User:TheWayOfTheCon/Various discoveries in Range-2 OT rules

Since April 2026, I've been looking at the range-2 larger than life rulespace, as it would be not too far removed from normal Life-like rules, but not too far removed from higher-range LTL, which might be interesting. My goal has been to find a rule similar in potential or nature to Conway's Game of Life (so basically a good rule), and doing so, I've come across many interesting and uninteresting things. And so, I've finally decided to lay those findings down in a user page.

Specific patterns

Range-two switch engine

In the rule S6-10,18, B7,9-10 there is a common 8c/118 diagonal puffer quite similar to the switch engine, except it does not fail. It has been corderized by a user named MDA.

x = 51, y = 41, rule = R2,C2,S6-10,18,B7,9-10 26b2o$26b3o$26b3o$26b2o5$18b2o$18b3o$18b3o$18b2o3$48b2o$47b4o$10b2o35b 4o$10b3o$10b3o$10b2o3$40b2o$39b4o$3b2o34b4o$3obo$3obo$3bo3$32b2o$31b4o $31b4o4$7bo$5b2o2bo$5b2obo15b2o$6b3o14b4o$23b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART LOOP 236 ZOOM 15 TRACK -8/118 8/118 WIDTH 500 HEIGHT 500 X -16 Y 16 ]]

(click above to open LifeViewer)

x = 92, y = 119, rule = R2,C0,S6-10,18,B7,9-10 8b2o$8b3o$8b3o$8b2o5$2o$3o$3o$2o5$20bo$18b2o$18bo2bo$18b3o$19b2o11b2o$ 32b3o$33bobo$33b4o$35b2o$3bo$b2o$bo2bo$b3o$2b2o$14b3o$13bo2bo$14b2o$ 14b2o$14bobo$38bo$17b2o17b2o2bo$17b3o16b2obo$17b3o17b3o$17b2o14$20bo$ 18b2o$18bo2bo$18b3o39bo$19b2o37b2o$31b3o24bo2bo$30bo2bo24b3o$31b2o26b 2o11b2o$31b2o39b3o$31bobo39bobo$73b4o$34b2o39b2o$34b3o$34b3o$34b2o8$ 78bo$76b2o2bo$76b2obo$77b3o3$37bo$35b2o$35bo2bo$35b3o$36b2o$48b3o$47bo 2bo$48b2o$48b2o$48bobo38b2o$88b4o$51b2o35b4o$51b3o$51b3o$51b2o3$81b2o$ 80b4o$80b4o6$73b2o$72b4o$72b4o$54bo$52b2o$52bo2bo$52b3o$53b2o$65b3o$ 64bo2bo$65b2o$65b2o$65b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART LOOP 236 ZOOM 4 TRACK -8/118 8/118 WIDTH 800 HEIGHT 600 ]]

Corderized with 8 engines. (click above to open LifeViewer)

Photon

In S3, B3 there is a photon that strongly resembles the Moon found in explosive rules like Seeds. Because it is in a range-2 rule, it moves at two cells per generation (equivalent to the speed of light in this neighborhood). This probably exists in other rules but this is the only one I've found where it stays as a spaceship.

x = 15, y = 10, rule = R2,C2,S3,B3 6b3o$5bo3bo$5b2ob2o2$4bo5bo$3b2o5b2o$b2o9b2o$ob2o7b2obo$2obo7bob2o$b2o 9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 2 LOOP 12 TRACK 0 -2 WIDTH 500 HEIGHT 500 ]]

(click above to open LifeViewer)

Elementary flamingoship

Yep, you read that right. In a Pottery variant (S4,6-9,20-24, B7-9,19-22), there exists a somewhat common spaceship moving flamingowise at (6,1)c/20. I think this is also the first oblique spaceship I've discovered in any OCA.

x = 9, y = 8, rule = R2,C2,S4,6-9,20-24,B7-9,19-21 4bo$3b4o$2b2ob3o$2o5b2o$o7bo$2o5b2o$b3o2b3o$2b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART GPS 20 LOOP 60 TRACK 6/20 -1/20 WIDTH 600 HEIGHT 500 ]]

Amazing. Might make this my new profile picture on the forums. (click above to open LifeViewer)

Specific rules

Pottery (S4,6-9, B7-9)

Pottery
x=64, y = 64, rule = R2,C2,S4,6-9,B7-9,NM ! #C [[ THEME Fire ]] #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	R2,C2,S4,6-9,B7-9,NM
Character	Chaotic

This rule, which I have nicknamed Pottery, is the most promising (along with its variants) range-2 rule I have seen during my investigation. It features moderately long-lived chaos and two elementary spaceships. Its name comes from an oddly-specific class of large still lifes that frequently appear. They are hollow, geometrical, fragile, and come in many different shapes, just like actual pottery. A few high-period oscillators exist as well, such as a sparky period-34 and period-50.

x = 87, y = 59, rule = R2,C2,S4,6-9,B7-9 16b2o5b3o16b3o8b2o5b2o7bo$15b4o4b3o15b4o8b3o3b3o6b3o$14b2o2bo3bo3bo14b o3bo6b4o3b4o5bob2o$14b2o2bo3bo3bo18bo6b3o5b3o4bo2b2o$15b3o5b3o16b3o10b o3bo7b2obo19$3b2o52bo2bo$2b4o30bo19bo4bo$b2ob2o30bobo16bo6bo15b2o$2o2b o31b2o17b2o4b2o15b2o$5o31b2o18b2o2b2o15b3o$4o$b2o28b4o43b2o$10b2o21b2o 2bo41bo$3bo4b5o19bo47bo$4bo2b2o2b2o68b2ob3o$6b3ob2o44b2o2b2o20bob3o$6b 5o44b2o4b2o21bo$7b3o45bo6bo$56bo4bo$57bo2bo16$28b3o13b3o14bo$27b2ob2o 11b2ob2o12b3o$27bo3bo11bo3bo12b3o$27b2ob2o11bo3bo12b3o$28b3o12b5o12b3o $44b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 800 HEIGHT 600 ]]

Various patterns in the rule, including high-period oscillators, elementary and rare spaceships, and pottery predecessors. (click above to open LifeViewer)

S5-9, B7-9

S5-9, B7-9
x=64, y = 64, rule = R2,C2,S5-9,B7-9,NM ! #C [[ THEME Fire ]] #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	R2,C2,S5-9,B7-9,NM
Character	Chaotic

This rule harbors some life-like dynamics, such as recognizable evolutionary sequences, spurty and long-lived chaos, and a couple constellations. Unfortunately, no spaceships exist in this specific rule, and within the whole rulespace I have found just a couple.

S4,6-9,20, B7-9,18 (HighPottery)

See also: TheWayOfTheCon/Pottery

HighPottery
x=64, y = 64, rule = R2,C2,S4,6-9,20,B7-9,18,NM ! #C [[ THEME Fire ]] #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	R2,C2,S4,6-9,20,B7-9,18,NM
Character	Chaotic

This rule, which I've named HighPottery (or simply Pottery on the forums) is a variant of Pottery which I have found to be better to work with, and ultimately the rule I will continue to investigate. It shares many patterns and similarities with Pottery, but has more common spaceships, greater chaos, and a few more high-period oscillators.