Recently I've been looking at Povray, pyprocessing, and cfdg (version 3.0) as tools for creating digital images. I have branched two separate blogs where I mainly explore jruby + processing and processing.py

Sunday, 18 October 2009

Rotational Symmetry and the "missing tile"

The following tiling pattern and the previous 'Glide Symmetry' were both inspired by illustrations in "Finding Moonshine" (A Mathematicians Journey Through Symmetry) by Marcus du Sautoy. This pattern is loosely based on a pattern he found on a wall of the Harem at the Alhambra. Mountain View John has suggested a far a more elegant way of creating the triangle shape, see my next posting.

   1 startshape start
   2 
   3 size{s 6 6 x -2.5 y -3.5} // trim to hide the ragged edge
   4 
   5 rule start{
   6   10*{x .97}{
   7     10*{y .85 x -.46}{triangle{h 360 b .8 sat .8}
   8     }
   9   } 
  10 }
  11 
  12 path triangle{
  13   MOVETO{x -.5 y -.2887}
  14   CURVETO{x 0 y -.2887 x1 -.25 y1 -.1987 x2 -.25 y2 -.1987}
  15   CURVETO{x .5 y -.2887 x1 .25 y1 -.3787 x2 .25 y2 -.3787}
  16   CURVETO{x .25 y .14434 x1 .3 y1 -.14 x2 .3 y2 -.14}
  17   CURVETO{x 0 y .557 x1 .21 y1 .4 x2 .21 y2 .4}
  18   CURVETO{x -.25 y .14434 x1 -.05 y1 .3 x2 -.05 y2 .3}
  19   CURVETO{x -.5 y -.2887 x1 -.46264 y1 -.01 x2 -.46264 y2 -.01}
  20   CLOSEPOLY{p align}  // these parameter adjustments don't do much
  21   FILL{p roundjoin}
  22 }
 

  
 
 
 
 
The white "tiles" are missing, because they are just the background, 

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Pembrokeshire, United Kingdom
I have developed JRubyArt and propane new versions of ruby-processing for JRuby-9.1.5.0 and processing-3.2.2