B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78 is a very interesting self-inverse rule that shows very erratic growth at some points, as well as being barely apgsearchable. To start, there is this extensible greyship that travels at c/2, and is period 4:
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x = 40, y = 25, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
15bob5o2$13b12o2$9bob17o2$7b24o2$3bob29o2$b36obo$37bobo$39o2$2bob32o2$
6b27o2$8bob20o2$12b15o2$14bob8o2$18b3o!
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x = 6, y = 3, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
b4o$ob2obo$bo2bo!
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x = 24, y = 23, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
11b2o2$9b6o2$7b10o2$5b14o2$2b20o2$b22o2$b22o$o22bo$2b20o2$4b16o2$7b10o
2$9b6o2$11b2o!
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x = 6, y = 6, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
6o$6o$6o$6o$6o$6o!
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x = 12, y = 14, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
3b4o$2bob2obo$3bo2bo5$5b2o2$2b8o$2o8b2o$12o$2o8b2o$4b4o!
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x = 17, y = 8, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
11b2o2b2o$11b2o2b2o4$5o$3bobo$3obo!
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x = 57, y = 18, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
9bo14bo10bo16bo$7bobo12bobo8bobo14b3o$7bobobo10bobobo8bobo14bo$7bobobo
10bobobo4bo3bobo$9bobobo7b2obobo8bobo$3b3o3bobobo4b7obo3b6obo$8b2obobo
8bobobo9b2o$b9obobo3b7ob2o5b6o12b5o$8bo2bo12b2o27bobo$10obo7b6o25b3obo
2$2b6o2$4b2o$52b4o$50b5obo$50b5obo$52b4o!
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x = 122, y = 96, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
90b3o2$86bob8o2$84b15o2$80bob20o2$78b27o2$74bob32o2$73bob36o2$77b37obo
$114bobo$79bob35o2$83b30o$68b8o$85bob23o$66b16o$89b18o$64b20obo$91bob
11o$62b26o$95b6o$60b30o$97bo$58b37o2$30bobobobobobobobobobobobobob44o
2$28b75o2$26b80o2$24b85o2$22b90o2$20b95o2$18b100o2$16b105o$119bobo$14b
105obo2$12b104o2$10b103o2$8b102o2$6b101o2$4b100o2$2b99o2$98o2$95o2$2b
90o2$4bob83o2$8b78o2$10bob71o2$14b66o2$16bob59o2$20b54o2$22bob47o2$26b
42o2$28bob35o2$32b30o2$34bob23o2$38b18o2$40bob11o2$44b6o2$46bo!
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Linear growth is common in the form of puffers and wickstrechers. Here is a p80 duoplet puffer:
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x = 62, y = 54, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
19b3o2$15bob8o2$13b15o2$9bob20o2$7b27o2$3bob32o2$b39o2$obobob37o2$8b
38o2$10b39o2$12b40o2$14b41o2$16bob40o2$20b41o$59bobo$22b37obo2$24b32o
2$26b27o2$28b22o2$30b14obo$47bob2o$32bob9o$42bo2b9o$36b5o$41bob14o2$
39b21o$60b2o$38b24o$60b2o$40b18o2$42bob11o2$46b6o2$48bo!
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x = 11, y = 9, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
5b2o$8bo$3b5obo$7b2o$b4o3bobo$8bobo$4o2bobo$6bobo$b2o3bo!
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x = 8, y = 4, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
2obo$bobo2b2o$bobo2b2o$2obo!
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x = 5, y = 10, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
o2bo$ob2o$o2bo$obo$obobo$obobo$obo$o2bo$ob2o$o2bo!
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x = 9, y = 4, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
b2ob4o$2b2o2bobo$ob4obo$2bo!
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x = 13, y = 27, rule = B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78
3bo2bo2bo$b2ob2ob2ob2o$b11o$ob9obo$b11o$b11o$ob10o$b11o$ob10o$b11o$ob
10o$b11o$b11o$ob10o$b11o$b11o$ob10o$b11o$ob10o$b11o$ob10o$b11o$b11o$ob
9obo$b11o$b2ob2ob2ob2o$3bo2bo2bo!