 72 6f 74  |prite..  .I wrot|
00000800  65 20 74 68 69 73 20 70  72 6f 67 72 61 6d 20 61  |e this program a|
00000810  66 74 65 72 20 72 65 61  64 69 6e 67 20 22 53 79  |fter reading "Sy|
00000820  6d 6d 65 74 72 79 20 61  6e 64 20 43 68 61 6f 73  |mmetry and Chaos|
00000830  22 2c 20 77 68 69 63 68  20 69 73 20 76 65 72 79  |", which is very|
00000840  20 69 6e 74 65 72 65 73  74 69 6e 67 20 69 66 20  | interesting if |
00000850  79 6f 75 20 61 72 65 20  69 6e 74 6f 20 74 68 61  |you are into tha|
00000860  74 20 6b 69 6e 64 20 6f  66 20 74 68 69 6e 67 2e  |t kind of thing.|
00000870  20 49 74 20 69 73 20 65  78 70 61 6e 64 61 62 6c  | It is expandabl|
00000880  65 2c 20 73 6f 20 69 66  20 61 6e 79 6f 6e 65 20  |e, so if anyone |
00000890  6b 6e 6f 77 73 20 6f 66  20 61 6e 79 20 6d 6f 72  |knows of any mor|
000008a0  65 20 69 74 65 72 61 74  69 76 65 20 66 75 6e 63  |e iterative func|
000008b0  74 69 6f 6e 73 2c 20 74  68 65 6e 20 77 72 69 74  |tions, then writ|
000008c0  65 20 74 6f 20 6d 65 20  61 74 20 74 68 65 20 61  |e to me at the a|
000008d0  64 64 72 65 73 73 20 62  65 6c 6f 77 2e 20 0a 0a  |ddress below. ..|
000008e0  4d 79 20 61 64 64 72 65  73 73 20 69 73 20 3a 0a  |My address is :.|
000008f0  20 20 4a 61 6d 65 73 20  48 61 72 76 65 79 2c 0a  |  James Harvey,.|
00000900  20 20 20 20 31 2c 20 57  6f 6f 64 6c 61 6e 64 73  |    1, Woodlands|
00000910  20 44 72 69 76 65 2c 0a  20 20 20 20 20 20 48 61  | Drive,.      Ha|
00000920  72 72 6f 67 61 74 65 2c  0a 20 20 20 20 20 20 20  |rrogate,.       |
00000930  20 4e 2e 20 59 6f 72 6b  73 2c 0a 20 20 20 20 20  | N. Yorks,.     |
00000940  20 20 20 20 20 48 47 32  20 37 41 54 0a 20 20 20  |     HG2 7AT.   |
00000950  50 6c 65 61 73 65 20 77  72 69 74 65 20 69 66 20  |Please write if |
00000960  79 6f 75 20 6c 69 6b 65  20 74 68 65 20 70 72 6f  |you like the pro|
00000970  67 72 61 6d 2c 20 65 6e  63 6c 6f 73 69 6e 67 20  |gram, enclosing |
00000980  68 65 6c 6c 6f 73 2c 20  63 6f 6d 6d 65 6e 74 73  |hellos, comments|
00000990  2c 20 62 75 67 20 72 65  70 6f 72 74 73 2c 20 6d  |, bug reports, m|
000009a0  6f 6e 65 79 20 28 49 20  77 69 73 68 21 29 2c 20  |oney (I wish!), |
000009b0  69 64 65 61 73 20 66 6f  72 20 6e 65 77 20 61 70  |ideas for new ap|
000009c0  70 6c 69 63 61 74 69 6f  6e 73 2c 20 50 44 20 73  |plications, PD s|
000009d0  6f 66 74 77 61 72 65 20  65 74 63 2e 20 49 20 63  |oftware etc. I c|
000009e0  61 6e 6e 6f 74 20 67 75  61 72 61 6e 74 65 65 20  |annot guarantee |
000009f0  72 65 70 6c 69 65 73 20  62 65 63 61 75 73 65 20  |replies because |
00000a00  49 20 68 61 76 65 20 65  78 61 6d 73 2e 20 74 68  |I have exams. th|
00000a10  69 73 20 77 69 6e 74 65  72 20 62 75 74 20 49 20  |is winter but I |
00000a20  77 69 6c 6c 20 62 65 61  72 20 61 6e 79 20 63 6f  |will bear any co|
00000a30  6d 6d 65 6e 74 73 20 69  6e 20 6d 69 6e 64 20 66  |mments in mind f|
