OCA:Pedestrian Life

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Pedestrian Life
Pedestrian Life rule
Rulestring 23/38
Rule integer 6408
Character Chaotic
Black/white reversal B0123478/S1234678

Pedestrian Life is a Life-like cellular automaton in which cells survive from one generation to the next if they have 2 or 3 neighbours, and are born if they have 3 or 8 neighbours.

Many patterns from regular Life are compatible with this rule, since the rules differ only in one transition. However, traffic lights are much less common, as most predecessors tend to die, giving the rule its name.[1]

Notable patterns

The rule is particularly notable for its plurality of distinct natural linear growth mechanisms:

Rotating gun

The first is a statorless, rotating period-106 glider gun:

x = 8, y = 6, rule = B38/S23 o2bo$5bo$o3bob2o$o3bo$ob2o$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The rotating p106 gun (Catagoluehere)
(click above to open LifeViewer)
RLE: here Plaintext: here

(5,2)c/190 spaceships

The second is a family of naturally occurring (5,2)c/190 oblique spaceships, using mechanisms meshed together similarly to switch engines:

x = 40, y = 28, rule = B38/S23 2o$2o2$8b2o$7bo2bo$5b2ob2o$5b2ob2o$7bo5$18b3o$18bobo$18b3o7$24b2o$23b 3o$23bo2bo$24b2o$37b2o$37bobo$38bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 10 TRACKLOOP 190 -1/95 -1/38 ]]
The first (5,2)c/190 oblique spaceship found (Catagoluehere)
(click above to open LifeViewer)
RLE: here Plaintext: here

There are at least 692 variants of these in the simplest form of two engines,[2] and many more such as one which deletes and recreates a blinker, resulting in a period of 380.[3] Many similar technologies result in puffers, rakes and the like.

Symmetric puffers

The third is a natural 31c/589 diagonally-symmetric ark, which has arisen several times in asymmetric soups. It emits two backward streams of gliders, which can lead to high-novelty interactions. One such example is a 750000-generation methuselah in which an ark is born and eventually destroyed by a retrograde glider produced from the chaos hassled by the glider streams.

There is a similar 57c/488 orthogonally-symmetric puffer, but that has only arisen in soups with even orthogonal symmetry.

(101,3)c/1884 oblique puffer

The fourth is a (101,3)c/1884 puffer.[4] Due to its massive ash trails no spaceships have been derived from it.


The Turing-completeness of EightLife was mentioned in a poor quality article,[5] but the article failed to list the necessary patterns and reactions inherited from Conway's Game of Life for creating any kind of pattern that proves universality. The same applies to HoneyLife and EightLife; the latter rule has a constructive proof for its Turing-completeness.

There is a proof sketch of Pedestrian Life's universality. It is on ConwayLife forums,[6] which contains a proof-scheme covering all rules in the outer-totalistic rulespace between B3/S23 and B3678/S23678.


  1. Tropylium (April 9, 2013). "Re: What do you want out of (conway's) life this year?". ConwayLife.com forums. Retrieved on June 24, 2016.
  2. David S. Miller (June 24, 2016). "Re: B38/S23". ConwayLife.com forums. Retrieved on October 31, 2016.
  3. Apple Bottom (October 27, 2016). "Re: Soup search results in rules other than Conway's Life". ConwayLife.com forums. Retrieved on October 31, 2016.
  4. Adam P. Goucher (November 9, 2016). "Re: Soup search results in rules other than Conway's Life". ConwayLife.com forums. Retrieved on November 19, 2016.
  5. Francisco José Soler Gil, Manuel Alfonesca (July 2013). "Fine tuning explained? Multiverses and cellular automata". Journal for General Philosophy of Science. Retrieved on January 21, 2017.
  6. Peter Naszvadi (December 12, 2016). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums

External links