HROT,NW (Higher-range outer-totalistic, weighted)

[Saka]

That is definitely diagonal

hmm, well if you open it in hexgrid.lua, it looks like this


im not sure how hexagonal speeds are named, so I just called that "orthogonal".

[bubblegum]

https://cdn.discordapp.com/attachments/ ... nknown.png

im not sure how hexagonal speeds are named, so I just called that "orthogonal".

Using attachments -> Broke
Using Discord as an image hosting service -> Woke

We can take the square grid as an analogy—orthogonal goes through the centres of the cell borders, while diagonal goes through the vertices. (Alternatively, orthogonal goes perpendicular to a side while diagonal goes parallel to a side.)

[muzik]

This only really applies to small ships but if the trail left behind has a light zigzag on the edges (2 different line slopes) as follows

Code: Select all

x = 25, y = 6, rule = B/S0123456H
20o$b20o$2b20o$3b20o$4b20o$5b20o!

they're orthogonal whereas more prominent teeth (3 different line slopes)

Code: Select all

x = 19, y = 23, rule = B/S0123456H
14bo$13b2o$12b4o$11b5o$10b7o$9b8o$8b10o$7b11o$6b13o$5b13o$4b13o$3b13o$
2b13o$b13o$13o$b11o$b10o$2b8o$2b7o$3b5o$3b4o$4b2o$4bo!

is an indication of it being diagonal.

[lemon41625]

This rule has alot of toads

Code: Select all

x = 95, y = 22, rule = R2,C0,S20-31,43,B20-31,NG
35bo9bo15b4o11b4o8b5o$35b2o7b3o13bo4bo10b5o7b6o$35b2o22bo6bo10bo3bo8bo3bo$36bo7b3o13bo4bo15bo12bo$3b7o35bo12b3o4b3o12b2o8bo3bo$2bo7bo46b12o9bo15bo$b2o7b2o44b3o3b2o3b3o21bobo$o11bo43b2o10b2o$o11bo$o11bo$o11bo20b3o8b3o$o11bo20b2o9b4o$o11bo21bo2bo7b3o$o11bo24b2o7b2o29b2o$b2o7b2o24b3o37bo2b2o$2bo7bo65bob4o$3b7o66b3o3bo$82b2o$82b2o$81b2obo$81bo2bo$81b3o!

=============================================

Another rule

Code: Select all

x = 109, y = 58, rule = R2,C2,S2-4,B4,8-10,NN
37bo65bo5b$3o5bobo6b3o6bobo5b2obobo4b3ob2o5b3ob3o20b2o18b3o4b$o9b2o5bobo5bo3bo4bo9bobo2bo5bo2bo2bo19bo2bo19b2o3b$obo5b2o7bobo7bo11bo4bo2bo10bob2o18b6o16bo3bo2b$obo6bobo5bobo5bo3bo4bobob2o10bo5bobo20bob4obo16bo2b2ob$3o15bo7bobo7bo9b2o8b2o21b3o2b3o17bo2b2o$46b2o11bo18bo3b2o3bo17bobob$80b2o2b2o23b$79b3o2b3o22b$76b2obo2b2o2bob2o19b$75bo4b2o2b2o4bo18b$75bo2bob2o2b2obo2bo18b$5b2o20b2o2b2o2b2o8b2o10b2o19bob6obo21b$b2o3bo6b2o2bobo6b3o2b2o2b3o6bo3bo6bo3bo16bo2bo6bo2bo19b$o2bo9b2obobo7b12o6bobo2b2o2b2o2bobo16bo2bo6bo2bo19b$15bo2b2o8b3o2b3o13bo4bo22bo10bo15b2o3b$14bo13b2o4b2o9bo2bo6bo2bo15bo3bo8bo3bo10bo2b2o2b$o12bo12b3o6b3o8b2o8b2o16b3ob2o6b2ob3o10bo6b$2o12b2o10b3o6b3o8bo10bo16bob2obo6bob2obo10bob3o2b$13bobo12b2o4b2o37b3obo10bob3o16b$28b3o2b3o38bo4b3o2b3o4bo17b$26b12o8bo10bo17bo4bo4bo4bo18b$26b3o2b2o2b3o8b2o8b2o21bo2b2o2bo22b$27b2o2b2o2b2o8bo2bo6bo2bo20bo2b2o2bo22b$49bo4bo23b4o2b4o21b$44bobo2b2o2b2o2bobo19b8o22b$44bo3bo6bo3bo22b2o25b$45b2o10b2o19b4o2b4o21b$78bo3b2o3bo21b$78b3ob2ob3o21b$2b9o68b3o2b3o22b$5bobo14bo58bo2bo24b$o11bo8b3o56b2o2b2o23b$o11bo67bo4bo23b$o3bo3bo3bo10bo17bo6bo29b2o2b2o2b2o21b$2o9b2o10bo16b3o4b3o26b4o6b4o19b$o11bo9bo18bo6bo27bo2bo6bo2bo19b$2o9b2o10bo53bobo6bobo20b$o3bo3bo3bo10bo51bo14bo18b$o11bo64bo10bo20b$o11bo8b3o18b6o27b3obo6bob3o18b$5bobo14bo11bo5b2obo2bob2o5bo18bobo2bob4obo2bobo17b$2b9o22b3o4bobo4bobo4b3o17bobo12bobo17b$34bo4bob2o4b2obo4bo21bobobo2bobobo20b$39b2o8b2o23bo16bo17b$39bo4b2o4bo26bo4b2o4bo20b$39bo4b2o4bo23bo2bo10bo2bo17b$39b2o8b2o24bo14bo18b$34bo4bob2o4b2obo4bo19bo14bo18b$33b3o4bobo4bobo4b3o52b$34bo5b2obo2bob2o5bo53b$42b6o61b$109b$109b$109b$41bo6bo60b$40b3o4b3o59b$41bo6bo!

