B457/S0123578

[Apple Bottom]

I don't know if this is considered interesting, so all y'all forgive me if it ain't, but when I was looking for/at random rules recently I noticed that B457/S0123578 had quite a large number of oscillator periods. A bit (and I do mean a bit) of soup-searching across different symmetries has, so far, yielded the following periods for this rule:

2-30, 32-34, 36-44, 46, 48-52, 54, 56, 58, 60-61, 64-66, 68-69, 71, 74, 76, 78, 80, 88, 90, 96-97, 100, 106, 109-110, 117, 122, 128, 154, 162, 164, 176

Of these, the following had not previously occured in any rule/symmetry in the Catagolue, to the best of my knowledge:

61, 69, 97, 109, 117, 122, 128, 162, 164, 176

Examples for each of those:

p61:

Code: Select all

x = 10, y = 6, rule = B457/S0123578
4b2obo$3bo2bo2bo$3bo2bo$3bo2bo$o2bo2bo$2bob2o!

p69:

Code: Select all

x = 6, y = 9, rule = B457/S0123578
2o$2bo$o$2bo$4b2o$5bo$3bobo$3bo$5bo!

p97:

Code: Select all

x = 5, y = 11, rule = B457/S0123578
5o$5o$b3o$ob2o$2ob2o$b2obo$2ob2o$ob2o$b3o$5o$5o!

p109:

Code: Select all

x = 9, y = 7, rule = B457/S0123578
obobobobo$o7bo$b2o3b2o$obo3bobo$b2o3b2o$o7bo$obobobobo!

p117

Code: Select all

x = 11, y = 9, rule = B457/S0123578
2o3bo3b2o$obo5bobo$2b7o$3bobobo$b4ob4o$3bobobo$2b7o$obo5bobo$2o3bo3b2o
!

p122:

Code: Select all

x = 11, y = 11, rule = B457/S0123578
2bobo$2b4o$2bo2b2ob3o$4bo4bo$2bo4bob2o$b2o5b2o$2obo4bo$bo4bo$3ob2o2bo$
5b4o$6bobo!

p128:

Code: Select all

x = 12, y = 12, rule = B457/S0123578
4bob3o$5b2o$3b4obo$ob2ob5o$o2b5obobo$5o2b4o$b4o2b5o$obob5o2bo$2b5ob2ob
o$3bob4o$5b2o$3b3obo!

p162:

Code: Select all

x = 9, y = 9, rule = B457/S0123578
9o$2b2ob2o$b2obob2o$2b5o$2bo3bo$2b5o$b2obob2o$2b2ob2o$9o!

p164:

Code: Select all

x = 9, y = 9, rule = B457/S0123578
2o$2bobo$2b2ob2o$4obo$2bo3bo$3bob4o$2b2ob2o$4bobo$7b2o!

p176:

Code: Select all

x = 6, y = 8, rule = B457/S0123578
2o2b2o$o2bobo$2obobo$b2ob2o$b2ob2o$2obobo$o2bobo$2o2b2o!

The following oscillator periods are still missing from the Catagolue, again to the best of my knowledge:

47, 53, 67, 73, 75, 77, 79, 81, 83, 89, 91, 92, 93, 101, 103, 107, 111-113, 116, 118, 121, 123-125, 127, 129, 131, 133-137, 139, 141, 143, 149, 151, 153, 157-161, 163, 165, 167, 169, 172-173, 175, 177 (other than ov_p177), 179-181, 183-185, 187-188, 191-195 (other than ov_p192), 197, 199-203, 205-207, 209, 211-227, 229, 231-233, 235-237, 239, 241-244, 246, 248-259, 261-263, 265-293 (other than ov_p288), 295-309, 311-347 (other than ov_p336), 349-359, 361-389, 391-407, 409-419, 421-434, 436-467, 469-475, 477-489, 491-509, 511-569, 571-608 (other than ov_p576), 610-611, 613-779 (other than ov_p672 and ov_p720), 781-839, 841-... .

[Bullet51]

P47:

Code: Select all

x = 12, y = 12, rule = B457/S0123578
6bo$6bo$4b2o$5bobo$2bob5o$2b4obo2b2o$2o2bob4o$3b5obo$4bobo$6b2o$5bo$5bo!

Weird signal:

Code: Select all

x = 108, y = 5, rule = B457/S0123578
obobobobobobobobobobobobobobobobobobobobobobobobob2obobobobobobobobobo
bobobobobobobobobobobobobobobobobobobo$bobobobobobobobobobobobobobobob
obobobobobobobobobo2b2o2bobobobobobobobobobobobobobobobobobobobobobobo
bobobo$51bob2o$obobobobobobobobobobobobobobobobobobobobobobobobob4obob
obobobobobobobobobobobobobobobobobobobobobobobobobo$bobobobobobobobobo
bobobobobobobobobobobobobobobobob4obobobobobobobobobobobobobobobobobob
obobobobobobobobo!

Not sure whether someone could use the signal to prove omniperiodicity.

[Saka]

p56

Code: Select all

x = 5, y = 4, rule = B457/S0123578
2o2bo$b4o$4bo$b2o!

p71

Code: Select all

x = 5, y = 4, rule = B457/S0123578
5o$4bo$b4o$4bo!

p12

Code: Select all

x = 6, y = 4, rule = B457/S0123578
5bo$b4o$2obo$3o!

p23

Code: Select all

x = 4, y = 6, rule = B457/S0123578
2o$obo$3o2$2o$3bo!