Patterns That Remain Polyominos

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Tropylium
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Joined: May 31st, 2011, 7:12 pm
Location: Finland

Patterns That Remain Polyominos

Post by Tropylium » July 1st, 2012, 3:28 pm

Random idea: does anyone know Life patterns that remain polyominoes for as long as possible during their evolution?

Ie. a polyomino A that becomes polyomino B that becomes polyomino C that… and A ≠ B ≠ C ≠ … (the trivial solutions are the block and blinker, but that ain't news).

Polyominos that become another polyomino are quite simple to create (eg. lines of any length). There are at least three that then become yet another polyomino:
• L-tetromino > Z-tetromino > pre-beehive
• T-pentomino > T-tetromino > bullet heptomino
• V-pentomino > W-pentomino > pre-loaf 1

And with some experimentation, for a 4-generation chain, this is a 15omino that becomes an L-tetromino:

Code: Select all

x = 7, y = 5, rule = life
3bo$3bo$2b3o$5o$2b5o!
Can anyone think of more long-lived examples?

knightlife
Posts: 566
Joined: May 31st, 2009, 12:08 am

Re: Patterns That Remain Polyominos

Post by knightlife » July 4th, 2012, 4:24 pm

67-omino 5-generation chain:

Code: Select all

x = 13, y = 14, rule = B3/S23
4bo3bo$4bo3bo$2b4ob4o$4b4ob4o$4b2obob2o$3b2o2bo2bo$3b2o2bo2b2o$2b2o3bo
2b2o$5o2b4o$2b4o3b2o$4bobob2o$5b5o$6bobo$6bobo!

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