or, in partial notation (note that 8s are optional):
pB2n3aceijknr-qy4qy-ainrwz5-acijknr6-aei78S2aceik-n3ceijnqr-a4atz-ijknrwy5-aijr6-k78
The "type rule" is B2n3-qy4eqy6n7c/S2-n3-a4atz5k
(maybe it's worth it to narrow it down more, like at most N transitions away from the type rule, but I'm not sure how to do it or if it makes much of a difference)
These 2^28 rules contain very interesting dynamics for high-period oscillators and spaceships as well as complicated puffers and rakes with wildly differing mechanisms depending on the rule. They have high engineering potential just from the sheer numbers of sparky objects but also have many endemic or near-endemic patterns.
From a previous post in Misc Disc O C A:
And some new addenda.Rhombic wrote: May 16th, 2026, 5:17 pm Reaction-based triple rake with two consecutive 90º reflections and sextuple rake:Code: Select all
x = 14, y = 9, rule = B2n3-qy4qy7c/S2-n3-a4atz8 11b3o2$3b3o$6bo$obo2b2o$o6bo$b3obobo$5bob2o$4b2ob2o!c/160d:Code: Select all
x = 75, y = 40, rule = B2n3-qy4qy7c/S2-n3-a4atz6i 73b2o$72bobo$72b2o9$40bobo$40bo2bo4b2o$40bo2bo4b2o$40bo3bo3b2o$41bo3bo $41b2o2bo$45bob2o$46b3o$46bo$43b5o$43b2ob2o$45b2o15$b2o$obo$2o!(13,3)c/159 puffer and 23c/312d:Code: Select all
x = 3, y = 4, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5y bo$obo$2o$bo!Code: Select all
x = 4, y = 3, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5k b3o$2obo$3o!In a rule combining the two previous ones, a glide-symmetric 6c/500 with transient gliders (and a rake from 2x):Code: Select all
x = 5, y = 14, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5k o$o$o8$2b2o$2bobo$2b3o$3b2o!Code: Select all
x = 8, y = 42, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5ky b2o$3o$2o10$5b2o$5bobo$6b2o7$7bo$5b3o$4bo2bo$5b2o$5b2o14$4b2o$3b3o$3b 2o!Knightrake:Code: Select all
x = 78, y = 30, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5ky 15b3o6b2o$15bo6b5o$14bo2bo4b2o3bo$15bo6bo4b2o$21b3o2b2o$b2o$obo$2o$32b o7b2o$33b2o4bobo$32b2o5b2o5$59b2o$59bobo$59bobo$60bo4$37b2o$36bobo$36b 2o$76b2o$75bobo$70bo4b2o$71b2o$70b2o!Code: Select all
x = 6, y = 10, rule = B2n3-qy4ceqty7c/S2-n3-a4atz5k 3o$2obo$obo$obo$b2o$3o$bobo$b2ob2o$2bob2o$3bo!
Complex natural rakes and a double knightrake:
Code: Select all
x = 18, y = 18, rule = B2n3-qy4eqy6n7c/S2-n3-ak4atz5ky6e
7bo$4bo2b2o$3b2ob2o2$o3b2o$3bobo$3b2ob2o$6bo$5bobo$6bobo7bo$9bobo3b3o$
8bob2o3bo$9bo2b2o$11bobob2o$11b2o2bo3$13bo!
Code: Select all
x = 68, y = 64, rule = B2n3-qy4eqy6ck7c/S2-n3-a4aetz5ky7
62b2o$61bobo$62bo4$18b2o47bo$17b3o47bo$16bo3bo6bo39bo$18b2o5b2obo$15b
4ob4ob2ob2o$15b3o2b2obo5bo$15bob2o2bo$16b4o4bo2bo$17b2o2bobo2b3o3bo$
20b3o4bo2bobo$19bobo2bobo$23bo$21bo2$45bo$44b4o$43bo$42b2o5bo$42b3o2b
3o$42b2ob2ob3obo$43b2obo$5b2o39bo2bo$5bobo37bob2o$6bo37b3o$45bo4$3o4$
34b3o$33b4o27bo$32b2o31b2o$34b2o28b2o$32bo2bo$34bo$32b3o2b3o$39bo$36bo
b2o$36b2o7$62b2o$61bobo$62bo4$67bo$67bo$67bo!
Code: Select all
x = 12, y = 11, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5k6n7e8
10bo$9bobo$9b2o4$2bo$4o$2bo$2bo$2o!
Code: Select all
x = 11, y = 11, rule = B2n3-qy4eqy5ce6n7c/S2-n3-ak4atz5eky6i
6b3o$5bo3b2o$5b2o3bo$b2o4bo2bo$2obo4b3o$2bo5b2o$8b2o$7b2o$5bo2bo$5bobo
$6b2o!
Code: Select all
x = 10, y = 17, rule = B2n3-qy4ceqy6n7c8/S2-n3-ay4atz5ky6a
7bo3$7bo4$3b2o$4bo2b2o$4b2ob3o$4bo2b2o$3b5o$2b2obobo$o3bo2bo$2bobob2o$
7o$bo!
Code: Select all
x = 3, y = 6, rule = B2n3-qy4ceqy6n7c8/S2-n3-ay4atz5ky6a
b2o$2bo2$o$o$o!
Code: Select all
x = 5, y = 5, rule = B2n3-qy4eqy6n7c/S2-n3-a4atz5y6c
b3o$obobo$o2b2o$2b2o$2bo!
Code: Select all
x = 75, y = 25, rule = B2n3-qy4eqy5e6n7c/S2-n3-a4atz5ky
66b2o$67bo$67b2o5$53bo$52b5o$53bo2bo$o2bo47bob2obo$55bo2$7bo$6bob2o$6b
o3bo$10bo63bo$10bo61b3o$6bo3bo61bo$6bob2o$7bo2$56b2o$o2bo53bo$57b2o!
Code: Select all
x = 5, y = 6, rule = B2n3-qy4eqy6c7c/S2-n3-a4atz5ky
3bo$2b3o$bo2bo$2ob2o$bobo$2bo!
Code: Select all
x = 30, y = 14, rule = B2n3-qy4eqy5e6n7c/S2-n3-a4atz5ky
13b2o$12bobo$11b2ob2o$11b2obo$12b2o3$2o$3o$b2o2$28b2o$27bobo$27b2o!Code: Select all
x = 11, y = 9, rule = B2n3-qy4ekqy6k7c/S2-n3-a4aetz5ky
9b2o$8bobo$4b3ob2o$3bob2o$3b4o$o3b2o$bo$bo2bo$2b2o!