OCA:Just Friends

Just Friends
x=0, y = 0, rule = B2-a/S12 ! #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	12/2-a B2-a/S12
Character	Semi-stable

Just Friends is a two-state rule created by David Bell and first described in June 2000, making it one of the first isotropic non-totalistic cellular automata considered. It normally stabilizes into a maze-like structure consisting of lines and oscillators with escaping 3-cell spaceships.

Rule definition

The original description goes as follows:

“ My idea was to investigate Life rules which had birth on only two

neighbors. Using totalistic rules, this is a lose (in my opinion) since objects explode when they get two cells adjacent vertically or horizontally. But if we abandon totalistic rules, then we can fix this problem. I was looking for the combination of nicest behavior and simplest rule I could find.

The most interesting rule I found was this one:

A cell stays alive only if it has 1 or 2 live neighbors (in any position). A cell is born only if it has exactly two live neighbors which are not adjacent vertically or horizontally.

So in the following figure, the central cell is born if there are live cells at any two cells marked ac, ad, ae, af, ag, bd, be, bf, bg, bh, ce, cf, cg, ch, df, dg, dh, eg, eh, or fh.

abc
hid
gfe

” — David Bell, Mon, 19 Jun 2000

In Hensel notation, the rule is written as B2-a/S12, where "B2-a" transition indicates that birth does not happen on a domino surface. This prevents the rule from being explosive like B2/S12. A related rulespace named "SansDomino" was briefly considered in 2012, in which Just Friends would be expressed as sansdomino_s12.

Patterns

Just Friends contains still lifes, oscillators, spaceships and some linear growth patterns including guns, puffers and rakes. Examples can be found in the Just Friends archive in the External Links section below.

Still lifes

Just Friends has an infinite number of still lifes because any straight and crooked (though not curved) line is a still life. All still lifes are lines, or stabilizations of lines.

x = 85, y = 66, rule = B2-a/S12 2o10$3o7b2o$11bo9$4o7bo$11bo$10bo$10bo7$5o6bo$11bo$11bo$10bo$10bo6$6o 5bo9bo9bo9bo9bo8bo$11bo9bo9bo9bo8b2o8bo$11bo9bo8bo2bo6bo12bo7bo$11bo8b o11bo7bo11bo8bo$10bo9bo11bo8bo10bo9bo$10bo9bo20bo20bo5$7o6bo7bo9bo9bo 9bo9bo10bo8bo$13bo7bo9bo9bo9bo9bo8b2ob2o6bo$14bo6bo11b2o6bo8bo2b2o6bo 18bo2b2o$10b2obo7bo8b2o9bo9bo8bo2bo7b2o9bo$13bo7bo10bo7bo10bo10bo19bo$ 20bo19bo21bo$20bo19bo4$10b3o2b2o5bo7b2o3b2o8b2o8b2o4bo9bo$13b2o5b2o10b 3o8b2o7b3o5b2o9bo$23b2o15b3o7b2o11b2o6bo$21b2o39bo7bo$62bo9b2o$72bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 6 WIDTH 600 HEIGHT 480 ]]

Still lifes in Just Friends from 2 to 7 cells (click above to open LifeViewer)

Oscillators

Just Friends features a natural, strictly volatile period-236 rotating oscillator, and a versatile line-supported period-26 oscillator with a Y-tetraplet as rotor.

Dean Hickerson's drifter-searching program covers this particular non-totalistic rule, which had found turning and flipping components for a signal and proved the rule omniperiodic. The example below is made of copies of a 27-generation 90 degree turn component and a 23-generation flipping component, whose repeat time is 13 ticks.

A list of smallest known oscillators by population is maintained by Jeremy Tan in Skopje repository.

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2bo11bo5bo109bo7bo14bo99bo6bo7bo13bo11bo$206bo14bo8bo11b4o24b2obo14bob o18bo14bo23bobobobo13bobobobo18bob7o28bo23bo14bo112bo7bo14bo99bo6bo2b 3o2bo$206bo14bo33b3o6b3o4bobo3b5o6bobo5b6o8b3o9bo25bobo21bobo10b2o2bob obo4bo3b2o26bo23bo14bo112bo2b3o2bo6bo2b3o2bo16bo110b2ob9ob2o$206bo6b6o 2bo21bo27bobo2bo11bobo16b2o14b5o22bo2bo6bobo6bo2bo16bobobo6bo29bo23bo 11bo5bo117bo6bo24bo111bo11bo$243bo27bo6b5o7bob8o9b3o10bo61b2o3bo5bo4bo 29bo23bo11bo5bo117bo6bo$278b2o10bo32b3o25bo19bo16b2ob3obobo32bo2b6o7b 6o2bo11bobobobo117bo6bo$306b4o10bo38bobobo18b2o5bo7bo192bo6bo$320bo36b o7bo20b2obob3o5bo65b2obobob2o116bo6bo2b6o$359b5o25bo9bo$355bo11bo20bo 2bo76b3o$357b9o22bo2bo2$358b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 2 WIDTH 1800 HEIGHT 600 ]]

