# Variant using periodic bundary conditions

• #1

Does anyone know of a chess variant where periodic boundary conditions are used?

• #2

I certainly hope not!

• #3

Of course, it makes sense only for rows. For example, 1. b3 b6 2. Bc1-h4 would be a valid opening.

• #4

I sincerely hope you come down soon.

• #5

Why would this be such a bad idea?

• #6

For all I know, it's a wonderful idea (if only I understood it).

• #7

1. Qxe8 (wrapping around through the bottom) wins by force.

• #8

What is a periodic bundary condition?

• #9

I guess that gets to the heart of the matter, yes...

• #10
macer75 wrote:

What is a periodic bundary condition?

Maybe they lock the door to the room every now and then so you can't go to the bathroom?

• #11
macer75 wrote:

What is a periodic bundary condition?

Periodic boundary conditions mean that rows wrap around and it is legal to move from column a to h, and back. You can move off the edge of the board and enter on the other side. So, for example, if your bishop is on a3, it can move to h4, g5, f6, etc.. A knight on a3 could additionally move to h5 and g4. Only horizontal wrapping makes sense, of course.

The term periodic boundary conditions comes from physics, and you can read the introduction on Wikipedia to get an idea how it is used there. In effect, it would make the board infinitely long (horizontally), with the position repeated every 8 columns. No corners and no absolute center squares.

• #12

Here is an illustrative example of a valid periodic game: 1. b3 e5 2. Bc1xd8, where the bishop goes Bc1-b2-a3-(wraps around the periodic boundary on the edge of the board)-h4-g5-f6-e7-xQd8.

• #13

O, I get it. So sort of like those super unrealistic plane flying games, where your plane goes off the screen on one end and comes out on the other end?

• #14

It's a very interesting idea, despite my joke about 1.Qxe8#. I wish I knew people in the real world who played chess so I could try a game.

• #15
EscherehcsE wrote:
macer75 wrote:

What is a periodic bundary condition?

Maybe they lock the door to the room every now and then so you can't go to the bathroom?

The weatherman said it had something to do with colliding fronts.

• #16
macer75 wrote:

O, I get it. So sort of like those super unrealistic plane flying games, where your plane goes off the screen on one end and comes out on the other end?

Exactly. A good, down to Earth illustration.

• #17

Cylinder Chess, where the a-file connects in the same orientation to the h-file, is one example. The Fairy-Max engine can play this under WinBoard.

Another example is one particular brand of Circular Chess. This is usually described as Chess on an annulus of 4 squares radially, and 20 squares along the circumference, with complex rules for crossing through the hole in the center. Similar to the board depicted here:

If you think about it, this is equivalent to a 10x8 Moebius board, where you connect the left and right edge of the board in reverse order (rank 1 to rank 8, 2 to 7 etc.)

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