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We skipped right over the opportunity for non-integer fractal dimensional chess! In all seriousness, this looks super interesting. I’d love to see some live gam

We skipped right over the opportunity for non-integer fractal dimensional chess! In all seriousness, this looks super interesting. I’d love to see some live gameplay of it.

MereInterest 6y ago
Hmm, fractal dimensional chess could perhaps be implemented as having subboards within each tile of a standard chessboard. Completely spitballing over lunch, I propose the following rule set: * Every square of a chessboard is itself a chessboard. This applies recursively. The top-level chessboard is named "Prime". All other chessboards are named according to the subdivision of Prime where they are located. So, the board located one level deep at F3 is called "Prime-F3". The board located two levels deep at A7 of Prime-F3 is called Prime-F3-A7. * All infinite chessboards start in the standard board starting position. * Black and white alternate making moves. Each move consists of moving a single piece within a single chessboard, following standard chess rules. * The game is won when a player does not have a King located in Prime. So far, this only introduces additional moves that can be made, which have no impact on the Prime board. Apart from being harder to force a draw, the subboards have no impact. Next up, adding rules to allow boards to influence the boards above/below them. * If player X has a piece on board Z in location Y, then all pieces belonging to player X in board Z-Y may, in addition to their normal move, also move like the piece in board Z. For example, at the start of the game, white has a queen on Prime at location D1. Therefore, in board Prime-D1 may move like a queen, in addition to their normal movement. * If player X does not have a King in board Z-Y, then their opponent may, as their move, move any piece from board Z-Y to board Z in location Y. For example, if Black has captured White's King on board Prime-D8, then Black may move any piece on Prime-D8 to the Prime board at location D8. Now, there is an incentive to playing on the lower level boards. Play here goes much faster, by virtue of having more moves available. By investing time into the subboards, you can gain additional pieces on the main board. If a subboard is being used to funnel more pieces in, then it may be worth investing in a subsubboard, in order to pull a king in from the subsubboard to the subboard.
jerf 6y ago
Arguably, that's what this is. The bifurcating timelines are better thought of as n-dimensional space. Describing the location of a piece requires a description of the bifurcations, which won't be a fixed number of numbers but will go up as the game progresses. Integer dimensions don't really cover this.
- dihedral 6y ago
  Yeah, great point, the dimensionality of the game increases as it progresses. I can't tell from the article, is there a bound on the number of parallel board timelines that can run simultaneously? Theoretically, without a bound, the dimensionality could increase indefinitely (there could be non-terminating paths that loop between the same game states enabling an arbitrary number of bifurcations).

We skipped right over the opportunity for non-integer fractal dimensional chess! In all seriousness, this looks super interesting. I’d love to see some live gameplay of it.

MereInterest 6y ago

Hmm, fractal dimensional chess could perhaps be implemented as having subboards within each tile of a standard chessboard. Completely spitballing over lunch, I propose the following rule set: * Every square of a chessboard is itself a chessboard. This applies recursively. The top-level chessboard is named "Prime". All other chessboards are named according to the subdivision of Prime where they are located. So, the board located one level deep at F3 is called "Prime-F3". The board located two levels deep at A7 of Prime-F3 is called Prime-F3-A7. * All infinite chessboards start in the standard board starting position. * Black and white alternate making moves. Each move consists of moving a single piece within a single chessboard, following standard chess rules. * The game is won when a player does not have a King located in Prime. So far, this only introduces additional moves that can be made, which have no impact on the Prime board. Apart from being harder to force a draw, the subboards have no impact. Next up, adding rules to allow boards to influence the boards above/below them. * If player X has a piece on board Z in location Y, then all pieces belonging to player X in board Z-Y may, in addition to their normal move, also move like the piece in board Z. For example, at the start of the game, white has a queen on Prime at location D1. Therefore, in board Prime-D1 may move like a queen, in addition to their normal movement. * If player X does not have a King in board Z-Y, then their opponent may, as their move, move any piece from board Z-Y to board Z in location Y. For example, if Black has captured White's King on board Prime-D8, then Black may move any piece on Prime-D8 to the Prime board at location D8. Now, there is an incentive to playing on the lower level boards. Play here goes much faster, by virtue of having more moves available. By investing time into the subboards, you can gain additional pieces on the main board. If a subboard is being used to funnel more pieces in, then it may be worth investing in a subsubboard, in order to pull a king in from the subsubboard to the subboard.

jerf 6y ago

Arguably, that's what this is. The bifurcating timelines are better thought of as n-dimensional space. Describing the location of a piece requires a description of the bifurcations, which won't be a fixed number of numbers but will go up as the game progresses. Integer dimensions don't really cover this.

dihedral 6y ago
Yeah, great point, the dimensionality of the game increases as it progresses. I can't tell from the article, is there a bound on the number of parallel board timelines that can run simultaneously? Theoretically, without a bound, the dimensionality could increase indefinitely (there could be non-terminating paths that loop between the same game states enabling an arbitrary number of bifurcations).