# OCA:Pedestrian Life

Pedestrian Life | |

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Rulestring | 23/38 B38/S23 |
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Rule integer | 6408 |

Character | Chaotic |

Black/white reversal | B0123478/S1234678 |

**Pedestrian Life** is a Life-like cellular automaton in which a cell survives from one generation to the next if it has 2 or 3 neighbours, and is born if it has 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 (giving the rule its name), as most predecessors tend to die because of the B8 transition.^{[1]}

## Notable patterns

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

### Rotating gun

A statorless rotating four-barrelled glider gun, with period 424 and mod 106:^{[2]}

The rotating gun (click above to open LifeViewer) RLE: here Plaintext: hereCatagolue: here |

### (5,2)c/190 spaceships and puffers

There is a family of naturally occurring (5,2)c/190 oblique spaceships, using R-pentominoes meshed together similarly to switch engines in Life:

The first (5,2)c/190 oblique spaceship found (click above to open LifeViewer) RLE: here Plaintext: hereCatagolue: here |

The most common variant by far has a simple predecessor consisting of a beehive+B-heptomino collision and some distant junk (click above to open LifeViewer) Catagolue: here |

There are at least 692 variants of these in the simplest form of two engines,^{[3]} including some such as one which deletes and recreates a small object, resulting in a period of 380.^{[4]} There might be many more two-engine ships not in this list. Puffers and rakes with the same speed are possible, based on the same mechanism. In 2016, Luka Okanishi constructed a bootstrapping rake gun for one of the variants.^{[5]}

### 31c/589 diagonal puffer

There 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^{[6]} is a 750213-generation methuselah in which an ark is born and eventually destroyed by a retrograde glider produced from the chaos hassled by the glider streams.

the 31c/589 diagonal puffer (click above to open LifeViewer) Catagolue: here |

### 57c/488 orthogonal puffer

There is a 57c/488 orthogonally-symmetric puffer with interrupted queen bees at the front, but that has only arisen in soups with even orthogonal symmetry.

the 57c/488 orthogonal puffer (click above to open LifeViewer) Catagolue: here |

### (101,3)c/1884 oblique puffer

Predecessor for a variant of the puffer (click above to open LifeViewer) |

There is a (101,3)c/1884 puffer consisting of two mutually stabilizing copies of an unstable engine, which is essentially a collision between a glider and a ship+block constellation produced by Herschel.^{[7]} Like the (5,2)c/190 spaceships, the engines can be combined in different ways, and indeed two variants of the puffer have occurred naturally. It has massive ash trails, and no spaceships have been derived from it.

## Stable circuitry

A number of stable conduits from Life work in this rule. Many Herschel conduits but Bx125, Fx158, R190, Rx202, Bx222, Bx106, L122, H-to-MWSS and the simplest variant of Fx119 function well. Snark, semi-Snark, semi-cenark, tremi-Snark and quadri-Snark can be imported as well. On the other hand, glider-to-Herschel converters other than Callahan G-to-H and Speed tunnel will fail unsalvagably; the initial glider+block reaction used in Herschel receiver, syringe and bronco gives an R-pentomino instead of the pi-heptomino.

The following stable converter was found by EvinZL and improved by praosylen on July 11, 2021.^{[8]} It accepts an input glider and produces an output R-pentomino 119 generations later as well as an extra 180-degree glider soon. It is considered Spartan because it is composed of a bait beehive, a block, a tub and four eater 1s. With a repeat time of 214 generations, it is the second fastest known such converter in this rule.

The stable G-to-R converter, shown connected to RF28B and BFx59H. A ghost Herschel marks the final output location (click above to open LifeViewer) |

## Universality

The Turing-completeness of Pedestrian Life was mentioned in an article published in *Journal for General Philosophy of Science*;^{[9]} 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.

On November 21, 2017, Peter Naszvadi constructed a Rule 110 unit cell in Pedestrian Life, proving the rule Turing-complete.^{[10]} The polyglot pattern is based on eater 1, middleweight spaceship, twin bees shuttle and p46 gliderless MWSS gun, therefore it also applies to HoneyLife and EightLife.

There is also an earlier proof sketch of Pedestrian Life's universality. It is on ConwayLife forums,^{[11]} which contains a proof-scheme covering all rules in the outer-totalistic rulespace between B3/S23 and B3678/S23678.

## See also

## References

- ↑ Tropylium (April 9, 2013). Re: What do you want out of (conway's) life this year? (discussion thread) at the ConwayLife.com forums
- ↑ DivusIulius (April 10, 2013). [B38/S23] Four-directional glider gun (discussion thread) at the ConwayLife.com forums
- ↑ David S. Miller (June 24, 2016). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
- ↑ Apple Bottom (October 27, 2016). Re: Soup search results in rules other than Conway's Life (discussion thread) at the ConwayLife.com forums
- ↑ Luka Okanishi (May 2, 2016). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
- ↑ Catagolue:
`hashsoup/C1/m_QqTfZV8QwHst4253469/b38s23` - ↑ Adam P. Goucher (November 9, 2016). Re: Soup search results in rules other than Conway's Life (discussion thread) at the ConwayLife.com forums
- ↑ praosylen (July 11, 2021). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
- ↑ 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. - ↑ Peter Naszvadi (November 21, 2017). FWSS-less MWSS-track-only Rule-110 Unit Cell (discussion thread) at the ConwayLife.com forums
- ↑ Peter Naszvadi (December 12, 2016). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums

## External links

- Pedestrian Life at Adam P. Goucher's Catagolue
- B38/S23 (discussion thread) at the ConwayLife.com forums
- Richard Holmes (2016-07-09). "Big and natural and (5,2)c/190".
- Pedestrian Life at David Eppstein's Glider Database