OCA:Pedestrian Life

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Pedestrian Life
x=64, y = 64, rule = B38/S23 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 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 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 which is not often triggered in life patterns [note 1]. However, traffic lights are much less common (giving the rule its name), as most predecessors tend to die because of the B8 transition.[note 2] [note 3][1]

Notable patterns

In addition to a number of alien oscillators [note 4], this rule is particularly notable for its plurality of distinct natural spaceships and linear growth mechanisms with unusual speeds and slopes.

Rotating gun

A statorless rotating four-barrelled glider gun, with period 424 and mod 106.[2] It can be stabilized into statorless oscillators[3]:

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

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 20 TRACKLOOP 190 -1/95 -1/38 ]]
The first (5,2)c/190 oblique spaceship found
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: 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 has a simple predecessor consisting of a beehive+B-heptomino collision and some distant junk
(click above to open LifeViewer)
Catagolue: here
x = 39, y = 22, rule = B38/S23 20b2o$20b2o2$26bob2o$25bo2bo$25bo4$2o$2o2$6bob2o$5bo2bo$5bo5$36b2o$36b obo$37bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 6 AUTOSTART GPS 20 TRACKLOOP 190 -1/95 -1/38 ]]
The smallest form, where the r-pentominoes are in the same phase
(click above to open LifeViewer)
Catagolue: here


There are at least 692 variants of these in the simplest form of two engines,[4] including some such as one which deletes and recreates a small object, resulting in a period of 380.[5] 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.[6]

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[7] 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.

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
(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.

x = 166, y = 114, rule = B38/S23 135bo2bo$13bo56bo63b2ob2o$12bobo54bobo62b2obo$12bobo54bobo64bo$13bo56b o67bo4$17b3o54b3o3$140bo$140bo$124b2o14bo$124b2o$33b2o55b2o$33b2o55b2o 2$124b2o$124b2o8b2o$135b2o2$21b3o54b3o54b2o$22b3o3b2o49b3o3b2o47b2o$ 27bobo54bobo37b2o$8b2o18bo36b2o18bo25bo12b2o$7bo2bo53bo2bo42bobo$8b2o 55b2o42bo2bo$48bo61b2o7b2o16b2o$47bobo69bobo14bobo$47bobo69bo17bo$48bo 62b2o$110bo2bo14b3o$111b2o14bo$b2o55b2o66bo3bo$o2bo53bo2bo69bo$bobo54b obo68bobo$2bo56bo66bo5bo$127b2o$130b2o22bo$125bo27b3o$8b2o2b2o51b2o2b 2o53b3o25b3obo$8b2o2b2o51b2o2b2o53bo2bo23bobo9b2o$124b2ob2o22b2o9bo2bo $124bo2bo25bo9b2o$8bo56bo57bo3bo28bo$7bobo54bobo57bobo24bo$8b2o55b2o 58bo24b2o4bo$150b2o$3b2o55b2o90bo2bo$3b2o55b2o90b3o$7b2o55b2o55b3o24b 2o3bo$7b2o9bo18b2o25b2o9bo18b2o25bobo24b2o$13b2o2bobo17b2o31b2o2bobo 17b2o25b3o$13b2o3b2o50b2o3b2o2$b2o55b2o55b2o$b2o55b2o55b2o2$13b2o3b2o 50b2o3b2o$13b2o2bobo17b2o31b2o2bobo17b2o25b3o$7b2o9bo18b2o25b2o9bo18b 2o25bobo24b2o$7b2o55b2o55b3o24b2o3bo$3b2o55b2o90b3o$3b2o55b2o90bo2bo$ 150b2o$8b2o55b2o58bo24b2o4bo$7bobo54bobo57bobo24bo$8bo56bo57bo3bo28bo$ 124bo2bo25bo9b2o$124b2ob2o22b2o9bo2bo$8b2o2b2o51b2o2b2o53bo2bo23bobo9b 2o$8b2o2b2o51b2o2b2o53b3o25b3obo$125bo27b3o$130b2o22bo$127b2o$2bo56bo 66bo5bo$bobo54bobo68bobo$o2bo53bo2bo69bo$b2o55b2o66bo3bo$111b2o14bo$ 110bo2bo14b3o$48bo62b2o$47bobo69bo17bo$47bobo69bobo14bobo$48bo61b2o7b 2o16b2o$8b2o55b2o42bo2bo$7bo2bo53bo2bo42bobo$8b2o18bo36b2o18bo25bo12b 2o$27bobo54bobo37b2o$22b3o3b2o49b3o3b2o47b2o$21b3o54b3o54b2o2$135b2o$ 124b2o8b2o$124b2o2$33b2o55b2o$33b2o55b2o$124b2o$124b2o14bo$140bo$140bo 3$17b3o54b3o4$13bo56bo67bo$12bobo54bobo64bo$12bobo54bobo62b2obo$13bo 56bo63b2ob2o$135bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 30 TRACKLOOP 976 57/488 0 ]] [[ ZOOM 2.6 ]]
the 57c/488 orthogonal puffer
(click above to open LifeViewer)
Catagolue: here

(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)

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.[8] 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.

