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. However, traffic lights are much less common, as most predecessors tend to die, giving the rule its name.[1]

There are several natural patterns of interest. One is a statorless, rotating period-106 glider gun:

The rotating p106 gun.
View animated image.
RLE: here

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

The first (5,2)c/190 oblique spaceship found.
View animated image.
RLE: 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.

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


Its Turing-completeness was mentioned in a poor quality article,[5] but it is baloney in this aspect, because didn't list the necessary patterns and reactions inherited from Conway's Game of Life for creating any kind of patterns that proves universality, just mentioning their existence. 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 that support glider and their rulestring matches B3[678]*/S23[678]*.


  1. Tropylium (April 9, 2013). "Re: What do you want out of (conway's) life this year?". forums. Retrieved on June 24, 2016.
  2. David S. Miller (June 24, 2016). "Re: B38/S23". forums. Retrieved on October 31, 2016.
  3. Apple Bottom (October 27, 2016). "Re: Soup search results in rules other than Conway's Life". forums. Retrieved on October 31, 2016.
  4. Adam P. Goucher (November 9, 2016). "Re: Soup search results in rules other than Conway's Life". 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. Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the forums

External links