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Given a tile of a tiling, its Conway signature is an infinite-to-the-left sequence of symbols taken in {0,1,2,3,4,5,6,7}
that records the subdivision history that originated it.
Most recent subdivision history is recorded to the right, in particular the last symbol of the signature is 0 iff we are focusing on
a mystic tile.
The meaning of the symbols is clarified in the image on the left showing the subdivision process for a "spectre" tile. In a signature we do not allow for the consecutive pair of symbols ...03... The notation "[w]p." denotes the periodic signature "...wwwwp." where w is any nonempty finite sequence of symbols and p is a possibly empty finite sequence of symbols. |
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[0].
partial tiling, density = 2/3 (bay)
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[1].
partial tiling, density 1/2 (coast)
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[2].
complete tiling
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[3].
partial tiling, density 1/6 (cape Horn)
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[4].
partial tiling, density 1/3
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[5].
partial tiling, density 5/6 (fjord tip)
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[6].
partial tiling, density 1/3
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[7].
complete tiling
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[40].
Core of the spectre tile. Tripod tiling
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[40].
Subdivision of the previous. Tripod tiling.
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[0]. and [3]. twice union of [0]. and two copies of [3].Name: Hydra 2 |
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[1]. twice union of two copies of [1].
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[5]. and [3]. union of [5]. and [3].Name: Hydra 1 |
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[4]. three times union of three copies of [4].
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[6]. three times union of three copies of [6].
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