User:Iddi01/OCA:tflock2

tflock 2
x=64, y = 64, rule = B3-n/S1e2-a3-e4e ! #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
Rulestring	1e2-a3-e4e/3-n B3-n/S1e2-a3-e4e
Character	Chaotic

tflock 2 is an isotropic non-totalistic cellular automaton devised by iddi01 at March 23, 2024. It was initially referred to as tflock, whose name is already taken. The ash of random patterns resembles a midpoint of flock and tlife.

Patterns

Still lives

The domino is the most common still life, being slightly less common than the t-ship.

Still lives up to 35 cells have occurred naturally. The most common 35-bit still life is shown below:

x = 6, y = 15, rule = B3-n/S1e2-a3-e4e b2o$o2bo$4o2$2b3o$5bo$6o2$5o$5bo$2b3o2$4o$o2bo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer) Catagolue: here

Oscillators

tflock 2 is omniperiodic, having a 90-degree reflector with repeat time 18, and (semi-)natural occurrences of all periods below 18.

The most common non-trivial oscillators of each period up to 11:

x = 115, y = 14, rule = B3-n/S1e2-a3-e4e 94bo$71bo7bo11bo2bo2bo$70bobobobobobo10bobobobo$57bo3b2o7bobobobobobo 12bob2o12bo$44b2o8b2obo13bo2bobo2bo13bo13bobob2o$43bobo11bo2b3o44bobo 3bo$14bo18b3o7b3o27bo39bo$14bo8bo9bobo23b2o10bobo35b2o$12bo10bo9bobo8b 2o27bo$2bo11bo9bo8b3o7bo13b4o$b2o9bo9b2o19bo12bo$bo10bo43bobo$57bobo$ 58bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Semi-natural occurrences of non-trivial oscillators periods 12 to 17:

x = 170, y = 37, rule = B3-n/S1e2-a3-e4e 3$151b2o2b2o$151b2o2b2o$151b2o2b2o$144b2o16b2o$143bo20bo$143bo20bo$61b 2o18bo2bo$61b3o17bo2bo$62bo18bo2bo2$8bo8bo11b2o11b2o22bo37b2o5bo9bo5b 2o$6bobo8bobo8bo15bo14bo5b3o35bo2bo4bo3bobo3bo4bo2bo10b3o22b3o$4bobo 12bobo6bo15bo14b2o5b2o7b3o10b3o12bo2bo3bo11bo3bo2bo10b3o22b3o$4bo2bo4b 2o4bo2bo12bo3bo18b2o2bo41bo2bo4bo3bobo3bo4bo2bo$7bo3bo2bo3bo15bo3bo19b o2b2o41b2o5bo9bo5b2o$11bo2bo19bo3bo13b2o5b2o14b3o10b3o49b3o22b3o$11bo 2bo13bo15bo7b3o5bo79b3o22b3o$12b2o14bo15bo8bo$29b2o11b2o$57bo23bo2bo$ 56b3o22bo2bo$57b2o22bo2bo$143bo20bo$143bo20bo$144b2o16b2o$151b2o2b2o$ 151b2o2b2o$151b2o2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Spaceships

x = 2, y = 3, rule = B3-n/S1e2-a3-e4e o$2o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 4 AUTOSTART TRACKLOOP 2 0.5 0 GPS 2 ]]

The t-ship, the most common and useful spaceship in tflock 2.
(click above to open LifeViewer)

There are natural spaceships of simplified speeds c/2 and c/3:

x = 82, y = 17, rule = B3-n/S1e2-a3-e4e $51bo$22bo6bo10bo9b4o14b3o$21b3o4bobo7b2obo12bo13bo2bo2b3o$7b3o10bo6b 2ob2o7bob2o11b2o12bo3bo$6bo65b3o$5bo4bo61bo$6bo2b2o30b3o10b3o$40bo12bo $41bo12bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