00000a40  6f 72 20 66 75 74 75 72  65 20 76 65 72 73 69 6f  |or future versio|
00000a50  6e 73 20 6f 72 20 70 72  6f 67 72 61 6d 73 2e 20  |ns or programs. |
00000a60  49 20 61 6d 20 77 69 6c  6c 69 6e 67 20 74 6f 20  |I am willing to |
00000a70  73 77 61 70 20 50 44 20  73 6f 66 74 77 61 72 65  |swap PD software|
00000a80  20 28 65 73 70 65 63 69  61 6c 6c 79 20 54 72 61  | (especially Tra|
00000a90  63 6b 65 72 73 29 20 2d  20 49 20 61 6d 20 74 72  |ckers) - I am tr|
00000aa0  79 69 6e 67 20 74 6f 20  62 75 69 6c 64 20 75 70  |ying to build up|
00000ab0  20 61 20 64 65 63 65 6e  74 20 63 6f 6c 6c 65 63  | a decent collec|
00000ac0  74 69 6f 6e 2c 20 73 6f  20 69 66 20 61 6e 79 6f  |tion, so if anyo|
00000ad0  6e 65 20 77 61 6e 74 73  20 74 6f 20 73 77 61 70  |ne wants to swap|
00000ae0  20 73 6f 6d 65 20 73 6f  66 74 77 61 72 65 20 74  | some software t|
00000af0  68 65 6e 20 70 6c 65 61  73 65 20 77 72 69 74 65  |hen please write|
00000b00  2e 20 41 6c 73 6f 20 69  66 20 61 6e 79 6f 6e 65  |. Also if anyone|
00000b10  20 68 61 73 20 61 6e 79  20 68 69 6e 74 73 20 6f  | has any hints o|
00000b20  72 20 74 69 70 73 20 74  68 61 74 20 6d 69 67 68  |r tips that migh|
00000b30  74 20 62 65 20 75 73 65  66 75 6c 20 74 6f 20 6f  |t be useful to o|
00000b40  74 68 65 72 20 70 65 6f  70 6c 65 20 74 68 65 6e  |ther people then|
00000b50  20 70 6c 65 61 73 65 20  77 72 69 74 65 20 61 6e  | please write an|
00000b60  64 20 49 20 77 69 6c 6c  20 63 6f 6d 70 69 6c 65  |d I will compile|
00000b70  20 74 68 65 6d 20 61 6c  6c 20 61 6e 64 20 68 6f  | them all and ho|
00000b80  70 65 66 75 6c 6c 79 20  72 65 6c 65 61 73 65 20  |pefully release |
00000b90  74 68 65 6d 20 61 6c 6c  20 6f 6e 20 6f 6e 65 20  |them all on one |
00000ba0  64 69 73 63 2e 20 41 6c  73 6f 20 69 66 20 61 6e  |disc. Also if an|
00000bb0  79 6f 6e 65 20 68 61 73  20 61 6e 79 20 6d 61 6e  |yone has any man|
00000bc0  75 61 6c 73 20 74 68 61  74 20 74 68 65 79 20 64  |uals that they d|
00000bd0  6f 6e 27 74 20 77 61 6e  74 20 74 68 65 6e 20 70  |on't want then p|
00000be0  6c 65 61 73 65 20 73 65  6e 64 20 74 68 65 6d 20  |lease send them |
00000bf0  74 6f 20 61 20 70 6f 6f  72 20 69 6d 70 6f 76 65  |to a poor impove|
00000c00  72 69 73 68 65 64 20 79  6f 75 6e 67 20 70 72 6f  |rished young pro|
00000c10  67 72 61 6d 6d 65 72 20  28 79 6f 75 72 73 20 74  |grammer (yours t|
00000c20  72 75 6c 79 29 20 77 68  6f 20 63 61 6e 27 74 20  |ruly) who can't |
00000c30  61 66 66 6f 72 64 20 74  6f 20 73 68 65 6c 6c 20  |afford to shell |
00000c40  6f 75 74 20 a3 31 30 30  20 66 6f 72 20 6e 65 77  |out .100 for new|
00000c50  20 6f 6e 65 73 2e 0a 20  0a 54 68 61 6e 6b 73 20  | ones.. .Thanks |
00000c60  66 6f 72 20 72 65 61 64  69 6e 67 2e 0a 0a 4a 52  |for reading...JR|
00000c70  48 20 27 39 34 20 0a 20  20 20 0a 0a 20 20 20 20  |H '94 .   ..    |
00000c80  20 20 20 20 20                                    |     |
00000c85