16 directed graphs, one for each of the movement directions: 8 for queen, 8 for knight. all graphs share the same set of nodes, corresponding to locations.
on any graph, on any node, there can be only one directed edge exiting the node. this defines ranged movement: movement can continue along the outgoing edge. (this framework allows nightrider.)
graphs could be constrained to preserve features from orthodox chess. pieces can go backwards the way they came: for a given piece, for every directed edge on a graph, there is another graph with the edge oriented the other direction. the union of bishop movement graphs has two disjoint connected components (colorbound); every other piece can reach all nodes.
no castling. need to define pawn promotion areas.
motivation is to invent random games for AI to learn how to play.
geometry makes chess interesting. pieces can obstruct the movement of other pieces, providing tactics like pin and skewer. original thought was chess on general graphs without geometry, but that seemed not interesting.
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