User:Tropylium/Siamese

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:

• Ship: two boats
• Barge: two tubs
• Long boat: boat and tub
• Long ship: two boats
• Trans-boat with tail: boat and tub with tail

The same applies to diagonal 2+cell ties:

• Bi-loaf 2: two loaves and tub

Simple 2-cell orthogonal siamese stlifes:

• 10 cells: Snake siamese snake, carrier siamese snake, carrier siamese carrier
• 11 cells: Snake siamese eater, carrier siamese eater
• 12 cells: Eater siamese eater (3 isomers)

Other simple non-tie examples:

• 9 cells: Cis-boat with tail (= boat, tub with tail, and hook with tail (!))
• 11 cells: Loaf siamese loaf, elevener
• 12 cells: Big beehive (rank 4)
• 15 cells: Bee hat (= beehive and hungry hat)

Rank 5:

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

Non-simple examples:

• 10 cells: Loaf siamese barge (rank 2, multiplicity 3)