Oscillator stamp collection (click above to open LifeViewer) RLE: here Plaintext: here

x = 107, y = 86, rule = B2-a/S12Super 38.D4.2D$38.D.D4.4D$35.D2.D.D.2D$34.2D8.D2.D$37.6D.D2.D$36.D9.D$36.D 5.3D.D4.3D.3D$36.D.D7.D6.D3.D$38.D.D.3D.RD3.3D.3D$38.D.D5.D4.D5.D$42. D.D.D4.3D.3D$37.2D3.D.D.D$42.D.D.D$38.2D2.D.D2.2D$42.D2.D$39.2D.D2.D$ 36.3D3.D6$38.I4.2I17.I4.2I$38.I.I4.4I13.I.I4.4I$35.I2.I.I.2I15.I2.I.I .2I$20.K2.K10.2I8.I2.I10.2I8.I2.I$13.6K.K2.K13.6I.I2.I13.6I.I2.I$11. 2K9.K13.I9.I13.I9.I$18.3K.K.3A3.A5.I5.3I.I.3A3.A5.I5.3I.I.2K$10.3K.K 7.K4.2A.A2.A2.I.I7.I4.2A.A2.A2.I.I7.I5.4K14.2D$7.K6.K.K.3K2.K6.A2.A4. I.I.3I.2I6.A2.A4.I.I.3I2.I26.4D$7.K.4K.K.K5.K3.2A2.A.A2.2A.I.I5.I3.2A 2.A.A2.2A.I.I5.I3.2K2.K$7.K10.K.K.K7.A.A.A7.I.I.I7.A.A.A7.I.I.I7.K.K 15.2D2.D$7.K5.2K3.K.K.K2.2A3.A.A.A2.2I3.I.I.I2.2A3.A.A.A2.2I3.I.I.I2. 2K3.K.K.K17.D.D$9.K8.K3.K7.A.A.A7.I.I.I7.A.A.A7.I.I.I7.K.K.K12.2D3.D. D.D$9.K.K.3K2.K4.2K.A.A5.A3.2I2.I.I2.2I.A.A5.A3.2I2.I4.2I.K.K6.K16.D. D.D$6.K4.K6.K.2K4.A.A.3A2.A6.I2.I4.A.A.3A2.A6.I.2I4.K.K.3K2.K12.D.D6. D$.I4.K6.I.I.K3.K2.A.A7.A4.2I.I2.I2.A.A7.A4.2I.I3.3I.K8.K12.D.D.3D2.D $.I.2I3.I4.I.I2.K5.A5.3A.A.3I3.I5.A5.3A.A.3I3.I11.2K3.K12.D8.D$.I3.3I .4I2.I2.K5.A9.A13.A9.A13.K10.K16.2D3.D$.I12.I10.6A.A2.A13.6A.A2.A10. 2K.5K.K.K.K10.D10.D$I2.2I.I.I.3I.I7.2A8.A2.A10.2A8.A2.A19.K.K10.2D.5D .D.D.D$I.I3.I.I14.A2.A.A.2A15.A2.A.A.2A17.K2.2K.K.K.2K16.D.D$2.I.I.I. I.7I9.A.A4.4A13.A.A4.4A11.2K21.D2.2D.D.D.2D$4.I21.A4.2A17.A4.2A11.A6. 4K.3K11.2D$.2I.I3.2I5.I51.2A5.K4.K3.2K12.4DR3D$4.I8.I.I54.3A.K6.A14.D 4.D3.2D$3I.I2.3I.I.I2.I52.A6.A4.A14.D$4.I6.I4.I48.3A.A2.3A.A.A2.A$5. 