There are also unnatural spaceships of c/4, 2c/5, 3c/9, and 16c/48 orthogonal, and c/4, c/5 diagonal:

x = 213, y = 66, rule = B3-n/S1e2-a3-e4e 13$18b2o$15b3o2bob2o$14bo2bo3bo$13b2obo3bobo$14b2o2b2o$17b3o$16b3obobo $9bo12bob2o$8bobo15bo$7b2o13bo3bo33b2obo14b2o5b2o11b2o5b2o9b2o9b2o6bo 11bo$6b2o3bo10b2o2bo32bo3b2o15b2ob2o15b2ob2o9b2obo9bob2o2b2ob2o7b2ob2o 6bo28bo$11bo10b3o2bobo29bo15b4o2bobo2b4o5b4o2bobo2b4o7bo9bo6bo13bo5b2o b2o4b3o10b3o4b2ob2o$5bo23b3o26b2o19bobobobo13bobobobo11bo9bo6bo13bo6bo bo5bob2o8b2obo5bobo$5bo3b2o15bo4b2o23b3o18bo3bobo3bo9bo3bobo3bo7bo13bo 6b2o7b2o15bo16bo24b3o$6bo15b2o31bo23bo5bo13bo5bo9b2o2bo5bo2b2o5bo11bo 10bo24bo17b4ob4o$9bobo9bo3b4o26bo22b2o5b2o11b2o5b2o12bo5bo12bo5bo12b3o bo3bobo6bobo3bob3o20bo$6b2obo2b2o6bo8b3o44b3obo3bob3o7b3obo3bob3o29b2o 3b2o14b4obo3bo4bo3bob4o20b2ob2o$6b2o4bo2b3o2bo5bo3bo24b2o23bo3bo15bo3b o14bobobobo13bo3bo21bobo6bobo27bobo$7bo7b3obobo9bo24bo20b3o2bo2b3o9b3o 2bo2b3o11bo2bo2bo12b2obob2o13bo7bo8bo7bo20bobo$12b2o2b2o12b2o50bo19bo 13b3obobobob3o7bo4bo4bo10bo3bo18bo3bo$13bo3bo3bo9b3o84bobobobobo7b2obo bobobobob2o9bo24bo$17bo2b3o6b2o46bo9bo9bo9bo14bo11b2obobobobobob2o$14b o2bo2b2o6bo51b5o15b5o17bo14bobobobobo10bo28bo$16b2o2bo2bo3bo4b3o41b3o 7b3o7b3o7b3o27bo2bobobo2bo8bobo26bobo$20bo6bo5bo9b3o35b3o17b3o17bobo 12bo2bobobo2bo7b2ob2o24b2ob2o$18bobo2b2o2bo7b3o4b4o31bo9bo7b2o11b2o10b o3bo14bobobo$18bo6bob2o5b2o2b2o2bo32b2o3b5o3b2o7bo2b5o2bo13bobo$19bo5b 2obobo6b2obobo36bo5bo7b2o4bo5bo4b2o9bobo16b3o14b3o22b3o$29b2o8b2obo2bo bo34bo19bo18bobo35b4o16b4o$29b2o8b2obo2bo33b2o3b2o13b2o3b2o33bo3bo$30b o11b2o2bobo33bo19bo36b2ob2o15b3o18b3o$37b3ob3o3bo30bo7bo11bo7bo32bo3bo 14b3o20b3o$31b2o4bo3b2o34b3o5b3o9b3o5b3o49b2o4bo14bo4b2o$31b2o4bo124bo bo3bo4bo3bobo$32bo2bob2o36bobo9bobo5bobo9bobo55bobo6bobo$34b2ob2o35bo 2bo9bo2bo3bo2bo9bo2bo51bobo3bo4bo3bobo$31bo3b2o38bo13bo5bo13bo$30b3o$ 30bo$30b3o$30b2ob2o$34bo2bo$35bo$36bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

(click above to open LifeViewer)

Infinite growth

tflock 2 has a surprisingly large numbers of distinct puffers, wickstretchers, and rakes. The natural 5c/10 alone has several different combinations that create infinite growth:

x = 90, y = 11, rule = B3-n/S1e2-a3-e4e 2$9b3o4b3o20b3o5b3o20b3o6b3o$3b3o2bo2bo4bo2bo2b3o8b3o2bo2bo5bo2bo2b3o 8b3o2bo2bo6bo2bo2b3o$7bo3bo4bo3bo16bo3bo5bo3bo16bo3bo6bo3bo$5b3o12b3o 12b3o13b3o12b3o14b3o$7bo12bo16bo13bo16bo14bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 10 LOOP 60 ]]

