[R-sig-Geo] Hexagonal lattice

[White.Denis at epamail.epa.gov]

Dear Sreedevi,

It depends on what kind of topological manifold you embed the lattice
in.  On a sphere the answer is no, because hexagons cannot tessellate a
sphere.  There can be 8 or 12 pentagons, for example, depending on
whether you use a spherical octagon or icosahedron model.  Perhaps
hexagons can tessellate a torus, but I have not examined that.  If so,
then all cells would have six neighbors.

But the question to ask is why do you want to wrap the boundaries?
Unless you are in fact modeling the entire sphere or doing strictly
theoretical studies, real world study areas have limits and it is
appropriate to impose restricted neighborhoods on boundary hexagons.

If you do want to work on a sphere you should visit the web site
http://www.sou.edu/cs/sahr/dgg/, where software for implementing
hexagons on spheres is available.

With respect to dynamic modeling on square or hexagonal grids, you may
be interested in the attached paper accepted for publication: White D,
Kiester AR; Topology matters: network topology affects outcomes from
community ecology neutral models; Computers, Environment and Urban
Systems.

best wishes,
Denis White
   US EPA, 200 SW 35th St, Corvallis, Oregon, 97333 USA
   voice: 541.754.4476, email: white.denis at epa.gov
   web: www.epa.gov/wed/pages/staff/white/


(See attached file: topology.matters.pdf)

----- Forwarded by Denis White/COR/USEPA/US on 2007-11-26 17:39 -----

Tony Olsen/COR/USEPA/US wrote on 2007-11-26 17:33:04:

> FYI.  He might be interested in your hex biodiversity papers and
algorithms.
>
> tony
>
> ----- Forwarded by Tony Olsen/COR/USEPA/US on 11/26/2007 05:32 PM
-----
>
> From: "Sreedevi E.P" <sreedeviep at gmail.com>
> Date: 11/26/2007 03:39 PM
> To: "r-sig-geo at stat.math.ethz.ch" <r-sig-geo at stat.math.ethz.ch>
> Subject: [R-sig-Geo] Hexagonal lattice
>
> Hi
>
> I am a student from Novs Scotia Agricultural College,Canada.
> I am working on modleing of biod diversity in a natural eco system.
> Now we are dealing with 2D hexagonal lattices.
> If you could clear doubt,it will be very nice.
> I just want to know whetehr,all the corner elemets in a hexagonal
lattice
> with any number of rows will have 6 neighbours after applying cyclic
> boundary conditions?
>
> Hope that am not disturbing you much
>
> Sincerely
> Sreedevi
>
>
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