05/Mar/2008
Postscript Rocks Spirograph
I was fascinated by a particular pattern from the Spirograph book, which I had a Spirograph set when I was a child. I still remember the ring and wheel dimensions today (being 105 / 52) The pattern troubled me, as I really desired to draw it but never mastered the pen control needed.
Later I found computer simulators of spirograph sets. Sin and Cosine to calculate the big arm and then a smaller arm on top of that. However none of the Programs would produce the 105/52 pattern as I remembered. I wrote my own Spirograph in AMOS basic, and managed to get a more correct result.
Today my language of choice for line art graphics is Postscript. So you may've seen, that I have a postscript spirograph program floating around this site.
Cleaning out my cupboards the other day, I happened to come across the old spirograph booklet showing patterns and procedure to produce them. So I cleaned up my Postscript code, made some refinements so that my postscript subroutines closely matched the language used in the book and ended up with something that closely resembles the original.
The language, if you aren't familiar with postscript, is reverse polish, where the arguments to a function come first, then the function name. The function simply pulls as many arguments off the stack as required. The % symbol is used for comments.
The code for an example pattern would look like:
96 ring % set the ring size to 96 63 wheel % set the wheel size to 63 1 270 paint % in hole 1, using colour purple (270) paint the graph 3 210 paint % in hole 3, using colour blue (210) paint the graph 5 45 paint % in hole 5, using colour orange (45) paint the graph 7 0 paint % in hole 7, using colour red (0) paint the graph
of course I can use standard postscript "for" loops to do very repeative patterns
105 ring % set the ring to 105
30 wheel % set the wheel to 30
1 1 5 { 270 paint } for % paint, in colour purple, holes 1 to 5
45 wheel % set the wheel to 45
1 1 5 { 45 paint } for % paint, in colour orange, holes 1 to 5
60 wheel % set the wheel to 60
1 1 5 { 0 paint } for % paint, in colour red, holes 1 to 5
Using the postscript translate command I can simulate patterns that move the ring between two rack pieces.
96 ring % set the ring to 96
48 wheel % set the wheel to 48
1 1 17 { 0 paint -10 0 translate } for % paint, in colour red, holes 1 to 17,
% moving 10 points down each time
Currently I do not have the ability to;
- draw on the outside of rings.
- draw on the outside of racks.
- move only top or bottom ring teeth between two racks.
I hope you like the patterns.