[R-sig-Geo] Hex GIS, (was) Moving-window ...

[White.Denis at epamail.epa.gov]

Dear Sandor,

A major issue is fidelity of dynamical processes in different
topologies.  Frisch et al. and Toffoli and Margolis (see below) show
that the representation and implementation of Navier-Stokes equations in
a square rather than hexagonal lattice produce anisotropic anomalies.
Quite possibly there may be similar problems in the simulation of
discrete particle movement, such as organisms in a biological population
viability model, for example.

A number of other examples in percolation theory, self-avoiding walks,
survey sample design, and quantization (e.g., hexbin) show different
behavior for hexagon tessellations than for squares.

I hope this is a little introduction to the issues.

Denis

Frisch U, Hasslacher B, Pomeau Y. 1986. Lattice-gas automata for the
Navier-Stokes equations. Physics Review Letters 56:1505-1508.

Toffoli T, Margolis N.  1987.  Cellular automata machines.  MIT Press,
Cambridge.

r-sig-geo-bounces at stat.math.ethz.ch wrote on 2005-01-25 10:46:07:

> Hi Dennis and Frank,
>
> Could you en light me on possible references (papers, books) about the

> use of hexagons in spatial analysis? Did your search give any
direction?
>
> I am using the hexbin package (find it at bioconductor.org) and can
> highly recommend it. Nicholas (the maintainer) is currently updating
the
> package!
>
> Although hexbin and R are not a GIS, much of the 'GIS' functionality
is
> available in R!!
>
> Cheers,
>
> Sander.
>