🚀 go-pugleaf

Hello, all.

Finals have begun, but in my graphics class we are finishing up a small
project.  We (meaning the three in my group) have written a rule-based
L-Sytems/fractal program for the SGIs.  We have it generating all the
standard curves (Sierpinsky, dragon, Hilbert) and also some plants of
different types.  Each curve or plant is described by a set of grammar
rules, which combine to generate a sequence of turtle commands.

This approach is very interesting, especially when you start getting into
the context-sensitive languages vs. the context-free.

The final example I was trying to develop was, ideally, a 3-D Hilbert
curve.  However, this has proved to be challenging.  What I want to ask
of you folks is, do you have a set of grammar rules that describe *any*
3-D curves?  I could generate a 3D plant quite easily, but I was thinking
a Hilbert curve would be great.

Thanks, any info is appreciated (whether posted or emailed).
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For those who don't know, the curves specified by a grammar follow the
basic setup:

Axiom:  <This is the initial string you start with>
Rules:  A -> BC...  <Each rule has this form, where 'A' is a symbol 
                     either in the axiom, or in generated strings which
                     is replaced by 'BC', a set of turtle commands or
                     other rule names>

Example:  Hilbert curve

Axiom: X                   [Hilbert curve is context-free]
Rules: X -> -YF+XFX+FY-
       Y -> +XF-YFY-FX+

The turtle commands are embedded in the above rules; they are:
  '-' turn left
  '+' turn right
  'F' forward, drawing a line segment
  '?' any other character is ignored.
 <There are many others for 3D control, position save/recall, etc>

Given a turtle's starting point and a direction, then you would iterate
the above rules to generate a string.

iteration   string
   0          X
   1          -YF+XFX+FY-
   2          -+XF-YFY-FX+F+-YF+XFX+FY-F-YF+XFX+FY-+F+XF-YFY-FX+-
   n          +-+-...... lots of gunk here by replacing X & Y ......-+-+

By scanning left to right through the above generated strings, you
draw out the Hilbert curve.

-Brent
-- 
+-------------------------+
| Brent Burton    N5VMG   |    
| bpb9204@tamsun.tamu.edu |  
+-------------------------+