3I.A6.I4.A47.A8.A.A$2.2I5.A4.A3.2A.A44.2A.A3.2A5.A17.3D.3D$3.I6.4A.3A 3.A47.A30.D3.D$7.2A12.A45.A.A.A.A.7A16.3D3.D$9.4A.A.A.2A2.A42.A.A3.A. A24.D5.D$14.A.A3.A.A42.A2.2A.A.A.4A19.3D3.D$6.7A.A.A.A.A45.A12.2A$18. A47.A3.3A.4A6.I$7.A5.2A3.A.2A44.A.2A3.A4.A5.2I$7.A.A8.A47.A4.I6.A.3I$ 6.A2.A.A.3A2.A.3A48.I4.I6.I$6.A4.A6.A52.I2.I.I.3I2.I.3I$6.A6.K.3A54.I .I8.I$3.2K3.K4.K5.2A51.I5.2I3.I.2I$5.3K.4K6.A11.2A4.A17.2A4.A21.I$14. 2K11.4A4.A.A13.4A4.A.A9.7I.I.I.I.I$3.2K.K.K.2K2.K17.2A.A.A2.A15.2A.A. A2.A14.I.I3.I.I$6.K.K19.A2.A8.2A10.A2.A8.2A7.I.3I.I.I.2I2.I$4.K.K.K. 5K.2K10.A2.A.6A13.A2.A.6A10.I12.I$4.K10.K13.A9.A13.A9.A5.K2.I2.4I.3I 3.I$4.K3.2K11.I3.3I.A.3A5.A5.I3.3I.A.3A5.A5.K2.I.I4.I3.2I.I$4.K8.K.3I 3.I.2I4.A7.A.A2.I2.I.2I4.A7.A.A2.K3.K.I.I6.K4.I$4.K2.3K.K.K4.2I.I6.A 2.3A.A.A4.I2.I6.A2.3A.A.A4.2K.K6.K4.K$4.K6.K.K.2I4.I2.2I3.A5.A.A.2I2. I.I2.2I3.A5.A.A.2K4.K2.3K.K.K$5.K.K.K7.I.I.I7.A.A.A7.I.I.I7.A.A.A7.K 3.K8.K$5.K.K.K3.2K2.I.I.I3.2I2.A.A.A3.2A2.I.I.I3.2I2.A.A.A3.2A2.K.K.K 3.2K5.K$7.K.K7.I.I.I7.A.A.A7.I.I.I7.A.A.A7.K.K.K10.K$9.K2.2K3.I5.I.I. 2A2.A.A2.2A3.I5.I.I.2A2.A.A2.2A3.K5.K.K.4K.K$16.I2.3I.I.I4.A2.A6.I2. 3I.I.I4.A2.A6.K2.3K.K.K6.K$8.4K5.I7.I.I2.A2.A.2A4.I7.I.I2.A2.A.2A4.K 7.K.3K$14.2K.I.3I5.I5.A3.3A.I.3I5.I5.A3.3A.K.3K$17.I9.I13.I9.I13.K9. 2K$16.I2.I.6I13.I2.I.6I13.K2.K.6K$16.I2.I8.2I10.I2.I8.2I10.K2.K$20.2I .I.I2.I15.2I.I.I2.I$15.4I4.I.I13.4I4.I.I$19.2I4.I17.2I4.I! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 4 WIDTH 600 HEIGHT 480 ]]

