Hex rule B2o45/S2o45H

[strake]

I've been playing with this for a while.

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@RULE B2o45_S2o45H

@TABLE
n_states:2
neighborhood:hexagonal
symmetries:rotate6reflect
var r={0,1}
var s={0,1}
var t={0,1}
var u={0,1}
var v={0,1}
var w={0,1}
var x={0,1}
var y={0,1}
var z={0,1}
w,1,1,0,0,0,0,1
w,0,0,1,1,1,1,1
w,0,1,0,1,1,1,1
w,0,1,1,0,1,1,1
w,0,1,1,1,1,1,1
t,u,v,w,x,y,z,0

@COLORS
0  48  48  48
1 255 255 255

EDIT by dvgrn 8/18/2024: replaced rule name "B2o45.S2o45" throughout this thread with "B2o45/S2o45H" per Discord request, for better LifeViewer displays. Changed rule table from "B2o45.S2o45" to "B2o45_S2o45", again on a suggestion from Discord.

Gliders are extremely common. The natural gliders I have seen, all speed (1/3, 1/3, 0):

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x = 22, y = 6, rule = B2o45/S2o45H
2o6b2o6b2o$3bo15bo$b2o6b3o5b4o$b3o5b3o5b3o$b3o5b3obo3b3obo$5bo7bo7bo!

Natural oscillators:

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x = 81, y = 19, rule = B2o45/S2o45H
65bo2$66bo2$67bo$67b2o6bo$3o29b3o32b3o4bo$4o29b2o31bo6bo$b3o26bo3bo3bo
12bo3bo9bo6bo$2b2o18bo7b2o6b2o8b3o4bobo$21bo8b3o2bo2b3o6bob2o4b4o$3b2o
8b2o6bobo10bo2bo9b2o5bob3o7b2o6bo$3b3o7b3o6b3o22b2o6bo2bo7b3o5b2o$3b4o
6b4o6bobo9bo2bo7bo10bo8b4o4b3o$4b3o7b3o8bo6b3o2bo2b3o24b3o3bo4bo$24bo
8b2o6b2o15bo13bo7bo$34bo3bo3bo$38b2o$38b3o!

A glider bouncing between 3 reflectors:

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x = 39, y = 42, rule = B2o45/S2o45H
31bo3bo$bo12b2o15bob2obo$o2bo13bo13bobobobo$2ob2o10b4o14bo2bo$15b3o16b
3o$bobobo9b3obo$3b2o14bo15b3o27$30bo7bo$32bo4bo$34b3o$35b2o$36bo2$37bo
2$38bo!

A natural duplex rake:

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x = 13, y = 13, rule = B2o45/S2o45H
7b2o$10bo$8b4o$8b3o$8b3obo$12bo$3o2$b3o$bo2bo$obobobo$bob2obo$2bo3bo!

The lone still life I know:

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x = 5, y = 5, rule = B2o45/S2o45H
bo$4o$bobo$b4o$3bo!

[wildmyron]

I've been playing with this for a while.

An interesting rule. You can simplify the rule table by using the rotate6reflect symmetry - see the first post in the 22da thread for an example.

Here's another p6 oscillator formed from a pair of truncated triangle oscillators

Code: Select all

x = 9, y = 6, rule = B2o45/S2o45H
3o$4o$b3ob2o$2b2ob3o$5b4o$6b3o!

Gliders are extremely common. The natural gliders I have seen, all speed (1/3, 1/3, 0):

This seems to be a common velocity in hexagonal rules.

The lone still life I know:

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x = 5, y = 5, rule = B2o45/S2o45H
bo$4o$bobo$b4o$3bo!

This still life can be used to suppress growth of other sparks to form complex inducting patterns

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x = 34, y = 13, rule = B2o45/S2o45H
7bo19bo$bo4b4o11bo4b4o$4o3bobo10b4o3bobo$bobo3b4o10bobo3b4o$b4obo2bo
11b4obo2bo$3bo2b2o15bo2b2o2$8bo17b2o2bo$7b4o13bo2bob4o$8bobo12b4o3bobo
$8b4o12bobo3b4o$10bo13b4o4bo$26bo!

Edited to add...

And some other related oscillators, including synthesis from known patterns:

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x = 55, y = 91, rule = B2o45/S2o45H
3$44bo2$45bo$44bob2o$44b2obo$45b2obo$46b2o2bo$9bo$8b4o$9bobo$4b2o3b4o
22b2o2b2o$5b2o4bo24b2ob2o2$8bo30bo$8b2o29b2o$9bo30bo14$46b2o2$47b3o$
47b3o$10b3o34b3obo$51bo$11b3o$11bo2bo24b2o2b2o$10bobobobo23b2ob2o$8b2o
bob2obo$8b3obo3bo26bo$8b4o31b2o$5bo3b3o24bo7bo$4b4o27b4o$5bobo28bobo$
5b4o27b4o$7bo30bo22$6b3o27b3o2$7b3o27b3o$7bo2bo26bo2bo$6bobobobo23bobo
bobo$4b2obob2obo21b2obob2obo$4b3obo3bo21b3obo3bo$4b4o26b4o$5b3o23bo3b
3o$30b4o$31bobo$31b4o$33bo2$21bo$21bob3o$23b3o$23b3o2$25b2o!

Here are a few interesting interactions, including a pulling reaction, reflection and duplication reactions combined with conversion between one ship to another - unfortunately the phases don't quite work out to make a gun.

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x = 315, y = 199, rule = B2o45/S2o45H
34$66b2o98b2o98b2o$252b2o2b2o$67b3o97b3o83b2ob2o9b3o$67b3o97b3o97b3o$
67b3obo95b3obo84bo10b3obo$71bo99bo84b2o13bo$257bo$56bo2$57bo$154bo$58b
o97b3o$58b2o95bobobo$58b3o95b3o$57bo4bo97bo$56bo7bo85$66b2o98b2o98b2o$
69bo99bo99bo$67b4o96b4o96b4o$67b3o97b3o97b3o$67b3obo95b3obo95b3obo$71b
o99bo99bo$157bo103bo$159b3o101b3o$158bobobo99bobobo$159b3o101b3o$70b2o
91bo103bo$70bo2bo$70b3o$69bo2bo$71b2o!

