After looking at my other Penrose macros, and always being annoyed that 
I needed an array of size [xtiles][ztiles][recursion_depth] to eliminate 
all the duplicates that the standard rules generate, I figured out how 
to...  (A little google here and there helped too, but surprisingly 
little, everybody just expands the tiles the way I used to.)

Split each kite, dart, or rhomb into a pair of triangles.  The new 
triangles do not overlap each other when expanded from an old set, so 
that huge array can disappear. As the new sets of tiles are generated, 
the new edges will now leave the border of the old set by 1/2 a tile or 
less.  I think the context parameters will allow the old semi-fractal 
tile perimeters to be generated, but I haven't tried it yet.

For these test images, I stripped off all the curvy tile decorations of 
the last images, but did put that new context parameter to use.  The 
first image is just two rhombs, a kite, and a dart expanded a few times.
The edges of each triangle are shown, but each rhomb, kite, or dart is a 
single color.

The second image is a cartwheel pattern.  The dark spokes will travel 
off to the far edges of the plane.  Each spoke can be reflected, and 10 
spokes make for 1024 combinations, but only 56 different ones, the rest 
are reflections or rotations of those 56.  (The light colored ring in 
the center determines all this, and is called a decagon.) This 
particular cartwheel pattern is the only one that can be properly filled 
at the center.  Other patterns to to get exact 5 way symmetry from the 
central point out are the sun and star, inflated and even number of 
times to what ever level you desire.

The third image I just did in the last few hours, and wanted to get the 
pentagon tiling that has been seen around here on a regular basis.  It 
might be interesting to put curves all over it, but I resisted to keep 
the demonstration code shorter and simpler.

I'll put the code in p.t.s-f...

Jon

Post a reply to this message

Attachments:
Download 'penrose0.png' (112 KB) Download 'penrose1.png' (384 KB) Download 'penrose2.png' (95 KB)

Preview of image 'penrose0.png'

Preview of image 'penrose1.png'

Preview of image 'penrose2.png'