We consider a spectrum of possible go 囲碁 board shapes. On one extreme is the traditional grid bounded by a square. Only 4 of the boundary points are corners (a point having only 2 neighbors). On the other extreme is diamond go in which most of the boundary points are corners. The different boundaries correspond to curves of the form
abs(x)^s + abs(y)^s < C^s
with s=infinity for traditional go and s=1 for diamond go. The exponents in between those extremes, as well as 0 < s < 1, yield a variety of other curvy shapes with a different mix of edge (3 neighbors) versus corner points along the boundary. s=2 yields go on the grid points inside a rasterized circle.
Permit coefficients on the terms, producing rectangles, ellipses, and superellipses. Consider using a different exponent for each quadrant. But these shapes are not as elegant.
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