[simsim314]

Natural occurring back rake:

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x = 43, y = 26, rule = B2o45/S2o45H
2o$2obo$2obo$bobo$3bo4bo4b2o$8b2o3b3o$8b11o$11b3o3b3o$12b2o4bo6bo$13bo
3b4ob3obo$13b2o2bob2o3b3o$13b3o2b3o2b3o8bo$14b7o3b3o6bo$17b2obo$18b2o
3b2o$22bob2o7b4o$23b4o4bob3o$24b2o5b4ob2o2bo$26bo6bo2b2obo$25b2o6b2o2b
3o$33b2ob2ob3o$34b6ob2o$35bobob4o$33bo2bo2bob2o2$34bo5bo!

Natural gun

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x = 16, y = 20, rule = B2o45/S2o45H
2$3b2o$2bobobo$3b4o$4b3o2$6bo$6b2o$6b3o$7b2o$8bo2$9bo2$10bo$9b4o$10bob
o$10b4o$12bo!

[wildmyron]

I haven't seen those come up in my own exploration, the gun in particular is very neat. I'm sure there are many reactions which will modify the output.

Here are a few ships with the same engine as the back puffer:

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x = 65, y = 15, rule = B2o45/S2o45H
62bo$60bob2o$60b2ob2o$61b2o$50bo11b2o$53bo$51b2o2bo$3ob2o44bob4obo$7o
43b3ob2o$bob5o43b3ob4o$8o42b5ob2o$3ob3o43b3ob2obobo$o2b2ob2o42bo2b6o$
2ob5o42b2ob4obo$5ob2o42b5ob2o2bo!

Edited to add...
Two guns based on the one above:

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x = 37, y = 24, rule = B2o45/S2o45H
33bo$32b4o$33bobo$33b4o$29b2o4bo$28bob2o$25b2ob2ob2o$29b2obo$26b3ob2o$
26b3o$26b3obo$21b3obo4bo$18bo4b2o$22b4o$19bo3bobo$o7bo9bob2o3bo$2bo4bo
10b2obo$4b3o7b2o3b2obo$5b2o13b2o2bo$6bo8b3o$15b3o$7bo7b3obo$19bo$8bo!

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x = 34, y = 35, rule = B2o45/S2o45H
30bo$29b4o$30bobo$30b4o$26b2o4bo$25bob2o$22b2ob2ob2o$26b2obo$23b3ob2o$
23b3o$23b3obo$18b3obo4bo$15bo4b2o$19b4o$16bo3bobo$15bob2o3bo$2o13b2obo
$3o8b2o3b2obo$4o13b2o2bo$b3o8b3o$12b3o$12b3obo$16bo6$12bo3bo$12bob2obo
$12bobobobo$14bo2bo$15b3o2$16b3o!

[simsim314]

I haven't seen those come up in my own exploration

Here is the soup the gun came from (I actually got it twice - but lost the first soup):

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x = 50, y = 67, rule = B2o45/S2o45H
b3o5b3o3bo7bo4b2o3b2ob2o3b3o2bo$o2bobo2bo2b5ob2obo2bo3b4o5bo3bo5bo2bo$
4b2obo3bo3bo4bo4bo3bo4b3o4bobo2bobo$3b2o5bobo6bobob4ob6o8bo3bobo$5b2o
5bobobo2b2o4b2obo2bobobo5bo2b2o2bo$bo4bo6b2o4b4ob2o4bobo4bo2b2ob5o$5bo
b2obo3bo4bo4b2obo2b4o4bobobo$6b2o2bo2bo5b2ob3o2b2o2b2ob4o3bo2b2obo$b4o
b2o3b3o6bobo10b2o4bo4bo2bo$2o4bo3b2o8b5obobo9bo2b2ob3obo$bo4bo8bo2bobo
b2obob2o2bo3bo3bo3bobobobo$b2obo4b2o2b3ob2o3b2ob4o3bo3b6o2b2o2bo$2ob2o
bo2b2o2bobo7b3o4bo3b2o5bo4bo2bo$o5bob2ob2o2b3ob4o2b2obob3ob2o3b3ob2o2b
o$obo5b3obob2o2b4obob4obo3bo4b2ob3obo2bo$3obo5bo2b5o4bo2bo10bob3ob2o4b
o$2bo3bo2b5ob3o6bobo2bo2b4ob2o2bo2bo3b2o$5o4b5obo16b2o9bob3obo$2bo2b2o
7bo2bobo4bo2bobobo2bob3obo2b3obo$o8bobo2bo2bo4bobo2bob2o5bo5bobo3bo$b
2ob2o2bo8bo2bo7b3o2b2obo4b2ob2o$6bob2o11bob4obobobo2bo4bo2bob3o$b2o2b
2o2b3o4bo5bo4bo2bobobobo8bobo$4bo2bo3b4o4b3o2bo2b2obo3bobobobo2b2o3b2o
$bobo2bo4bo3b2obo2bobobo2bo10b2o2b2o4bo$3ob5o2bo3bo2bo2bob2obo2bobobo
2bob2o2bo2bo$4o9bobo2bob6o3b2ob2ob6o2bobob2o$2b2o4bo3bo2bo2bobo4bobob
2o3bobo2bo5b2o$o3bo2bo3bob3o3bo2bobo6b2ob3o3b4obo$b2o2bo2bo2b4o5bo6bob
obo2bo3bo5bobobo$2b2o4b5obobobo10b3ob5o3b2o$3ob3o2bobo5bobob2o2bo7b2ob
obobo2b2obobo$o3bo4bo2bo2bob3ob2o2b4o4b3o4bobo3bo$obo3bobob3o2bo2bobob
2obob2o4b2ob3o3b2ob2o$2b4o3b4o2b2o2bob2o4bo2bo2bo3bo5bo3b3o$4o3b2o3b2o
b2obo7bo3bo13b2o2bo$2obobobobo3bo2b2o3b2o5b2o2b4ob3o3b3o$obob2o5bo3b3o
bob2o2bo3bo4bo5b2o2bo3bo$bo3b2o4bo3bo2bob3o7bo2bo4b2obo3b3o$bo2b3obo2b
ob3ob3o4bob2obob2o3b2o3b2obo4bo$bobobo4bo5b4ob2obob2o2bo2b4o5b2o$bobob
3o7bobo2bo6bo2bo2b2ob2ob6ob4o$3o4bob3o5bo2bobobob4o2b2obob4obo2bo2bo$b
2o4bo2bobo5bo5bo4b2o2bob3o4bo5bo$2obo3b8ob2ob6o2bo5b2o4b3o5bo$7b3o2bob
obob2o3bo2bobobobo11b2o$4bo2b2obo3b2ob3o4bobob3o4b2o2b4o2bo3bo$bobo3bo
6b2obob2o2bo2bobobobo3bo3bob2obob2o$2bo7b2ob2o3bobo3bob2o6b3o3b2o2bo2b
3o$o8b2o5bobo2bobo2bo2bob2o2b3ob2ob2o2bo2bo$3bobo2b2o4bobob2o2b3obo4bo
3b2o2b3ob5o$o2bo2bo2bo3b2obob3ob2o3b2obo4b2o2bo4b3o$ob5ob2o4b2ob2o4bob
o2bo3bo2b2o4b2obob2obo$2o3bob2o2b7ob3o3bobobob3o5bo5bob3o$b2obo3bobo5b
2o3b2o2bo2bobob3o3b2o2b2obo2b2o$3b2o3bobo4bo2bo6bo2b2o3bo3bo2b2o3b2ob
2o$2o7b2ob2obobo3bo2b5o4b2o3b3o5b3o$2o3b2o5b6obobobo3b2o2bo2bo3b2o3b2o
4bo$o4bo4bo3bo5b2o5bo4bo2bo9b2o$bo3b2obobo6b2obo7b2o4bobobo2bo2b2obo$o
b2o4bo2b2o2bobo6b3o2bob2o9bo$obo2bobob4o5b3ob3obo5b7o2bo$o2bo2bobo8bo
3b7o2b2o3bobobob3o3bobo$bo3b2o2bo2bo6bobo7bo3b5o3b2o4b3o$4bo5b3obobob
3o3bo2bo4bo2bo2b2o4bob4o$2bo3bo3bo2bob2obobo3b2obo3b3obobobo4bo2b2o$bo
b2o7bobobo2bob4ob2o9bobo4b4o!