(click above to open LifeViewer)

There is a natural period-12 gun, along with a double-barrelled variant of it:

x = 13, y = 47, rule = B3-n/S1e2-a3-e4e 3$8bo$6bobo$4bobo$2bobo3bo$2bobobobo$6bobo$7bo$8b2o17$7b2o$6bo$5bobo$b obobobo$bobobobo$3bobo$bobo3bo$bobobobo$3bobo$bobo3bo$bobobobo$5bobo$ 6bo$7b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 8 LOOP 60 ]]

(click above to open LifeViewer)

Constructed guns include:

x = 140, y = 101, rule = B3-n/S1e2-a3-e4e 32$39bo$37bobo44b2o16b2o30bo$35bobo63bo32bobo$35bo47b2o17b2o32bobo$ 138bo$82b2o9b3o5b2o$94bo$101b2o26b2o2$130b3o2$99b2o28b2o2$95bo2b2o$94b obo$92bobobob2o$92bo3bo3$129b2o2$128b2o2$127b2o2$134b3o$135bo4$9b2o$ 68b2o59b2o$8b2o22bo4b2o$30bobo34b2o61b2o2bo$7b2o23bo100bobo$66b2o62b2o bobobo$133bo3bo19$39bo$38b3o3$42bo$40bobo$38bobo$38bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 40 LOOP 336 ]]

(click above to open LifeViewer)

There are also two patterns with unusual growth rates:

x = 175, y = 186, rule = B3-n/S1e2-a3-e4e 52bo7bo12bo7bo$50b2ob2o4bobo10bobo4b2ob2o$51bobo4b2ob2o8b2ob2o4bobo2$ 54bo24bo$53b3obo18bob3o$55b4o16b4o$61b3o6b3o$54bo24bo$53bo3bo4bo8bo4bo 3bo$54bo24bo2$52bo$51bobo$50b2ob2o26b3o$81bobo$60bo12bo6bo3bo$53b3o6bo 2bo2bo2bo$2bo7bo12bo7bo23b4o3bo2bo2bo2bo2bo4b3o$2ob2o4bobo10bobo4b2ob 2o28bo2bo2bo2bo4b2o$bobo4b2ob2o8b2ob2o4bobo22b3o2bo12bo5bo$54b3o20b3o$ 4bo24bo23b2o$3b3obo18bob3o49b2o$5b4o16b4o2$4bo6b3o6b3o6bo$3bo3bo18bo3b o31bo8bo$4bo7bo8bo7bo$61b3o6b3o$2bo28bo$bobo26bobo$2ob2o24b2ob2o25b2o$ 12bobo4bobo36bo2bo$12bo2bo2bo2bo37b2o$3b3o6bobo4bobo6b3o$5b4o16b4o2$5b 3o18b3o$4b3o20b3o$3b2o7bo8bo7b2o$73bo$11b3o6b3o51b3o$75bo5$9b2o12b2o 16bo$8bo2bo10bo2bo14b2o37bo$9b2o2b2o4b2o2b2o16bo37b2o$79bo4$143bo7bo 12bo7bo$141b2ob2o4bobo10bobo4b2ob2o$142bobo4b2ob2o8b2ob2o4bobo2$145bo 24bo$144b3obo18bob3o$146b4o16b4o2$145bo24bo$45bo98bo3bo4bo8bo4bo3bo$ 43bobo57bo41bo6bobo6bobo6bo$45bo57b2o44bobo3bo4bo3bobo$71bo31bo39bo5bo 7b2o7bo5bo$142bobo6bo3bo4bo3bo6bobo$70b3o68b2ob2o6bobo6bobo6b2ob2o$ 153bo8bo2$144b3o22b3o$146b4o16b4o2$146b3o18b3o$145b3o20b3o$144b2o24b2o 3$69bo$67bobo3bo53bo22b2o12b2o$69bo4b3o50b2o20bo2bo10bo2bo$75bo51bo22b 2o2b2o4b2o2b2o14$135bo$135bobo$135bo8$71bo2$70b3o4$111bo$111bobo$111bo 14$87bo$87bobo$87bo$60b3o$60bobo$59bo3bo2$62b3o$66b2o$64bo$64b3o2$62b 2o3$121bobo$118b2obobob2o$65b2o50bo3bobobobo$64bobo4bo45bo8b2o$64b2o$ 70b3o51b5o$68bo$67b3o55b2o2$124b2o$126bo$126bo$101b2o$125b3o$68bo30b5o $59bobo5b3o55b3o$59bobo38b2o8bo11bo$100bobobobo3bo9bobo2b2o$101b2obobo b2o10bobobobo$62bo3bo37bobo15bob2o$61bobobobo54bo$60bo7bo$61bobobobo$ 51b2o9bo3bo9b2o$57bo13bo$51b2o3bobo11bobo3b2o$55bo3bo9bo3bo$56bobo11bo bo2$56bobo11bobo$55bo3bo9bo3bo$51b2o3bobo11bobo3b2o$57bo13bo$51b2o9bo 3bo9b2o$61bobobobo$60bo7bo$61bobobobo$62bo3bo3$59bobo5bobo$59bobo5bobo ! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ THUMBNAIL THUMBSIZE 2 ZOOM 1 ]]

