OCA:3-4 Life

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3-4 life
x=0, y = 0, rule = B34/S34 ! #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
View static image
Rulestring 34/34
B34/S34
Rule integer 12312
Character Explosive
Black/white reversal B0123678/S0123678

3-4 Life (or 34 Life) is a Life-like cellular automaton in which a cell will be alive in the next generation if it has 3 or 4 alive neighbours present. It thus has rulestring "B34/S34". It was one of the earliest variants of Conway's Life to be studied and discussed, initially thought to be a stable alternative to Life, until computer simulation found that most patterns tend to explode.

History

Research on 3-4 Life dates back to 1971, when Rici Liknaitzky and Steve Ward of the MIT group experimented and documented many forms including the still life block, oscillators of period 2, 3, 4, 6, 10, 12, and a period-3 orthogonal spaceship.[1] Since then, Lifeline began to report more findings under the section of "Excursions Into the Universe of '3-4' Life".[2]

Patterns

Still lives

Compared with Life, there are significantly fewer known still lives in 3-4 Life. Except for the 4-bit block, they are all extremely large and rare. They must all resemble large fortresses, whose outer walls must have corners resembling Life's ships or long ships, and connected by straight crenelations. All the still lives up to 51 bits are shown below.

x = 83, y = 9, rule = B34/S34 2o7b2ob2o12b2ob2o10b2obobob2o7b2obobob2o7b2ob2ob2o$2o6bob3obo10bob3obo 8bob7obo5bob7obo5bob6obo$8b2o3bobo8bobo3bobo7b2o7b2o5b2o7b2o5b2o6bobo$ 9bob2ob2o8b2ob3ob2o8bob2ob2obo7bob5obo7bob5ob2o$8b2ob2obo10bobobobo8b 2ob5ob2o5b2ob2ob2ob2o5b2ob2ob2obo$8bobo3b2o8b2ob3ob2o7bobo5bobo5bobo5b obo5bobo6b2o$9bob3obo8bobo3bobo8bob5obo7bob5obo7bob6obo$10b2ob2o10bob 3obo10b2obob2o9b2obob2o9b2ob2ob2o$26b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 10 WIDTH 1000 ]]
The smallest six still lives in 3-4 Life
(click above to open LifeViewer)

Oscillators

Oscillators of period 2, 3, 4, 5, 6, 8, 10, 12, 14, 20 have been found.