[strake]

An interesting rule. You can simplify the rule table by using the rotate6reflect symmetry - see the first post in the 22da thread for an example.

Good call, thanks, I so simplified the rule in the OP.

Natural occurring back rake

Natural gun

Neat, I haven't seen these naturally either.


Glider bouncing between 2 hexagrams:

Code: Select all

x = 24, y = 24, rule = B2o45/S2o45H
20bo$19b4o$20bobo$20b4o$22bo4$10bo$10bob3o$12b3o$11b4o$12bo$14b2o6$bo$
4o$bobo$b4o$3bo!

[Sphenocorona]

Everything so far has had a period divisible by 3, so let's break the trend with an oscillator that's p8:

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x = 7, y = 14, rule = B2o45/S2o45H
3bo$2b4o$3bobo$bob4o$obo2bo$2o$3bo$b2o2bo2$3bo$2b4o$3bobo$3b4o$5bo!

Here's another variant which has its lowest population in a different phase (perhaps a bit more recognizable, too):

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x = 15, y = 9, rule = B2o45/S2o45H
5bo$5b2o$bo3b3o3bo$4o6b4o$bobo7bobo$b4o6b4o$3bo3b3o3bo$8b2o$9bo!

And here's a p4:

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x = 16, y = 16, rule = B2o45/S2o45H
4bo$3b4o$4bobo$bo2b4o$4o2bo$bobo$b4ob2o$3bo2b2obo$6bob2o2bo$8b2ob4o$
12bobo$9bo2b4o$8b4o2bo$9bobo$9b4o$11bo!

EDIT: I found a p7 (edited again to show a version with slightly more accessible sparks):

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x = 20, y = 19, rule = B2o45/S2o45H
5bo$4b4o$5bobo$bo3b4o$4o3bo$bobo$b4o$3bo7b2o$12bo2$7bo$7b2o7bo$15b4o$
16bobo$12bo3b4o$11b4o3bo$12bobo$12b4o$14bo!

This may be p6 but it uses a previously unused component in the middle which reappears after only 3 generations, turned around:

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x = 49, y = 35, rule = B2o45/S2o45H
4$2b2o2$3b2o$2bo$4b2o$3bobo$2bobo5bo24b2o$3bo5bobo26bobo$9b2o20bo4b2o
4bo$12bo18bobo3bobobobo$11bo21b2o6b2o$10bo21bo$12b2o20bo$11bobo18bo$
12bo5bo15b2o6b2o$17bobo13bobo3bobobobo$17b2o15bo4b2o4bo$20bo21bobo$18b
o21b2o$16bobobo2$17b2ob2o$18bo2bo$20bo!

It was found from this p12:

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x = 19, y = 21, rule = B2o45/S2o45H
bo$4o$bobo$b4o$3bo2$7bo$6bobo$8b2o$7b3o2$9b3o$9b2o$10bobo$11bo2$15bo$
14b4o$15bobo$15b4o$17bo!

[glider_rider]

p5 oscillator:

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x = 14, y = 15, rule = B2o45/S2o45H
bo$4o$bobo$b4o$3bo2$3b2o$4bo2$3b2ob2o$bo2bo2bo2bo$4o5b4o$bobo6bobo$b4o
5b4o$3bo8bo!

[strake]

Extinguishing a rear-flaming glider:

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x = 9, y = 11, rule = B2o45/S2o45H
5b3o$5b4o$6b3o$7b2o2$bo$b2o$b3o$ob2obo$bobobo$3b2o!

