From Combinatorial Games to Shape-Symmetric Morphisms

Corner the Empress

“…The period doubling morphism a → ab, b → aa produces the P -positions for the Queen Bee. This connection between morphisms and combinatorial games was first studied by Duchêne and Rigo [3], see also [11]. A game is morphic if its P -positions can be retrieved from a recoding of a fixed point of a morphism.…”

“…In the first case, we need a move over (3,6), which is the difference between the Ppositions (3,7) and (6,13). In the second case, we need a move over (2,4), which is the difference between the P -positions (3,7) and (5,11). There does not seem to be a sensible way to define a Queen in this case, and it appears that a → ab, b → aaa does not produce a Morphic Queen.…”

“…Next in line is a → ab, b → aaa. It produces the positions (1, 2), (3,7), (4,9), (5,11), (6,13). Now consider the N -position (3,6).…”