A period-384 drifter oscillator constructed by Dean Hickerson in August 2000. Components are color coded in Super mode by Jeremy Tan. (click above to open LifeViewer)

Spaceships

Banana or L-tetromino is a small natural c/6 diagonal spaceship called glider. Normally a glider can follow another on the same lane separated by at least 18 ticks, but two L-tetrominoes may be placed 11 ticks apart so that the rear one becomes a tagalong; this new c/6 diagonal spaceship is named big glider. In asymmetric soups, glider is the third most common object while big glider ranks 12th.

Spaceships have also been found for speeds between c/3 orthogonal and c/9 orthogonal with unit displacement.

x = 133, y = 40, rule = B2-a/S12 3o12b2o21bobo19bo14bo11bobo3bobo9bobo12bobo7bobo$obo12bo2bo14bo2bo5bo 2bo29bo13bo3bo11bobo14bo9bo$18bo3b2o9bobo7bobo12bo3bo10bo3bo27bobo22bo $20bo2bo8bo2bobobobobo2bo13bo44b3o22bo$4b2o12bobo9bo3b3obobob3o3bo8b2o bob2o22bobo5bobo3bo11bo$bobobo26b2o11b2o10bo2bo2bo25bo3bo6bob3obob3obo $bo18bo12bo11bo11bo2bo2bo24bobobobo5bobo2bobo2bobo$bo36bobo14b2o2b3o2b 2o6bobobobo9bo2bo2bo5bobo2bobo2bobo$6bo24bo5bo3bo5bo24bob3obo12bo8bo5b o5bo$2bo2bo25bo6bobo6bo23bo7bo11bo8bo2bo5bo2bo$2b2o2b2o24bo13bo11bobob o8bo7bo20bo2bo5bo2bo$2b2o67bo7bo20bobob2ob2obobo$31b3o11b3o10bo3bo8bo 2bobo2bo7bo7bo4bobobo3bobobo$32bo13bo12bobo9bo2bobo2bo5b3obo3bob3o2bob o7bobo$70bo3b3o3bo7bo5bo5bo11bo$57bo5bo8bobobobo9bo5bo5bo11bo$33bo11bo 11bo5bo8bobobobo9bo5bo5bobo7bobo$32bobo9bobo9bo7bo7bo5bo10b2ob2o6bo11b o$56bob2ob2obo10bo11bo7bo4bo3bobobo3bo$31bo3bo7bo3bo8bo7bo6bo7bo7bobo 3bobo4bob2obobob2obo$56bo7bo9b3o23bo3bo3bo3bo$30bo5bo5bo5bo7bobo3bobo 10bo10bobo5bobo3bo3bo3bo3bo$55bo9bo23bobobo6bo4bobo4bo$57bobobobo8b2o 3b2o11bobo7bo2bobobobo2bo$57bo2bo2bo26bobo7bo2bo2bo2bo2bo$56bo7bo6bo7b o10b3o7bo2bo5bo2bo$56bo7bo8bo3bo22bo2bo5bo2bo$100bo2bo5bo2bo$55bob3ob 3obo22bo2bo2bo5bo2bo2bo2bo2bo$55bo4bo4bo22bo2bo2bo5bo2bobobobo2bo$55bo 9bo25bo8bo2bobobobo2bo$55bo9bo21b2o5b2o4bo4b3o4bo$55bo9bo34bob2o5b2obo $55bo9bo34bo4bobo4bo$55bo9bo34bo11bo$55bobobobobobo34bo4bobo4bo2$57b7o $60bo41bobo3bobo$102bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 6 WIDTH 840 HEIGHT 400 ]]

Spaceships in Just Friends (click above to open LifeViewer)

Linear growth patterns

A glider can be reflected and duplicated by the period-236 oscillator, giving glider guns at multiples of 236.

Over-unity reactions can start with converting a big glider to a Y-tetraplet by a temporary domino. The Y-tetraplet is then perturbed by a line to produce two gliders and a line of three, or by a period-26 oscillator to produce two big gliders.

x = 53, y = 46, rule = B2-a/S12 27bo$26bobo$28bo2b3o$26bobo$26bobo$7bo$7bo$6bo$3b3o$20bo$b2obobo$2bob 5o10b2o$o2$obo4$17b3o$17bo27bobo$43b2o3b2o$15bo3bo23bobobob2o$17bo25b 2o3b5o$11b2o31b5o$45bobo$45b3o12$25bo$21bo3bo$21bob3o21bo$22bo22b2o4$ 22bo$22bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 WIDTH 600 HEIGHT 480 ]]

p236 glider gun by Kellie Evans, July 2000 (click above to open LifeViewer)

x = 53, y = 9, rule = B2-a/S12 10bo29bo2$8bob2o5bo20bob2o$8bo8bo20bo13bo$8b2o7bo20b2o8bo3bo$17bo28b2o 4bo$bo15bo13bo16bo3bo$bo15bo13bo20bo$o16bo12bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 WIDTH 720 GPS 5 AUTOSTART PAUSE 2 LOOP 130 ]]

Two related over-unity reactions with a passing glider (click above to open LifeViewer)

On basis of the multiple spaceships are various wickstretchers, puffers, rakes, and growing spaceships.