[strake]

Wildmyron's gun is readily doubled, as the one oscillator keeps its phase invariant:

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x = 49, y = 49, rule = B2o45/S2o45H
31bo$30b4o$31bobo$31b4o$27b2o4bo$26bob2o$23b2ob2ob2o$27b2obo$24b3ob2o$
24b3o$24b3obo$19b3obo4bo$16bo4b2o$20b4o$17bo3bobo21bo$o3bo11bob2o3bo
20b4o$ob2obo10b2obo25bobo$obobobo5b2o3b2obo24b4o$2bo2bo12b2o2bo18b2o4b
o$3b3o7b3o24bob2o$13b3o21b2ob2ob2o$4b3o6b3obo23b2obo$17bo20b3ob2o$38b
3o$38b3obo$33b3obo4bo$30bo4b2o$34b4o$31bo3bobo$30bob2o3bo$15b2o13b2obo
$15b3o8b2o3b2obo$15b4o13b2o2bo$16b3o8b3o$27b3o$27b3obo$31bo6$27bo3bo$
27bob2obo$27bobobobo$29bo2bo$30b3o2$31b3o!

Glider AND gate:

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x = 184, y = 184, rule = B2o45/S2o45H
87bo$86b4o$87bobo$87b4o$83b2o4bo$82bob2o$79b2ob2ob2o$83b2obo$80b3ob2o$
19bo60b3o$18b4o58b3obo$19bobo53b3obo4bo$19b4o49bo4b2o$21bo54b4o$73bo3b
obo21bo$56bo3bo11bob2o3bo20b4o$56bob2obo10b2obo25bobo$56bobobobo5b2o3b
2obo24b4o$58bo2bo12b2o2bo18b2o4bo$59b3o7b3o24bob2o$69b3o21b2ob2ob2o$
60b3o6b3obo23b2obo$73bo20b3ob2o$35bo2bo2bo52b3o$35bobo2bobo51b3obo$37b
obobo47b3obo4bo$39b2o45bo4b2o$38bo3bo47b4o$40b2o45bo3bobo$2o2b2o80bob
2o3bo$b2ob2o35b2o28b2o13b2obo$71b3o8b2o3b2obo$4bo66b4o13b2o2bo$4b2o66b
3o8b3o$5bo77b3o$83b3obo$87bo6$83bo3bo$83bob2obo$83bobobobo$85bo2bo$86b
3o2$87b3o$52b2o$52b3o$52b4o$53b3o$48bo$47b4o$48bobo$48b4o$50bo5$74bo2b
o2bo$74bobo2bobo$76bobobo$78b2o$18bo2bo2bo52bo3bo$18bobo2bobo53b2o$20b
obobo$22b2o56b2o$21bo3bo$23b2o2$24b2o6$166bo$165b4o$166bobo$92bo73b4o$
91b4o67b2o4bo$92bobo66bob2o$92b4o62b2ob2ob2o$94bo67b2obo$159b3ob2o$98b
o60b3o$97b4o58b3obo$98bobo53b3obo4bo$98b4o49bo4b2o$100bo54b4o$152bo3bo
bo21bo$135bo3bo11bob2o3bo20b4o$135bob2obo10b2obo25bobo$135bobobobo5b2o
3b2obo24b4o$137bo2bo12b2o2bo24bo$138b3o7b3o$70b2o2b2o72b3o$71b2ob2o63b
3o6b3obo$152bo$74bo39bo2bo2bo$74b2o38bobo2bobo$75bo40bobobo$118b2o$
117bo3bo$119b2o$79b2o2b2o$80b2ob2o35b2o28b2o$150b3o$83bo66b4o$83b2o66b
3o$84bo8$162bo3bo$162bob2obo$162bobobobo$164bo2bo$165b3o2$166b3o$131b
2o$131b3o$131b4o$132b3o$127bo$126b4o$127bobo$127b4o$129bo5$153bo2bo2bo
$153bobo2bobo$155bobobo$157b2o$97bo2bo2bo52bo3bo$97bobo2bobo53b2o$99bo
bobo$101b2o56b2o$100bo3bo$102b2o2$103b2o9$171bo$170b4o$171bobo$171b4o$
173bo13$149b2o2b2o$150b2ob2o2$153bo$153b2o$154bo!

Glider ANDN gate, i.e. X=A∧¬B:

Code: Select all

x = 269, y = 269, rule = B2o45/S2o45H
bo117bo$4o114b4o$bobo115bobo$b4o114b4o$3bo4b2o111bo$8b2obo$8b2ob2ob2o$
9bob2o$11b2ob3o$15b3o$14bob3o$15bo4bob3o$22b2o4bo$22b4o$23bobo3bo103bo
$24bo3b2obo11bo3bo40bo3bo39b4o$29bob2o10bob2obo39bob2obo39bobo$29bob2o
3b2o5bobobobo38bobobobo38b4o$28bo2b2o12bo2bo41bo2bo35b2o4bo$36b3o7b3o
42b3o34bob2o$37b3o85b2ob2ob2o$36bob3o6b3o42b3o34b2obo$37bo88b3ob2o$
126b3o$126b3obo$121b3obo4bo$118bo4b2o$122b4o$119bo3bobo$118bob2o3bo$
46b2o55b2o13b2obo$46b3o54b3o8b2o3b2obo$46b4o53b4o13b2o2bo$47b3o54b3o8b
3o$115b3o$115b3obo$119bo6$115bo3bo$115bob2obo$89bo25bobobobo$88b4o25bo
2bo$89bobo26b3o$89b4o$91bo27b3o39$103b2o10bo3bo$103b3o9bob2obo$103b4o
8bobobobo$104b3o10bo2bo$118b3o2$119b3o3$115bo$115b2o$115b3o$114bob2obo
$115bobobo4$118b3o$118b4o2$119b4o$118bo2bo2bo3$122b2o$121bobobo$122b4o
$123b3o2$125bo2$126bo$126b2o$126b3o$125bob2obo$126bobobo2$128b3o$128b
4o2$129b4o$130b3o4$133bo117bo$132b4o114b4o$133bobo115bobo$133b4o114b4o
$135bo4b2o105b2o4bo$140b2obo102bob2o$140b2ob2ob2o95b2ob2ob2o$141bob2o
102b2obo$143b2ob3o95b3ob2o$147b3o94b3o$146bob3o93b3obo$147bo4bob3o82b
3obo4bo$154b2o4bo75bo4b2o$154b4o82b4o$155bobo3bo75bo3bobo21bo$156bo3b
2obo11bo3bo40bo3bo11bob2o3bo20b4o$161bob2o10bob2obo39bob2obo10b2obo25b
obo$161bob2o3b2o5bobobobo38bobobobo5b2o3b2obo24b4o$160bo2b2o12bo2bo41b
o2bo12b2o2bo18b2o4bo$168b3o7b3o42b3o7b3o24bob2o$169b3o61b3o21b2ob2ob2o
$168bob3o6b3o42b3o6b3obo23b2obo$169bo67bo20b3ob2o$258b3o$258b3obo$253b
3obo4bo$250bo4b2o$254b4o$251bo3bobo$250bob2o3bo$178b2o55b2o13b2obo$
178b3o54b3o8b2o3b2obo$178b4o53b4o13b2o2bo$179b3o54b3o8b3o$247b3o$247b
3obo$251bo6$247bo3bo$247bob2obo$221bo25bobobobo$220b4o25bo2bo$221bobo
26b3o$221b4o$223bo27b3o39$235b2o10bo3bo$235b3o9bob2obo$235b4o8bobobobo
$236b3o10bo2bo$250b3o2$251b3o39$265bo$264b4o$265bobo$265b4o$267bo!

