Triple pseudo still life

Triple pseudo still life[1] is the smallest pseudo still life that can be decomposed into three stable subpatterns (shown below; note that the first and third are themselves pseudo still lifes), but cannot be decomposed into two stable subpatterns.[2] It was found by Gabriel Nivasch in July 2001. It consists of a single block surrounded by two hook with tails and two snakes.

Triple pseudo still life
<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>x = 8, y = 10, rule = B3/S23 6b2o$2bobo2bo$bob2obo$bo4b2o$2ob2o$3b2ob2o$2o4bo$bob2obo$o2bobo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C Still life <nowiki></nowiki> <html></code></div></div><canvas width="200" height="300" style="margin-left:1px;"><noscript></html> <html></noscript></canvas></div></html>
Pattern type Pseudo still life
Number of cells 32
Bounding box 8×10
Discovered by Gabriel Nivasch
Year of discovery 2001

Uniqueness

Nathaniel Johnston showed on May 25 2017, via an exhaustive computer search using Simon Ekström's still life searcher, that the triple pseudo still life is the unique pseudo still life of 32 or fewer bits requiring a decomposition into 3 or more pieces.[3]

The first stable subpattern.
The second stable subpattern.
The third stable subpattern.
gollark: See, this is perfect and without flaw except that the time requirement to make the regex seems to increase exponentially due to greenery.
gollark: Here you go, `b(d(e(e(io|oi)|i(eo|oe)|o(ei|ie))|i(e(eo|oe)|oe{2})|o(e(ei|ie)|ie{2}))|e(d(e(io|oi)|i(eo|oe)|o(ei|ie))|e(d(io|oi)|i(do|od)|o(di|id))|i(d(eo|oe)|e(do|od)|o(de|ed))|o(d(ei|ie)|e(di|id)|i(de|ed)))|i(d(e(eo|oe)|oe{2})|e(d(eo|oe)|e(do|od)|o(de|ed))|o(de{2}|e(de|ed)))|o(d(e(ei|ie)|ie{2})|e(d(ei|ie)|e(di|id)|i(de|ed))|i(de{2}|e(de|ed))))|d(b(e(e(io|oi)|i(eo|oe)|o(ei|ie))|i(e(eo|oe)|oe{2})|o(e(ei|ie)|ie{2}))|e(b(e(io|oi)|i(eo|oe)|o(ei|ie))|e(b(io|oi)|i(bo|ob)|o(bi|ib))|i(b(eo|oe)|e(bo|ob)|o(be|eb))|o(b(ei|ie)|e(bi|ib)|i(be|eb)))|i(b(e(eo|oe)|oe{2})|e(b(eo|oe)|e(bo|ob)|o(be|eb))|o(be{2}|e(be|eb)))|o(b(e(ei|ie)|ie{2})|e(b(ei|ie)|e(bi|ib)|i(be|eb))|i(be{2}|e(be|eb))))|e(b(d(e(io|oi)|i(eo|oe)|o(ei|ie))|e(d(io|oi)|i(do|od)|o(di|id))|i(d(eo|oe)|e(do|od)|o(de|ed))|o(d(ei|ie)|e(di|id)|i(de|ed)))|d(b(e(io|oi)|i(eo|oe)|o(ei|ie))|e(b(io|oi)|i(bo|ob)|o(bi|ib))|i(b(eo|oe)|e(bo|ob)|o(be|eb))|o(b(ei|ie)|e(bi|ib)|i(be|eb)))|e(b(d(io|oi)|i(do|od)|o(di|id))|d(b(io|oi)|i(bo|ob)|o(bi|ib))|i(b(do|od)|d(bo|ob)|o(bd|db))|o(b(di|id)|d(bi|ib)|i(bd|db)))|i(b(d(eo|oe)|e(do|od)|o(de|ed))|d(b(eo|oe)|e(bo|ob)|o(be|eb))|e(b(do|od)|d(bo|ob)|o(bd|db))|o(b(de|ed)|d(be|eb)|e(bd|db)))|o(b(d(ei|ie)|e(di|id)|i(de|ed))|d(b(ei|ie)|e(bi|ib)|i(be|eb))|e(b(di|id)|d(bi|ib)|i(bd|db))|i(b(de|ed)|d(be|eb)|e(bd|db))))|i(b(d(e(eo|oe)|oe{2})|e(d(eo|oe)|e(do|od)|o(de|ed))|o(de{2}|e(de|ed)))|d(b(e(eo|oe)|oe{2})|e(b(eo|oe)|e(bo|ob)|o(be|eb))|o(be{2}|e(be|eb)))|e(b(d(eo|oe)|e(do|od)|o(de|ed))|d(b(eo|oe)|e(bo|ob)|o(be|eb))|e(b(do|od)|d(bo|ob)|o(bd|db))|o(b(de|ed)|d(be|eb)|e(bd|db)))|o(b(de{2}|e(de|ed))|d(be{2}|e(be|eb))|e(b(de|ed)|d(be|eb)|e(bd|db))))|o(b(d(e(ei|ie)|ie{2})|e(d(ei|ie)|e(di|id)|i(de|ed))|i(de{2}|e(de|ed)))|d(b(e(ei|ie)|ie{2})|e(b(ei|ie)|e(bi|ib)|i(be|eb))|i(be{2}|e(be|eb)))|e(b(d(ei|ie)|e(di|id)|i(de|ed))|d(b(ei|ie)|e(bi|ib)|i(be|eb))|e(b(di|id)|d(bi|ib)|i(bd|db))|i(b(de|ed)|d(be|eb)|e(bd|db)))|i(b(de{2}|e(de|ed))|d(be{2}|e(be|eb))|e(b(de|ed)|d(be|eb)|e(bd|db))))` matches all anagrams of `beeoid`.
gollark: I'll run that test later™, I have to test my new `beeoid` anagram regex.
gollark: I don't think it's an optimal regex, but it's generated from the FSM.
gollark: On the plus side, apparently `b(e(es|se)|se{2})|e(b(es|se)|e(bs|sb)|s(be|eb))|s(be{2}|e(be|eb))` matches all anagrams of `bees`.

See also

References

  1. Mark D. Niemiec (February 19, 2015). "29 Pseudo-still-lifes 26 bits and larger". Retrieved on April 3, 2016.
  2. Nivasch, Gabriel (July, 2001). "Still lifes". Retrieved on March 23, 2016.
  3. Nathaniel Johnston (May 25, 2017). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
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