On 7 Jun 2002 03:40:24 -0400, ingo wrote:
> in news:slr### [at] fwicom Ron Parker wrote:
> 
>> On 25 May 2002 18:08:09 -0400, ingo wrote:
>>> And this as an inspiration for Ron:
>>> http://glinda.lrsm.upenn.edu/~weeks/software/quasic.html
>> 
>> I'll bet you all thought I was dead.
> 
> and buried under a load of code..
> 
>> [...] one might choose instead to use the
>> projection of a 5-dimensional lattice onto a 3-dimensional space.  
> 
> What would the result look like? Would every single tile take a limited 
> amount of 3d space instead of being streched to infinity along one axis 
> (like the hexagon pattern). Would it tile/tesselate in all 3 dimensions?

Yes.  They'd be something like the crackle pattern, but with a stronger
appearance of periodicity.

See http://www.cmp.caltech.edu/~lifshitz/quasicrystals.html for the real-life
version, and http://www.geom.umn.edu/apps/quasitiler/about.html for the math.

-- 
#local R=rgb 99;#local P=R-R;#local F=pigment{gradient x}box{0,1pigment{gradient
y pigment_map{[.5F pigment_map{[.3R][.3F color_map{[.15red 99][.15P]}rotate z*45
translate x]}]#local H=pigment{gradient y color_map{[.5P][.5R]}scale 1/3}[.5F
pigment_map{[.3R][.3H][.7H][.7R]}]}}}camera{location.5-3*z}//only my opinions

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