[wildmyron]

A p4 orthogonal ship with speed (1,0,0)/4. Found with Paul Tooke and EricG's modified gfind adapted for hexagonal rules.

Code: Select all

x = 20, y = 16, rule = B2o45/S2o45H
4bo$3bo7b2o$2b5o3bo$bob3o5b3o$obob4obobob2o$bo3b3o3bob3o$4b2o2b7o$4b2o
3b6o$4bob7o2b2o$3bo2b4o2b2ob2o$6bo2bob4obobo$6bob4o2bob2o$6b3o2bo4b4o$
6bob3o$10bo$10bo!

[strake]

MMM Breeder:

Code: Select all

x = 771, y = 329, rule = B2o45/S2o45H
48b2o$48b2obo$48b2obo2bo3bo29b2o$49bobo3bo32b2obo$51bo3bo32b2obo36b2o$
55b2o32bobo36b2obo$54b2o35bo4bo31b2obo2bo3bo29b2o99b2o$60bo35b2o31bobo
3bo32b2obo96bobobo$62bo33b3o32bo3bo32b2obo36b2o60b4o$64bo70b2o32bobo
36b2obo54bo3bobo$58bo7bo67b2o35bo4bo31b2obo2bo3bo29b2o16bo3b5o$140bo
35b2o31bobo3bo32b2obo10bo3bob2o4bo$142bo33b3o32bo3bo32b2obo10bob2o2b2o
3bo$144bo70b2o32bob3o8bob4o$bo136bo7bo67b2o35bobo9bobobob3o$obo217bo
38b2o4b4o$4o37bo180bo29bo6b2o6b2o$2b2obo2bo31bobo181bo41bo$b3obo34b4o
37bo136bo7bo40b3o$5bobo34b2obo34bobo$9bo31b3obo34b4o37bo100bo65b3o$45b
o2b3o31b2obo2bo31bobo99b2o64b4o$8bo39b4o29b3obo34b4o37bo60b5o62b4o$49b
3o33bobo34b2obo34bobo61b3o23b2o37bo2b2o$50b2o37bo31b3obo34b4o37bo16bo
3bo2b2o60bo2bob3o$125bo2b3o31b2obo2bo31bobo15bo2bobo2b2o23b2o29b2o7b4o
$88bo39b4o29b3obo34b4o10bo2bo2bobobob3o21bo3bo8b2o2b2o13b2o4bo4b2o$
129b3o33bobo34b2obo8bobo2bobobo28b2o10b2ob2o14bob2o3bo$130b2o37bo31b3o
b2o9bob3obo28bobobo27b2ob2o$205b3o4bo2bob2ob2o28bobo2bobo9bo16bo2bo$
168bo42bobo4b3o2b2o26bo2bo2bo9b2o15b3o$212bobo4bo2bo45bo13b2o2b4o$213b
o6b2o60b2o4b2o$219bo22b2o$217bo3b2o$216bobo19b2o3b3o$217bobo23b3o$203b
o14bo20b2o2b3obo$238bo3bo4bo3b2o2b2o12b2o$204bo35b2o10b2ob2o$239bobobo
26b2o$205bo13bo18bobo2bobo9bo13bo3bo$205b2o12b2o18bo2bo2bo9b2o14b2o$
205b3o11b3o34bo13bobobo$204bo4bo59bobo2bobo$203bo7bo8b3o47bo2bo2bo$
220b4o$195bo24bobobo$222b2o$196bo$195bob2o40b2o2b2o12bo$195b2obo41b2ob
2o$196b2obo58bo2bo$197b2o2bo41bo13bo4bo$243b2o14bo$207b3o34bo13bobo$
190b2o15b4o46bobo2bo$208bobo47bo2bo2bo$191b2o$190bo3bo13b2ob2o$192b2o
15b4o$191bobobo15bo$190bobo2bobo12b4o13b2o2b2o$194bo33b2ob2o$191bobo2b
obo10bob4obo$193bobobo12bobobobo14bo$195b2o14bob2obo14b2o$194bo3bo14b
3o16bo$196b2o2$197b2o7$208bo2bo2bo$208bobo2bobo$210bobo$212bo$211bo6bo
$213bo3b3o2bo$218bob2o$214b2o2b3ob2o$221b4o$223b3o$222bo156$565bo$562b
3o$563b4o38bo$564b2ob2obo31b3o$566b2obo33b4o38bo$565bo2b4o32b2ob3o2b2o
28b3o98b3o$571bo34b2obo33b4o38bo57b4o$570bo34bo2b3o3bo29b2ob2obo31b3o
59bob2o$609bo6bo29b2obo33b4o38bo12bob2o2b4o$615bo29bo2b4o32b2ob3o2b2o
28b3o12bo3b3o2b2o$615bobo33bo34b2obo33b4obo8bobo3bo$612bobo2bobo30bo
34bo2b3o3bo29b4o9bob3ob2o$613bo2bo2bo69bo6bo32bo7b5o2bo$695bo29b2o4bob
o6b3o$695bobo35b2o3bobo3bo$692bobo2bobo32bo4bo2b4o$693bo2bo2bo34bo25bo
$762bo$736bo24bob2o$595b2o99b2o65b2o$595b2obo96bobobo62b5o$595b2obo36b
2o60b4o63bobo$596bobo36b2obo54bo3bobo24b3o35b2ob4o$598bo4bo31b2obo2bo
3bo29b2o16bo3b5o37bo19bo2b3ob3o$603b2o31bobo3bo32b2obo10bo3bob2o4bo23b
3o10bo2bo14b3o4b2obo2bo$603b3o32bo3bo32b2obo10bob2o2b2o3bo24bo2bo9b2ob
2o14b3o8bo$642b2o32bob3o8bob4o29bobobobo15bo9bob3o9bo$641b2o35bobo9bob
obob3o26bob2obo8bobobo11bob5obo$647bo38b2o4b4o30bo3bo10b2o4bo11b4o$
649bo29bo6b2o6b2o60b2obob2o$651bo41bo54bo8bo2bobo$645bo7bo40b3o62bo$
716b3obo$691b2o25b2o$649b2o40b2o19b3o2b4o$648bobobo65bobo6bo$650b4o23b
2o34b3o4bo5bo2bo$646bo3bobo60bo2bo9b2ob2o12b3o$628b2o16bo3b5o23b2o32bo
bobobo$628b2obo10bo3bob2o4bo22bo3bo31bob2obo8bobobo12b3o$628b2obo10bob
2o2b2o3bo25b2o12b2o19bo3bo10b2o13bo2bo$629bob3o8bob4o30bobobo8bo2bo48b
obobobo$631bobo9bobobob3o25bobo2bobo8b4o47bob2obo$639b2o4b4o29bo2bo2bo
60bo3bo$632bo6b2o6b2o45b4o$646bo48b3o$647b3o19b2o$715bo$644b2o24b3o41b
o2bo$644b2o24b3o41b2ob2o12b2o2bobo$670b3obo59bobo$630b2o42bo40bobobo
12b2obobo$717b2o13bo3bo$631b2o49bo48bobobo$630bo3bo47b2o48bob2obo$632b
2o30b3o13bob3obo46bo3bo$631bobobo46b4o$630bobo2bobo27b3o15b3o$631bo2bo
2bo27bo2bo15b2o$664bobobobo14bo17bo$665bob2obo14b2o15bo2bo$622b2o42bo
3bo12bob3obo12b2ob2o$666bob2obo12bob2obo$618b2o3b3o40bobobobo12b5o13bo
bobo$623b3o42bo2bo14b4o15b2o$619b2o2b3obo41b3o$618bo3bo4bo$620b2o48b3o
$619bobobo$618bobo2bobo$619bo2bo2bo5$683bo3bo$683bob2obo$683bobobobo$
685bo$686b2obo2bo$691b4o$687b3o2bob4o$692b5o$694b5o$696bobo$697bo!

