Tony Paletta wrote on Thu, Dec 11, 2003 02:41 PM UTC:
Charles,
3D Hex-based games present some really tough issues, partly because
there's no 'natural' generalization of a hex into a regular solid
(e.g., stacking boards gives a kind of hex prism) so our ability to use
analogies -- whatever they might be -- are somewhat strained.
One way to get a handle around SOME 'higher dim' chess is to think in
terms of areas -- maybe planes, maybe not -- with sets of paths defined
for within area moves and for between/among area moves. Essentially not
using coordinate geometry ('grid-like' games), but much closer to
'graph theory' - points and directed sets of paths between points. This
may or may not help in the evolution of your thinking.
BTW Mark Thompson's game is 'Tetrahedral Chess'; 'Tetragonal Chess'
(modest 'hexoid' game) is one of mine.
Charles, 3D Hex-based games present some really tough issues, partly because there's no 'natural' generalization of a hex into a regular solid (e.g., stacking boards gives a kind of hex prism) so our ability to use analogies -- whatever they might be -- are somewhat strained. One way to get a handle around SOME 'higher dim' chess is to think in terms of areas -- maybe planes, maybe not -- with sets of paths defined for within area moves and for between/among area moves. Essentially not using coordinate geometry ('grid-like' games), but much closer to 'graph theory' - points and directed sets of paths between points. This may or may not help in the evolution of your thinking. BTW Mark Thompson's game is 'Tetrahedral Chess'; 'Tetragonal Chess' (modest 'hexoid' game) is one of mine.