OCA:Pedestrian Life

Pedestrian Life
x=64, y = 64, rule = B38/S23 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
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Rulestring	23/38 B38/S23
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 because of the B8 transition, giving the rule its name.

Notable patterns

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

Rotating gun

The first is a statorless rotating four-barrelled glider gun, with period 424 and mod 106:

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 gun (Catagolue: here) (click above to open LifeViewer) RLE: here Plaintext: here

(5,2)c/190 spaceships and puffers

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

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 ]] #C [[ AUTOSTART GPS 10 TRACKLOOP 190 -1/95 -1/38 ]]

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

x = 47, y = 8, rule = B38/S23 3b2o$2bo2bo$3b2o2$45b2o$2bo42b2o$b3o$2obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 ]]

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

There are at least 692 variants of these in the simplest form of two engines, and many more such as one which deletes and recreates a blinker, resulting in a period of 380. Many similar technologies result in puffers, rakes and the like. In 2016, Luka Okanishi constructed a bootstrapping rake gun for one of the variants.

31c/589 diagonal puffer

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.

x = 48, y = 48, rule = B38/S23 43b3o10$45bo$44bobo$44bo2bo$30bo14b2o$28bobo$28b3o9b2o$28bo11b2o$46bo$46bo$46bo9$14b3o$15bo$13b3o10$15b2o$15b2o2$o$o10b2o$o9bo2bo$11bobo3b3o$12bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 30 TRACKLOOP 1178 -1/19 -1/19 ]]

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

57c/488 orthogonal puffer

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

(101,3)c/1884 oblique puffer

x = 305, y = 221, rule = B38/S23 9b2o$9bobo2b2o$10b2ob2o$15bo4$87b2o$87bobo$88b2o2$2o$2o6$78b2o$78b2o 199$302b2o$302bobo$302bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

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

The fifth 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. Like the (5,2)c/190 spaceships, the engines can be combined in different ways, and indeed two variants of the puffer have occured naturally. Due to its massive ash trails no spaceships have been derived from it.

Stable circuity

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 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 forums user EvinZL and improved by Aidan F. Pierce on July 11, 2021. 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 fastest known such converter in this rule.

x = 37, y = 75, rule = B38/S23 15b2o$16bo$16b3o16$17b2o$17b2o7b2o$26bo$24bobo$24b2o$8b2o$9bo$9bobo$ 10b2o5$8bo$7bobo$8bo5$9b2o$9b2o5$18bo$17bo$17b3o2$16bo$15bobo$2o13bobo $bo14bo$bobo$2b2o2$33b2o$33bobo$35bo$35b2o8$25b2o$25bobo$27bo$11b2o14b 2o$10bobo$10bo$9b2o5bo$15bobo$16bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ZOOM 8 WIDTH 600 HEIGHT 700 GPS 20 PAUSE 2 T 119 PAUSE 2 T 147 PAUSE 2 T 206 PAUSE 2 LOOP 207 ]]

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 a poor quality article, 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.

On November 21, 2017, Peter Naszvadi constructed a Rule 110 unit cell in Pedestrian Life, proving the rule Turing-complete. 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, which contains a proof-scheme covering all rules in the outer-totalistic rulespace between B3/S23 and B3678/S23678.

External links

Pedestrian Life at Adam P. Goucher's Catagolue Pedestrian Life at David Eppstein's Glider Database

• B38/S23 (discussion thread) at the ConwayLife.com forums
• Richard Holmes (2016-07-09). "Big and natural and (5,2)c/190".