It's a little messy, but it works ☺

While creating this I noted that the common duplex rake is non-monotonic and has speed 2/7, so one can't use a speed-1/3 glider to eat its output on one side; thus the slightly cumbersome unilateral triple rakes.

[c0b0p0]

Based on wildmyron's gun, I made a p264 gun, shown below.

Code: Select all

x = 449, y = 892, rule = B2o45/S2o45H
bo$4o$bobo$b4o$3bo3$4b2o$3bobobo$4b4o$5b3o$5b4o$5bobobo2$5bo2bo2bo$7b
4o2$8b4o$9b3o4$10bobobo$10bob2obo$12b3o$13b2o$14bo2$15bo2$15b3o$15b4o$
15bobobo$17b2o3$16bo2bo2bo$18b4o2$19b4o$20b3o4$29b3o$16b3o$16b4o10b3o$
17b3o10bo2bo$18b2o9bobobobo$27bo2bob2obo$25b2obo2bo3bo$28bo$26b3o$26b
4o$26bobobo$28b2o5$121bo$120b4o$116bo4bobo$115bo2b2ob4o$118b3o2bo$116b
2ob3o$115bob2ob2o$115b2ob2o$111b2o3b2obo2bo$117b2o2bo$112b3o$112b3o$
112b3obo$107b3obo4bo$104bo4b2o$108b4o$92b2o11bo3bobo$92b3o9bob2o3bo$
92b4o8b2obo$93b3o4b2o3b2obo$106b2o2bo$101b3o$101b3o$99bob3obo$96b2ob2o
4bo$98b2o$97b4o$98bobo$100bo$103bo3bo$103bob2obo$103bobobobo$46b3o56bo
2bo$46b4o56b3o$47bobo$47b4o56b3o$48b3o$48b4o$48bobobo$50b2o$78bo3bo$
78bob2obo$78bobobobo$48b2o6b2o25bo$48b3o5b3o18bo2bob2o$48b4o4b4o16b4o$
49b3ob3ob3o14b4obo2b3o$53b4o19b5o$54b3o18b5o$55b2o19bobo$78bo16$55b2o$
54b4o$52b4ob2o$54b5o$53b5o$54bobo$56bo30$8b3o$8b4o$9b3o$10b2o17$92bo2$
92b3o$92b4o$92bobobo$94b2o171$180bo2$180b3o$180b4o$180bobobo$182b2o
171$268bo2$268b3o$268b4o$268bobobo$270b2o171$356bo2$356b3o$356b4o$356b
obobo$358b2o171$444bo2$444b3o$444b4o$444bobobo$446b2o!

[wildmyron]

A p4 orthogonal ship with speed (1,0,0)/4. Found with Paul Tooke and EricG's modified gfind adapted for hexagonal rules.