x = 201, y = 229, rule = B34/S34 2o2b2o2b2o14b2o6bo7b3o85b2o2b2o2b2o14b2o7bo4bo$2o2b2o2b2o15b2o6b2o93b 2o2b2o2b2o14b2ob2o5b2obo2bo$33bo7bo110b2o6bo2bob2o$154bo7bo4bo$8b2o 118b2o6b2o$8b2o118b2o6b2o3$2o2b2o2b2o14b3o101b2o2b2o2b2o$2o2b2o2b2o15b o102b2o2b2o2b2o$25bo2$2o126b2o6b2o$2o126b2o6b2o3$2o2b2o2b2o118b2o2b2o 2b2o$2o2b2o2b2o118b2o2b2o2b2o7$24b2o6bobo5b2o7bobo5bo$24bob2o5bob2o3bo b2o4b2ob2o4b3o$24b2o7bobo4bobo7bo5b2o$58bo5$24bobo5bobobo3bobo6b3o4b3o 6b3o5bo7b3o4bo7bo7bo$24b2ob2o4bobo4b2ob2o30b3o11b2o6b2o6b2o$25bobo5b3o 4bobo5bo2bo5bo8bo5b3o5b2ob2o4bo2bo4bo7bo$57bo7bo10bo14b2o7bo6bo$48b3o 31bo10bo5b2o7b2o$56b3o5b3o34bo6bo3$24bobobo5bo8bo4bobo6bobo4bo63b2o6b 2o2b2o2b2o15bobo13bo3bo13b3o$24b2ob2o3bobo6bobo4b2o2bo4bobo5b2o61b2o6b 2o2b2o2b2o15bo2b2o12b2obobo9b2o3b2o$25bobo6bo8bo4bo3bo3b2ob2o4bo94bo 15bobob2o11bo5bo$33bo8bo7bobo5bo8b2o96bo12bo3bo9bo7bo$34bo7bo26b2o57b 2o6b2o6b2o14b2o2bo27bo7bo$32bobo5b2o27bo58b2o6b2o6b2o16bobo27bo7bo$34b o6bo150bo7bo$193bo5bo$128b2o6b2o6b2o47b2o3b2o$128b2o6b2o6b2o49b3o3$ 128b2o6b2o6b2o$128b2o6b2o6b2o3$128b2o6b2o2b2o2b2o$128b2o6b2o2b2o2b2o7$ 2o2b2o2b2o15bo7b3o8b4o8b4o13bo10bo14b6o$2o2b2o2b2o14b3o5bo3b2o6bo3b2o 6bo3b2o10b3o8b3o11b2o6b2o$25bo6bo4bo6bo4bo6bo4bo11bo2bob2obo2bo12bo8bo $32bo5bo5bo5bo5bo5bo15b2o16bo3b4o3bo$8b2o23bo4bo6bo4bo6bo4bo33bo2bo4bo 2bo$8b2o23b2o3bo6b2o3bo6b2o3bo33bo2bob2obo2bo$35b3o9b3o9b4o33bo2bob2ob o2bo$96bo2bo4bo2bo$2o2b2o2b2o86bo3b4o3bo$2o2b2o2b2o87bo8bo$97b2o6b2o$ 99b6o$8b2o$8b2o3$2o2b2o2b2o23bo19b2obobob2o66b2o6b2o2b2o2b2o14b3o5b4o 6b2obo$2o2b2o2b2o22b3o17bob7obo65b2o6b2o2b2o2b2o14b2o8b4o4b2o2bo$33bo 17bobo7bobo96bo15b2o4bo$51b2ob7ob2o113bo4b2o$32bobo17bobobobobobo65b2o 14b2o31bo2b2o$30bobobobo14b2obo5bob2o64b2o14b2o32bob2o$29bobo3bobo14bo b2o3b2obo$30b2obob2o12bo4bobobobo4bo$25bo2b2o2b3o2b2o2bo7bo2b3ob3ob3o 2bo62b2o6b2o2b2o2b2o14bo$24b3o4b5o4b3o5b2o5bo3bo5b2o61b2o6b2o2b2o2b2o 14b2o3b3o5b3o$25bo2b2o2b3o2b2o2bo7bo2b3ob3ob3o2bo94b3o4bo5b2o$30b2obob 2o12bo4bobobobo4bo98bo2bo5bo$29bobo3bobo14bob2o3b2obo65b2o6b2o27b3o$ 30bobobobo14b2obo5bob2o64b2o6b2o$32bobo17bobobobobobo$51b2ob7ob2o$33bo 17bobo7bobo64b2o6b2o2b2o2b2o$32b3o17bob7obo65b2o6b2o2b2o2b2o$33bo19b2o bobob2o22$2o6b2o15bo8bo6b3o4b3o6b3o5bo2bo6b3o12bobo35b2o6b2o6b2o19bobo $2o6b2o15b3o6bobo14b6o7bob2obo5bob2o9b2obo2bobo31b2o6b2o6b2o18b2obo$ 24bo8bo6bo2b2o4bo8bo6bo2bo5b2ob3o9bobo2bobo66bo3b2o$26bo6bo2bo16b2o10b o2bo10bo9bobo2bob2o64b2o$2o6b2o22b2o6b2o2bo19bob2obo7b3o13bobo32b2o6b 2o6b2o15bo3b2o$2o6b2o24bo30bo2bo8bo50b2o6b2o6b2o14b2o2bo$41b3o120bo$ 160b3o$2o2b2o2b2o118b2o6b2o2b2o2b2o16bo$2o2b2o2b2o74b2ob2o39b2o6b2o2b 2o2b2o$41bobobo27bobobo7b3obo$28b5o8b2ob2o7bo12bo6b2ob2o6bo3bobo$8b2o 14b3o7b3o5bobo7b2o5b2o5b2o6bobo8b3ob2o37b2o14b2o$8b2o17bo5bo6bobobobo 7b2o8b2o6b3obobo5bo2bobo38b2o14b2o$25bo9bo5bobobo11b6o10bobobo9bob2o$ 29b3o9bobobo10bo6bo9bobobo8bobobo$8b2o118b2o14b2o$8b2o118b2o14b2o23$2o 2b2o2b2o17bo100b2o2b2o2b2o6b2o2b2o2b2o14b2o3bo10b2o3bo$2o2b2o2b2o16bob o99b2o2b2o2b2o6b2o2b2o2b2o14b3o13b3o$28bo140bo15bo$25bo3bo142bo15bo$2o 23bob2o107b2o6b2o6b2o17b3o13b3o$2o22bo2bo108b2o6b2o6b2o14bo3b2o10bo3b 2o$25bob2o$25bo3bo161b2o3bo$2o2b2o2b2o18bo99b2o2b2o2b2o6b2o6b2o37b3o$ 2o2b2o2b2o16bobo99b2o2b2o2b2o6b2o6b2o38bo$27bo167bo$194b3o$8b2o118b2o 14b2o6b2o37bo3b2o$8b2o118b2o14b2o6b2o3$2o2b2o2b2o118b2o2b2o2b2o6b2o2b 2o2b2o$2o2b2o2b2o118b2o2b2o2b2o6b2o2b2o2b2o23$2o2b2o2b2o15bo7bo7bo12b 4o6b3o4b3o6b3o5b3o5bo$2o2b2o2b2o14b4o5b3o5b2o9b2o4b2o7b4o12b5o9b2o$26b o5bo2bo4b2o23bo6bo8bo7bo7bo$35b2o4bo3bo7bob2obo26bo13b2o4b3o$2o32bo10b 2o54b4o$2o42b2o60bo$45bo2$2o2b2o2b2o15bo3bo$2o2b2o2b2o17bobobo58bo8bo$ 24b2o64bob2o4b2ob2o$30bo5b3o5bo7bo12bo3bo11bo6b3ob2o3b3ob2o$2o6b2o15bo 13b5o9b2o8b2o3b2o5bo5b2o8bo8bo$2o6b2o20b2o5bo7b2o6bo10bo5b2o7b2o8b2ob 3o3b2ob3o$24bobobo12bo5b2o6b2o4b2o10b5o11b2obo5b2obo$26bo3bo16bo9b4o 11bo5bo13bo8bo$2o2b2o2b2o$2o2b2o2b2o2$44bo$25b2o17b2o$25bob4o11b3o$25b o4bo11bo$25bobobo10b3o5bo$24bo4bo11bo5b3o$24b4obo17bo$28b2o15b3o$44b2o $45bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 4 WIDTH 1000 HEIGHT 1000 ]]
Oscillator stamp collection
(click above to open LifeViewer)

