Patterns That Remain Polyominos
Posted: 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:
Can anyone think of more long-lived examples?
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!