Logarithmic growth (click above to open LifeViewer)

x = 46, y = 71, rule = B3-n/S1e2-a3-e4e 13$11b2o23b2o2$10b3o23b3o2$9b2ob2o21b2ob2o$14bo19bo$8b2ob3obo17bob3ob 2o$15bo17bo28$24bo$24bo$13b2o9bo9b2o2$12bo3bo15bo3bo$16b2o2bo3bo3bo2b 2o$13b4o3b2ob3ob2o3b4o4$23b3o$20b2ob3ob2o$20bo7bo$20bobo3bobo2$21b2o3b 2o3$21bo5bo$22bo3bo$23b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]

Sawtooth alongside linear growth (click above to open LifeViewer)

Reactions

x = 40, y = 16, rule = B3-n/S1e2-a3-e4e 3$38b2o$14b2o$38b2o2$36b4o$o13bo$2o10bobo21b4o$o13bo$36b4o2$38b2o$14b 2o$38b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 25 LOOP 150 ]]

A semi-reflector, outputs one t-ship for every two
(click above to open LifeViewer)

tflock 2 is suitable for engineering, for reflectors and splitters are relatively easy to find. Here's a collection of small reflectors:

x = 19, y = 45, rule = B3-n/S1e2-a3-e4e 2$4b2o9bo$15bobo$2b5o8bo2$3b2o8bo$3bobobobo3bo$4b2obobob2o$7bobo3$5b2o 7bo$14bobo$6b2o6bo2$7b2o5$5b4o$5bo2bo5bo$5b4o5bobo$14bo5$6b2o$5bo2bo$ 5bo2bo7bo$5bo2bo6b2o$6b2o8bo4$15bo$6bo8bobo$6b2o7bo$7bo$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 15 LOOP 40 ]]

(click above to open LifeViewer)

Collection of splitters with non-overlapping output:

x = 147, y = 83, rule = B3-n/S1e2-a3-e4e 13$56bo$53b2obo8bobo$52bobobobo3b2obobob2o$52b2o2bobo2bo3bobobobo$56bo 4bo8b2o64b2o$51b3o$68b5o63b3o$51b3o$69b2o3bo62b3o$52bo21bo50bo$52bo19b 2o51b2o12b2o$53b2o68bobo$124bo15b2o$50b2o$141b2o$49b2o$95bo46b2o$48b2o 43bobo32bo$79bo3bo7bobo9bo24bo$79bobobo7bo11bobobo21b2o$81bo23bobo$81b o$53bo52b3o$53b2o50bo32bo$53bo9b2o41b2o28bobobo$136bobobo$107b2o10$54b o$54bobo$56bobo$7bo24b2o24bo$7bobo57bo$6b2obo21b2o32bobo$5bo2bo32b2o 20bobo$6b2o22b2o11bo19bo$43bo$7b3o19b3o2$7b2o10b2o7b3o$21bo$6b3o12bo5b 2o$43bo$5b3o35bo$41b2o$4b2o$21b2o17b2o2$21b2o15b3o2$39b2o$20b2o11bo$ 32b3o$21b2o2$10bo$9b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 30 LOOP 300 ]]

