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Joe Joyce wrote on Sat, Jun 27, 2009 07:21 PM UTC:
George, the first question you asked was about area-effect pieces: 'How is
''two-step bent nightrider'' Joyce mentions an example of an area
effect piece, as Joyce describes it?' 

The traditional western chesspieces are highly linear. Even the pawns are
'slow linear', if you think about it. The only pieces that aren't purely
linear are the knight and the king. The knight, which has a sort of
circular footprint, attacks a sort of 2D limited area, rather than some
undetermined number of squares along a straight line. This is an example of
an area-effect piece. The king is a weaker example. It does just hit a
small square area, the squares immediately around it. This can be seen as
an area effect, but you can also consider the king merely a fragile,
degenerate queen [in the chess and mathematical senses, of course.] The
knightzee's footprint [diagrams courtesy of J Good]: 

o o 2 o 2 o 2 o o
o 2 o 2 o 2 o 2 o
2 o o 1 o 1 o o 2
o 2 1 2 o 2 1 2 o
2 o o o N o o o 2
o 2 1 2 o 2 1 2 o
2 o o 1 o 1 o o 2
o 2 o 2 o 2 o 2 o
o o 2 o 2 o 2 o o

It doesn't go far, but it goes wide. The bent Hero and Shaman pieces are
also examples of area effect pieces that are complementary. From the center
of a 7x7 square, they cover all the squares that a zebra does not:

S Z S H S Z S
Z S H H H S Z
S H S H S H S
H H H O H H H
S H S H S H S
Z S H H H S Z
S Z S H S Z S

These represent one sort of area effect piece. The planar pieces in Prince
are another sort.