I was asked via PM about how to get this adapted version of gfind working. Here are a few details which may be of interest to others.

The code I built gfind from is at http://conwaylife.com/forums/viewtopic.php?p=6825#p6825 . I also added one or two of Paul Tooke's other patches which aren't included in sifFind-v2.c. I used the scripts there to generate the ruleTab array entries to build a Hex_B2o45/S2o45 specific gfind. I prefer not to distribute my version of the code further because I used MSVC to compile it as C++, so there are a few additional changes - which makes it a bit of a hack of a hack. It would be great to have a more polished version of gfind which can handle non-totalistic rules, but that's not a project I'm about to tackle.

The c/4 ship above was found with an 'orthogonal' search. The only useful symmetry option is 'a', as the weighted neighbourhood to simulate hexagonal rules breaks the other symmetry options. This version of gfind will try to run searches with the other symmetry options and may even find results, but they will (almost certainly) blow up.

For 'diagonal' searches, the symmetry options can be used. Results from these searches will move along (1, 1, 0).

[c0b0p0]

Here is a p792 gun.

Code: Select all

x = 1113, y = 946, rule = B2o45/S2o45H
874bo$873b4o$874bobo$874b4o$876bo3$877b2o$876bobobo$877b4o$878b3o$878b
4o$878bobobo2$878bo2bo2bo$880b4o2$881b4o$882b3o4$883bobobo$883bob2obo$
885b3o$886b2o$887bo2$888bo2$888b3o$888b4o$888bobobo$890b2o3$889bo2bo2b
o$891b4o2$892b4o$893b3o4$902b3o$889b3o$889b4o10b3o$890b3o10bo2bo$891b
2o9bobobobo$900bo2bob2obo$898b2obo2bo3bo$901bo$899b3o$899b4o$899bobobo
$901b2o5$994bo$993b4o$989bo4bobo$988bo2b2ob4o$991b3o2bo$989b2ob3o$988b
ob2ob2o$988b2ob2o$984b2o3b2obo2bo$990b2o2bo$985b3o$985b3o$985b3obo$
980b3obo4bo$977bo4b2o$981b4o$965b2o11bo3bobo$965b3o9bob2o3bo$965b4o8b
2obo$966b3o4b2o3b2obo$979b2o2bo$974b3o$974b3o$972bob3obo$969b2ob2o4bo$
971b2o$970b4o$971bobo$973bo$976bo3bo$976bob2obo$976bobobobo$919b3o56bo
2bo$919b4o56b3o$920bobo$920b4o56b3o$921b3o$921b4o$921bobobo$923b2o$
951bo3bo$951bob2obo$951bobobobo$921b2o6b2o25bo$921b3o5b3o18bo2bob2o$
921b4o4b4o16b4o$922b3ob3ob3o14b4obo2b3o$926b4o19b5o$927b3o18b5o$928b2o
19bobo$951bo16$928b2o$927b4o$168bo756b4ob2o$167b4o756b5o$168bobo755b5o
$168b4o755bobo$170bo758bo2$170b3o$170b4o$61bo107bob3obo$60b4o$61bobo
106bob3obo$61b4o107b4o$63bo$173b4o$63b3o108b3o$63b4o$62bob3obo2$63bob
3obo105bobobo$65b4o106bob2obo$177b3o$66b4o108b2o$67b3o109bo2$180bo2$
68bobobo107b3o$68bob2obo106b4o$70b3o107bobobo$71b2o109b2o$72bo2$73bo
107bo2bo2bo$183b4o$73b3o805b3o$73b4o107b4o693b4o$73bobobo107b3o694b3o$
75b2o806b2o2$1109bo$74bo2bo2bo105bobobo917b4o$76b4o106bob2obo912bo4bob
o$188b3o912bo2b2ob4o$77b4o108b2o915b3o2bo$78b3o109bo5b3o905b2ob3o$183b
3o917bob2ob2o$183b4o3b2o5b3o903b2ob2o$184b3o4bo5bo2bo898b2o3b2obo2bo$
79bobobo101b2o5b2o2bobobobo902b2o2bo$79bob2obo106b4o2bob2obo897b3o$81b
3o107bobobo2bo3bo897b3o$82b2o109b2o905b3obo$83bo5b3o1003b3obo4bo$76b3o
1013bo4b2o$76b4o3b2o5b3o1003b4o$77b3o4bo5bo2bo986b2o11bo3bobo$78b2o5b
2o2bobobobo984b3o9bob2o3bo$84b4o2bob2obo984b4o8b2obo$84bobobo2bo3bo
985b3o4b2o3b2obo$86b2o1006b2o2bo$1089b3o$1089b3o$1087bob3obo$1084b2ob
2o4bo$1086b2o$1085b4o$1086bobo$1088bo$bo1089bo3bo$4o1087bob2obo$bobo
1087bobobobo$b4o3bo1084bo2bo$3bo3bobo1084b3o$7b6obo$9b3o1083b3o$8b5o2b
o$11bo2b2obo$12bo2bob2o$15bob2o3b2o$14bo2b2o$22b3o$23b3o$22bob3o$23bo
4bob3o11bo3bo$30b2o4bo7bob2obo$30b4o10bobobobo$31bobo3bo8bo2bo$32bo3b
2obo7b3o$37bob2o59b3o$37bob2o7b3o$36bo2b2o60b3o$101bo2bo$49b2o49bobobo
bo$51bo49bo4bo$50bob3o47bobobo$50bob2o$52b4o49bo$45b2o6bobo48b4o$45b3o
6bo50bobo$45b4o56b4o$46b3o57b3o$106b4o$106bobobo$108b2o11$92b2o$92b4o$
92b2ob4o4b3o$93b5o5b4o$95b5o4b3o$97bobo5b2o$98bo$106b2o$106b3o$106b4o$
103b3ob3o$103b4o$104b3o$105b2o13$126b3o$126b4o$127bobo$127b4o$128b3o$
128b4o$128bobobo$130b2o75$162b2o$162b3o$162b4o$163b3o589$569b2o$569b3o
$569b4o$570b3o!