(click above to open LifeViewer)

On April 22, 2024, iddi01 enumerated all possible collisions between two t-ships:

x = 95, y = 287, rule = B3-n/S1e2-a3-e4e 8$10bo$10b2o$10bo$20bo$19b2o$20bo3$10bo$10b2o$10bo9bo$19b2o$20bo7$10bo $10b2o8bo$10bo8b2o$20bo6$10bo9bo$10b2o7b2o$10bo9bo7$10bo10bo$10b2o8b2o $10bo10bo6$10bo$10b2o9bo$10bo9b2o$21bo5$10bo$10b2o$10bo10bo$20b2o$21bo 4$10bo$10b2o$10bo$21bo53bo10bo$20b2o53b2o9bobo$21bo53bo10bo4$10bo$10b 2o9bo$10bo10bobo$21bo5$10bo$10b2o$10bo10bo$21bobo$21bo4$10bo$10b2o$10b o$21bo$21bobo$21bo4$10bo$10b2o$10bo2$14bo$13b3o5$10bo$10b2o$10bo4$14bo $13b3o6$10bo$10b2o$10bo5$14bo$13b3o6$10bo$10b2o$10bo6$14bo$13b3o6$10bo $10b2o$10bo7$14bo$13b3o6$10bo$10b2o$10bo8$14bo$13b3o4$14b2o$13bo$13bo 4$10bo$8bobo$10bo2$14bo$13b3o13$9bo$7bobo$9bo2$14bo$13b3o7$10bo$10b2o$ 10bo5$13b3o2$14bo13$7bo$5bobo$7bo2$14bo$13b3o6$6bo$4bobo$6bo$14bo$13b 3o16$85bo$85b2o$85bo3$89bo$88b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ ZOOM 1.5 AUTOSTART GPS 30 LOOP 250 T 0 PAUSE 3 ]]

All the possible collisions between two t-ships (click above to open LifeViewer)

All the possible collisions between a t-ship and a domino:

x = 15, y = 74, rule = B3-n/S1e2-a3-e4e 3$4bo$2bobo$4bo5b2o9$4bo$2bobo5b2o$4bo7$4bo$2bobo$4bo$10b2o10$10b2o2$ 4bo$2bobo$4bo10$4bo6bo$2bobo6bo$4bo6$11bo$4bo6bo$2bobo$4bo6$4bo$2bobo$ 4bo$11bo$11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ T 0 PAUSE 2 AUTOSTART GPS 15 LOOP 50 ]]

(click above to open LifeViewer)

Universality

On June 12, 2024, iddi01 constructed a Rule 110 emulator in tflock 2, proving the rule Turing-complete.

Variants

Arrow
x=64, y = 64, rule = B3-jkn4a/S1e2-a3ijnry4n ! #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
Rulestring	1e2-a3ijnry4n/3-jkn4a B3-jkn4a/S1e2-a3ijnry4n
Character	Chaotic

There is a more stable variant discovered in 2018, named Arrow, partly due to this series of adjustable-speed rakes:

x = 135, y = 27, rule = B3-jkn4a/S1e2-a3ijnry4n 4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo$4bo13bo13bo13bo13bo13bo13bo13b o13bo13bo3$2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o 5b2o5b2o5b2o5b2o5b2o2$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo$4bo13bo 13bo13bo13bo13bo13bo13bo13bo13bo4$3b3o$4bo12b3o$18bo12b3o$32bo12b3o$ 46bo12b3o$4bo55bo12b3o$4bo13bo55bo12b3o$18bo13bo55bo12b3o$32bo13bo55bo 12b3o$46bo13bo55bo12b3o$60bo13bo55bo$74bo13bo$88bo13bo$102bo13bo$116bo 13bo$130bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 40 LOOP 300 ]]

(click above to open LifeViewer)

External links

• tflock 2 (discussion thread) at the ConwayLife.com forums

• tflock 2 at Adam P. Goucher's Catagolue