Spaceships

There are only three common spaceships, all with a period of 3 and a velocity of c/3. One moves diagonally, and the other two orthogonally. The smallest one is the most common, and the basis for all syntheses (see below). The other two are extremely rare, but have been seen to escape from broths. The diagonal one is the most rare, and is only commonly seen escaping along the line of symmetry of some diagonal broths. It does, however, on occasion escape asymmetric broths, but this happens much more rarely.

x = 24, y = 4, rule = B34/S34 10b4o8bo$b2o7bo2bo6b4o$4o5b2o2bo6bobo$11bobo7b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 ]]
The three common c/3 spaceships
(click above to open LifeViewer)

With the advent of computer search programs, several large spaceships have been found; most also c/3 orthogonal, and some of other velocities.

x = 64, y = 30, rule = B34/S34 6b3o20b5o12b4o10b2o$5bo3bo19b5o13b2o11b2o$4b2o3b2o16b2o5b2o9b6o7bo4bo$ 4b7o18bo3bo12b4o$4b2o3b2o18bo3bo24b2o2b2o$3bobo3bobo18bobo12bo4bo8b4o$ 3b2o5b2o19bo13bo4bo$6bobo21b3o12b2o2b2o8bo2bo$2b5ob5o17b3o27b2o$2b2o7b 2o15b6o11bob2obo8b4o$b6ob6o13bo4bo13b4o9b3o$3b2o5b2o14bo3b2obo11b6o10b o$2bob2o3b2obo12b2o3b3obo11bo2bo8b5o$2b2ob2ob2ob2o12b9o11bob2obo$2obob 2ob2obob2o9b2o3b2o3bo10b2o2b2o7bo3bo$bobo7bobo19bo25bo2bo$ob3obobob3ob o9b2ob2o5bo11b4o8bo4bo$b2ob3ob3ob2o9b3o5b2o14b2o12b2o$2b4o3b4o12b3o3b 4o11b4o9b5o$bo11bo11bob4o$2b11o33b4o11bo$b13o11bobo3b2o13bo2bo$3bo3bo 3bo15bob2obo11b2ob2ob2o$b2o2bobobo2b2o11b4o3b2o12bo2bo$2bob7obo15bo5bo $4b3ob3o17bo3bob2o$3bobo3bobo18bo$3bobobobobo17bobo$6b3o$6bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 ]]
Other c/3 ships
(click above to open LifeViewer)

Orderly infinite growth

The following c/3 wickstretcher is an example of a regular (non-chaotic) linear growth pattern:

x = 23, y = 10, rule = B34/S34 bo$bobo13b2o$bo11bobo3b2o$2bo10b2obo3bo$o3bobo3bo2b2o3bobo$o3bobobobo 2bo3bob2obo$2bo5b3ob2o4bobo$bo8b3obobo3bo$bobo6b3o2bo3b2o$bo15b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 ]]
A wickstretcher
(click above to open LifeViewer)

Synthesis

Mark Niemiec has developed and catalogued a variety of glider syntheses in 3-4 Life, namely, using the c/3 orthogonal glider to construct other objects.

x = 80, y = 22, rule = B34/S34 7b2o$7b2o$6b4o2$55b4o$31bo19bo4b2o$2bo13bo13b2o18b2o$3o12b2o12b3o17b3o $3o12b2o46bo$2bo13bo46b3o$63b3o$48bo14bo$48b2o26b3o$48b2o26b2o$48bo27b o2bo$78bo4$52b4o$53b2o$53b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 WIDTH 1000 ]]
A 7-glider synthesis of the c/3 diagonal glider
(click above to open LifeViewer)

References

  1. ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 8,9.
  2. ↑ Lifeline vol 5, p5; vol 6, p4; vol 7, p5-6; vol 8, p6; vol 9, p7-8; vol 11, p15.

External links

Retrieved from "https://conwaylife.com/w/index.php?title=OCA:3-4_Life&oldid=136899"