[strake]

Another still and p3 oscillator:

Code: Select all

x = 16, y = 16, rule = B2o45/S2o45H
12bo$11b4o$12bobo$9b2ob4o$8bob2o2bo$8b2ob2o$6bo2b2obo$5b4ob2o$6bobo$4b
ob4o$3b3o2bo$bo2b3o$4obo$bobo$b4o$3bo!

[c0b0p0]

Here is an SG (sparky glider) -> 2G reaction.

Code: Select all

x = 47, y = 47, rule = B2o45/S2o45H
41bo2$44bo$41bobo$38b3obo$40b2obo2bo$39b4o$40bobo$42bo32$o3bo$ob2obo$o
bobobo$2bo2bo$3b3o2$4b3o!

[strake]

Memory cell:

Code: Select all

x = 70, y = 28, rule = B2o45/S2o45H
5bo$4b4o$5bobo$5b4o8bo$7bo$18bo$35bo$19bo12b3obo$19b2o12b3o$19b3o12b4o
$18bo4bo13bo$17bo7bo9b2o10$o$ob3o62bo$2b3o59b3obo$b4o60b3o$2bo63b4o$4b
2o63bo$67b2o!

[c0b0p0]

Here is a G -> SG reaction.

Code: Select all

x = 28, y = 12, rule = B2o45/S2o45H
24b3o$24b4o$25b3o$26b2o5$o2b2o$2bob2o$5b2o$6bo!

[strake]

Various glider-glider reactions:

Code: Select all

x = 261, y = 30, rule = B2o45/S2o45H
114bobobo$114bob2obo$34b2o80b3o$117b2o$34b3o51b2o28bo$35b3o53bo$8b2o
24bob3o50b4o$11bo23bo20b2o31b3o$9b4o42bo33b3obo58bo$9b3o43b4o34bo57bob
o$9b3obo43b3o91b5o$13bo29bo12bob3o92b5o$43b2o12bo54bo39b4ob2o$43b3o66b
ob3o38b4o22bo23bo35bo$42bob2obo66b3o40b2o22b2o22bob3o31bob3o$43bobobo
65b4o62bob3obo21b3o11b2o2bo17b3o$3o42b2o67bo66b4o6bo14b4o11b2obo18b3o$
4o112b2o70b3obo14bo13b2obo$95b2o45bo39b4o3b3o17b2o11bob2o19b2o$b4o60b
2o27bobobo43b2o39b3o4b4o30bo$ob3obo57bobobo26b4o43b3o48bo$3b2o60b4o27b
3o42bob2obo44b2o32bo32bo$4bo62b2o73bobobo108b3obo$97b3o156b3o$257b4o$
260bo$99b2o157b2o$99b3o$99b4o$100b3o!

[strake]

p24 compound glider:

Code: Select all

x = 18, y = 18, rule = B2o45/S2o45H
3o$2b2o$b4o$2bobo$4bo5$3b2o$6bo$4b4o$4b3o$4b3obo4b3o$8bo6b2o$14b4o$15b
obo$17bo!

[c0b0p0]

Here is a glider duplicator.

Code: Select all

#C[VIEWONLY]
x = 24, y = 24, rule = B2o45/S2o45H
o7bo$2bo4bo$4b3o$5b2o$6bo2$7bo2$8bo5$6bo$6bobo$6b4o5bo7bo$5bob2o8bo4bo
$6bob3o8b3o$2b3o2bo12b2o$2b4o15bo$3b3o$4b2o16bo2$23bo!

Using the glider duplicator, one can make guns with arbitrarily long periods without changing the population, as shown below.

Code: Select all

#C[VIEWONLY]
x = 28, y = 28, rule = B2o45/S2o45H
8bo$7bo2bo$7b2ob2o2$8bobobo$2o8b2o2$b2o$o3bo$2b2o6bo7bo$bobobo11bo$obo
2bobo8bo$bo2bo2bo7bo3$9b2o12bo$8bob2o10bo2bo$8b2ob2o5bo3b2ob2o$9b2obo$
10b2o11bobobo$15b2o8b2o2$16b2o$15bo3bo$17b2o$16bobobo$15bobo2bobo$16bo
2bo2bo!

Code: Select all

#C[VIEWONLY]
x = 1044, y = 1044, rule = B2o45/S2o45H
1024bo$1023bo2bo$1023b2ob2o2$1024bobobo$1026b2o10$1039bo$1038bo2bo$
1038b2ob2o2$1039bobobo$1041b2o1001$2o2$b2o$o3bo$2b2o6bo7bo$bobobo11bo$
obo2bobo8bo$bo2bo2bo7bo3$9b2o$8bob2o$8b2ob2o5bo$9b2obo$10b2o$15b2o2$
16b2o$15bo3bo$17b2o$16bobobo$15bobo2bobo$16bo2bo2bo!

[strake]

A (common p6 oscillator) puffer, speed (1,1,0)/3, puff period 24, synthesized of 2 sparky gliders:

Code: Select all

x = 21, y = 22, rule = B2o45/S2o45H
b2o$obobo$ob2obo$2b3o$3b2o$4bo10$14b3o$14b4o2$15b4o$14bob3obo$17b2o$
18bo!

By the way, I am henceforth calling this oscillator "raindrop" as it reminds me of a raindrop hitting the surface of a pond. Which I guess makes this puffer a "dripper".

[strake]

A p12 oscillator what I posted earlier is actually composite:

Code: Select all

x = 11, y = 11, rule = B2o45/S2o45H
3o$4o$b3o$2b2o4$7b3o$7b4o$8b3o$9b2o!

[strake]

A new kind of gun:

Code: Select all

x = 5, y = 10, rule = B2o45/S2o45H
3bo$3obo$b3o$2b3o$o$4bo$3o$b3o$ob3o$bo!

A p3 oscillator with stator which to my knowledge is novel:

Code: Select all

x = 12, y = 10, rule = B2o45/S2o45H
o2$bo$b2obo$b2ob2o$o3b2o2bo$4b2ob4o$8bobo$8b4o$10bo!