Grasshopper

algorithmic modeling for Rhino

I modified this nice script due to roly hudson (see here) for generating Penrose tilings to include a decoration of the tiling by triangles. The result is a non-periodic pattern on the plane by a system of corner-sharing triangles (i.e. there are two triangles at each vertex). This is sometimes called a 2-D combinatorial zeolite, see for example this talk. Sliders control the shapes of the triangles. 

penroseZeolites.gh

zeolite_start_here.3dm

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Comment by mark zirinsky on May 29, 2015 at 6:37am

thanks Elisa, I have been a lifelong mineralogist but haven't looked at zeolite crystal structures (on the micro level) in a long time. this is a fascinating area for geometrical study, and once I have worn out arabic tiling patterns i will have a deeper look at the theory. At the moment I am experimenting with surface engravings over complex forms, and perhaps will try engraving the meshes, it hadn't occurred to me to do that until i saw your colors superimposed on the patterns. thank you

Comment by Elissa Ross on May 28, 2015 at 12:45pm

Yes Mark, exactly. The actual zeolite minerals have an interesting repetitive structure, typically a system of corner-sharing tetrahedra (the tetrahedra are composed of a single silicon atom bonded with four oxygen atoms). Mathematicians (and others) are interested in modelling these as so-called "mathematical zeolites", which are basically corner-sharing n-simplices... In other words, two triangles at each vertex in 2D, two tetrahedra at each vertex in 3D, and so on. There is a bit of an industry in developing hypothetical zeolites (both finite and infinite) based on these combinatorial restrictions. 

I'll post the GH definition. I'm kind of a noob so it isn't a thing of beauty. 

Comment by mark zirinsky on May 28, 2015 at 9:25am

very interesting patterns. Named after the class of minerals called Zeolites, as often found in water softeners and ion exchange columns? I would be interested to see your script modifications to produce these.

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