x = 119, y = 58, rule = B2-a/S12 33bo$7bo7bo2b16o$7bo3b2o$6bobo7b3obob4o2b3o9bo50bo$4b2o8bo3bo2bo3b2o6b 8o23b4o2b3o2b15o$7bo2bo17bo3bo31bobob2obo$6bo64bob2obobob2o3b3o10bo$4b o14b10o2b9o21b2o5bo2b2o10b2o6b6o$4b3o54bo16bo6bob3o$5bo4bobo48b3ob2o 19b2obo$3bo2bo2b2ob2o23b4o20bo2b2ob3o6b10o4b7o2bo$5bo4bobo27bo24b2ob2o $4b3o55bo4bobo$4bo14b10o2b4obo23b2o33b2o$6bo29bo25bo4bobo24bo3bo$7bo2b o17bo3bo5b3o24b2ob2o23b2o$4b2o8bo3bo2bo3b2o6b5obob2o18bo2b2ob3o6b10o4b 3obo$6bobo7b3obob4o2b3o30b3ob2o19b2obo4bo$7bo3b2o26bobo19bo16bo6bob3o 21bobo$7bo7bo2b16o27b2o5bo2b2o10b2o6b4ob2o3bo9bobo$33bo37bob2obobob2o 3b3o7bo5bo4b2o4bo4b2o$50bo13bobob2obo29bo$30bo17b2o14b4o2b3o2b15o10b2o $4bo7bo2b16o7bo52bo$4bo3b2o28bo65bo$3bobo7b3obob4o2b3o77bo$b2o8bo3bo2b o3b2o6b5o3b3o20bo40b2obo$4bo2bo17bo3bo7bo21b2o42bo$3bo30bo68bo$bo14b 10o2b5o60bo$b3o90bo$2bo4bobo27bo34bo18b2obo$o2bo2b2ob2o23b4o32b2o20bo$ 2bo4bobo82bo$b3o78bo$bo14b10o2b9o46bo$3bo76b2obo$4bo2bo17bo3bo40bo10bo $b2o8bo3bo2bo3b2o6b8o17b14obo10bo$3bobo7b3obob4o2b3o9bo5bobo2b3obo16bo 5b3o$4bo3b2o33bobobo2bo4bobob2o2b5o7bobo$4bo7bo2b16o10b2o3bo5bo2bobo5b o7b3obobo$30bo25bo6b3obo9bo$41b2o23b2o5bo$41bo14b16obo$40b4obob3o$42bo bo2bobo27bo$39b3obob3ob2o23b2obo$42bobo2bobo26bo$40b4obob3o$41bo14b21o $41b2o23b2o$56bo6b3obo8bo$41b2o3bo5bo2bobo5bo7b5obo$43bobobo2bo4bobob 2o2b5o9bo$43bobo2b3obo16bo$55b14obo$70bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 6 WIDTH 800 HEIGHT 400 ]]

A breeder built by David Bell in August 2000. This uses a c/5 period-30 backward big glider rake and a period-30 c/5 sparking ship to create a row of c/3 wickstretchers. (click above to open LifeViewer)

Clean rakes at c/5 orthogonal can be made by combining puffers. Engineered adjustable rake at c/4 orthogonal also exists, though much larger. In July 2000, David Bell constructed a slightly dirty period-8256 forward rake for the 3-cell glider, which consists of a flotilla of c/4 orthogonal spaceships that circulate and duplicate gliders to burn a wick repeatedly. Its cleanup system was completed by FWKnightship in August 2019.

Signal circuitry

The period-26 oscillator can be used as a glider reflector at 180 degrees or 90 degrees. However, a 90-degree reflection delays the Y-tetraplet by 11 generations which requires a longer supporting line. The phase shift means that it can reflect a contiguous period-37 glider stream. If M is the number of contiguous period-37 gliders in the loop and N is the number of contiguous period-26 gaps in the loop, then glider loops can be built for any period of the form 37M + 26N, where M > 0 and N > 0.

A stable 90-degree big glider reflector with repeat time 76 was found in a symmetric soup and reported on October 26, 2022.

x = 52, y = 52, rule = B2-a/S12 20b7o2$23bo$23bo2$21bo3bo2$23bo13$51bo$48bo2bo$47bobobo$46bo4bo$47bobo bo$o47bo2bo$o3bo36bo9bo$o5bo$obo38b2o$o5bo$o3bo$o2$34bo$35b2o5$22b2o4b o$28b3o$22bo6$27bobo$27bobo$27bobo2$25b7o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 WIDTH 480 HEIGHT 480 ]]

Period-408 (= 37 × 4 + 26 × 10) glider loop found by David Bell in June 2000. (click above to open LifeViewer)

x = 36, y = 28, rule = B2-a/S12 29bo$29bo$22b6o$29b2o$24bo2$24bo$6bo17bo$6bo$8b6o$5b2o26bo$11bo21bo$ 33bo$11bo21bo$11bo21bo$33bo$32bo$2bo29bob2o$2bo29bo$2bo$2bo$2bo$2bo$3b o$2obo9b3o$3bo3b6o3b6o$14bo$14bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 WIDTH 480 HEIGHT 400 ]]

Period-252 big glider loop (click above to open LifeViewer)

See also

• OCA:Just Friends/3-cell spaceship

External links

• David Bell (November 12, 2017). "Archive of Just Friends objects (.zip download)". Retrieved on November 21, 2022.
• Just Friends at Adam P. Goucher's Catagolue
• MCell built-in General binary rules: JustFriends at Mirek Wójtowicz's Cellebration page
• Just Friends (B2-a/S12) (discussion thread) at the ConwayLife.com forums
• SansDomino rulespace (discussion thread) at the ConwayLife.com forums