"Janet" <par### [at] attnet> wrote:
> "PM 2Ring" <nomail@nomail> wrote:
> > Are those curves on the tiles derived from the Conway lines? If not they
> > sure look a lot look like Conway lines.
> >
> > With those colours it could be a stained glass wall as well as a floor.
>
> Stained Glass... that could be nice. I'd have to work on the leading. Thanks
> for the idea.
> I don't know what Conway lines are, but please enlighten me. The lines are a
> normal function:
> #declare phi=Phi-1;
> #declare Fc1 = Phi;
> #declare Fc2 = phi;
> #declare Func = function {
>          cos(x) * cos(z) + cos((sqrt(Fc1)*x-z)/Fc2) *
>          cos((x+sqrt(Fc1)*z)/Fc2) + cos((sqrt(Fc1)*x+z)/Fc2) *
>          cos((x-sqrt(Fc1)*z)/Fc2) }
>
> You can change Fc1 and Fc2 to get different patterns. I found this function
> here: http://www.interq.or.jp/blue/kawashu/gallery/unofficial.html

I'm not sure exactly what "PM2 Ring" meant by "Conway lines", but look at
the circles in the tiles on this page:

http://www2.spsu.edu/math/tile/aperiodic/penrose/penrose2.htm

The circles are usually used to make sure that the tiles are not put
together into rhombuses that just repeat across the plane like squares do.
I believe Conway added those circles as a simpler way of enforcing the rules
than what Penrose had done.

The other thing that comes to my mind (working on "lines" instead of
"Conway") is Ammon Bars.  To see them, take a look at the colored straight
lines running across all the tiles at:

http://www2.spsu.edu/math/tile/aperiodic/empires/ammanbars.htm

And now I have a question too.  The colors are wonderful, sometimes paired
up across an edge, and sometimes not.  How did you select them and apply
them to the triangles?

Jon

P.S. I have a set of macros that do Penrose Rhombs, and another that do
Penrose Kites and Darts (more like your image).  I have found them easier
to work with and more flexible than any other ones I've seen posted, but
I'm probably rather biased.  The others were helpful with a few hints and a
push to actually do it, though.  If you (or anyone else) is interested, I'll
finish cleaning them up and post them.

Post a reply to this message