User:Tropylium/Siamese

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A still life is siamese if its living cells can be divided in two or more partially overlapping subsets, all of which are still lifes on their own.

  • The minimal number of subsets required is the rank.
  • The maximal number of subsets possible is the multiplicity.

A siamese stlife is simple if the rank and multiplicity are equal.

(Restrict to 1-cell-deep connections??)

All larger vessels (and most (all?) still lifes containing them) are analyzable as siamese; a vessel of length N (starting from tub = 2) will be of multiplicity N-1. Simple examples:

The same applies to diagonal 2+cell ties:

Simple 2-cell orthogonal siamese stlifes:

Other simple non-tie examples:

Rank 5:

x = 8, y = 6, rule = b3s23
b2o$obo2bo$obobobo$bobobobo$2bo2bobo$5b2o!

Non-simple examples: