Separate HTML for Basic Foil 53 Mapping of Hypercubes into Three Dimensional Meshes

Basic HTML version of Foils prepared 21 October 1995

Foil 53 Mapping of Hypercubes into Three Dimensional Meshes

From New CPS615 Foils-- B 28 August 95 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox

In string e1 e2 e3 e4.......ed, one can write d=d1+d2+d3

Any set of d1 binary indices can be mapped into a one dimensional line with periodic (wrap-around) connections

the remaining d2+d3 indices give other two dimensions

This decomposes hypercube into a mesh with:

So Hypercube includes lots of meshes

e.g. d=6 hypercube has 4 by 4 by 4, 8 by 8, 4 by 64, 64 by 1 etc.

So can study one dimension without loss of generality!