[ysylvcyk] Go 囲碁 boards of different sizes

The popular smaller sizes of go 囲碁 seem to be 9x9 and 13x13, corresponding to roughly a quarter and a half of the area of a 19x19 board.  The next size following the progression would be 27x27, double the area of a 19x19.

Geometrically, edge length 2n+1 gives a board roughly 4 times the size.

Further smaller boards become even sized: 4x4 and 6x6, which slightly changes the feel of the game by not having a center point.  Using powers of 2 or 2^n-1 would avoid such a change for the standard quadrupling series, but the half sizes in between are awkward.  There is wisdom in the 19x19 size.

We can also imagine go 囲碁 being played simultaneously on multiple boards of different sizes, but, in the style of combinatorial game theory, playing on exactly one board per move: which board is the most urgent?  This captures the spirit of a bunch of local fights as seen on a single big board.  Arrange the multiple boards in a pretty pattern, perhaps 3 dimensionally.  1 largest board, odd number each of the smaller boards (not even to avoid mirror strategy).  1 19x19, 3 13x13, 5 9x9 gives 1273 total points, roughly 3.5 times the size of 19x19, or about the same as 36x36.  There remains the boring possibility of mirror strategies on all but one of the multiple copies of the smaller boards, so maybe a pyramid of smaller sizes is better: one each of 9 11 13 15 17 19 gives 1246 total points.  Adding 5 and 7 gives 1320.  19 15 11 7 gives 756, similar in size to 27x27.

Fibonacci series of boards arranged in a spiral.