Well, last I checked many problems of enumerating tessellations of the plane were still unresolved:
I think it may have been Golomb who wrote a book on tiling in the 1980's that characterized some large numbers of periodic tilings according to their symmetry groups. There are lots of ways of tiling, including some like Penrose tilings which are aperiodic and nonrepeating. Here is a hex tiling (with some rotations that are sorta fun): http://srufaculty.sru.edu/david.dailey/svg/pattern.svg It works ok in IE and Opera but seems to chug a bit in FF. Here is a quasi-random tiling for which the dual of the network defined over the tiles is four-regular but nondeterministic: http://srufaculty.sru.edu/david.dailey/svg/tiles.svg (I botched up the mouse events for Opera though). It could be used to model traffic flow in quasi random grids. I did this in the early 90's to demonstrate certain nonperiodic (nondeterministic) tilings using HTML -- there are lots better places on the web now -- http://srufaculty.sru.edu/david.dailey/tiles/tiling.html This thing takes any string of ascii text and converts it into a unique periodic tiling based on curvilinear edges -- it was done pre SVG but could easily enough be converted to SVG rather than bitmapped graphics: http://srufaculty.sru.edu/david.dailey/javascript/traverse.html It is sort of cute since it generates unique wallpapers reflecting the input string. I have a handful of other pseudo-cryptological investigations if you should be interested that convert strings to pictures. This thing uses HTML clipping to weave two pictures together with an arbitrary stitch pattern chosen by the user http://srufaculty.sru.edu/david.dailey/javascript/weave/PictureWeaver.html (again pre SVG and possibly IE only) This makes jig saw puzzles out of moving pieces: http://marble.sru.edu/~ddailey/svg/clipembed16.html done in SVG but back before I learned to make my stuff work anywhere but IE. It is a tiling of SMIL objects. To my knowledge the theories of tiling advanced thus far do not attempt to consider time-based considerations in the tiling, but one can consider a class of local perturbations to a tiling which result in new tilings of some fundamentally different global qualities. I could say more but it would get progressively weirder. cheers, David [Non-text portions of this message have been removed] ----- To unsubscribe send a message to: [EMAIL PROTECTED] -or- visit http://groups.yahoo.com/group/svg-developers and click "edit my membership" ---- Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/svg-developers/ <*> Your email settings: Individual Email | Traditional <*> To change settings online go to: http://groups.yahoo.com/group/svg-developers/join (Yahoo! ID required) <*> To change settings via email: mailto:[EMAIL PROTECTED] mailto:[EMAIL PROTECTED] <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