Circuitry

A number of stable conduits from Life work in this rule. Many commonly-used Herschel conduits such as L112, F116, F117, Fx153, L156, F166, Fx176, Lx200, Fx77, R64, B60, Lx65 duplicator, and the fast and suppressed forms of Fx119 remain functional in Pedestrian Life. By contrast, Bx125, L141, Fx158, R190, Rx202, Bx222, Bx106, L122, H-to-MWSS (There is a slightly modified version of the RT=120 converter that does work [9]) and the simplest variant of Fx119 are not compatible.

90-degree glider stream turners/period-multipliers like Snark, Snark64, semi-Snark, many Bumpers, semi-cenark, tremi-Snark and quadri-Snark can be used in Pedestrian Life. On the other hand, Bouncers fail (there are no known small color-changing reflector replacements) and most glider-to-Herschel converters other than Callahan G-to-H and Speed tunnel will fail unsalvageably; 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.[10] It accepts an input glider and produces an output R-pentomino 119 generations later, and then a 180-degree glider at T=190. The converter 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, and was the fastest outright prior to the discovery of Speed Tunnel.

x = 37, y = 75, rule = B38/S23History 15.2A$16.A$16.3A16$17.2A$17.2A7.2A$26.A$24.A.A$24.2A$8.2A$9.A$9.A.A$10. 2A5$8.A5.2D$7.A.A4.2D$8.A5$9.2A$9.2A5$18.A$17.A$17.3A2$16.A$15.A.A$2A 13.A.A$.A14.A$.A.A$2.2A2$33.2A$33.A.A$35.A$35.2A8$25.2A$25.A.A$27.A$11. 2A14.2A$10.A.A$10.A$9.2A5.A$15.A.A$16.A! #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. Note the R output can be suppressed by placing a single block (red) to form a 180 degree reflector with RT=214 [11]
(click above to open LifeViewer)

There is also a p164 Herschel Factory based on an R-pentomino hassler, which allows for a small p164 glider gun. [12]

Universality

The Turing-completeness of Pedestrian Life was mentioned in an article published in Journal for General Philosophy of Science;[13] however, 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.[14] 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,[15] which contains a proof-scheme covering all rules in the outer-totalistic rulespace between B3/S23 and B3678/S23678.

See also

Notes

  1. ↑ Highlighting the similarity to life, both the B-heptomino and Century evolve identically to life in this rule, but see the page for the latter.
  2. ↑ This rule likewise doesn't support most life patters based on traffic lights or their predecessors. Both traffic stops, effectively all pre-pulsar hasslers (see pulsar page for more information), and most other traffic light and interchange hasslers from life fail here. Period-29 oscillators, which in life mostly rely on Pre-pulsar or Traffic Light hasslers, are very rare in this rule as a result.
  3. ↑ The Pentadecathlon also fails in this rule, as do the many reactions which relied on it for support. Period-45 oscillators are quite scarce in particular, though they are not as rare as period-29 oscillators.
  4. ↑ The interchange is more volatile in Pedestrian Life, allowing for new interchange hasslers with periods of 17, 25, 30, 40, 62, 90, 120, and various multiples of those periods. Other notable oscillators include alien Traffic light hasslers at periods 10, 12, 16, 20, 35 (a v-sparker), 40, and 48, a p16 hexadecathlon hassler, a p26 which either hassles four B-heptomino-blinker pairs or four R-pentomino-TL pairs depending on the phase, and a p104 fourfold wing hassler

References

  1. ↑ Tropylium (April 9, 2013). Re: What do you want out of (conway's) life this year? (discussion thread) at the ConwayLife.com forums
  2. ↑ DivusIulius (April 10, 2013). [B38/S23] Four-directional glider gun (discussion thread) at the ConwayLife.com forums
  3. ↑ Naszvadi (October 8, 2023). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
  4. ↑ David S. Miller (June 24, 2016). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
  5. ↑ Apple Bottom (October 27, 2016). Re: Soup search results in rules other than Conway's Life (discussion thread) at the ConwayLife.com forums
  6. ↑ Luka Okanishi (May 2, 2016). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
  7. ↑ Catagolue: hashsoup/C1/m_QqTfZV8QwHst4253469/b38s23
  8. ↑ Adam P. Goucher (November 9, 2016). Re: Soup search results in rules other than Conway's Life (discussion thread) at the ConwayLife.com forums
  9. ↑ dvgrn (November 18, 2024). Re: Thread for advanced questions (discussion thread) at the ConwayLife.com forums
  10. ↑ praosylen (July 11, 2021). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
  11. ↑ WhiteHawk (May 16, 2025). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
  12. ↑ Sphenocorona (August 16, 2020). Re: B38/S23 (discussion thread) at the ConwayLife.com forums
  13. ↑ 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.
  14. ↑ Peter Naszvadi (November 21, 2017). FWSS-less MWSS-track-only Rule-110 Unit Cell (discussion thread) at the ConwayLife.com forums
  15. ↑ Peter Naszvadi (December 12, 2016). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
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