[muzik]

Just started messing with these:

Code: Select all

x = 42, y = 18, rule = R6,C2,S4-6,B6,NW1000000000001000000000000000000000000000000000000000000000000000000000222000000000020200000000002220000000000000000000000000000000000000000000000000000000001000000000001
3o$obo$obo!

Code: Select all

x = 289, y = 274, rule = R2,C2,S2-3,9-12,16-21,B3,15-25,NW1010104440140410444010101
159$68b2o$65bobo8bo$58bo3b3o4bobobo$60bobo4b2ob3o$58bob2o5bo4b2o$60b5o
b8o$58bo5bob4o2bo2bo$67b3o$69b4o!

Code: Select all

x = 141, y = 61, rule = R4,C2,S2-3,10,14-16,B3,14-16,NW100010001000000000000000000000555000100505001000555000000000000000000000100010001
99bob4o4bob4ob3obobobo3b2o4bob3o$97b2o2b2obobo2bo2b2obobobo3b2ob4obo4b
o2b2o$100bo2bo2b2o2bobobobo3b2o4b6o4b2obo$100bo2b3o6bobob6o2bo2bo2bob
2ob2obobo$98b3o3b3o2bob5o4b4obo3b3o4bo$97bob4o3b2o3bob6o2b2o2bobobo2b
obob2ob2o$99b2ob3o2bo3bobo2b3obob5obobo4bob2o$97b2obob2o5b3obo2bo3b3o
b2o2bo2bo3bo3bo$97b3obo2bo2b4o2b3obob3o2b3o2bobo2bobo$97bobobobo4bo11b
3o2bobobobo2b3ob3o$99b3o3bo3bo2b2o3bo2bob9o4bob2o$100bobobob2ob3obo2b
o2b2obobo3bob2obo2bobobo$97bo3bob3obob2o2bo4bob3ob2obo2bo3b2o2bobo$97b
ob2o2b3obob2ob2o5b4o2bo7b2o2b3o$98b2obo8bo2b5obo5bobob3obo2b2ob2o$54b
4o39b2obo2b2o4b2ob2o2bo2b2obobo4b2o2b2o2b3o$54bo3bo40b3o4b2ob2o2bob2o
b2o3bobobo2bobobo4bo$54bo42b3obobob2obo2b6obobob3o3bo3b2ob4o$55bo41b4o
2bo3bob5o2b2o2bob4o5b2ob2obob2o$98b2ob2o2bo2b2obo3b3ob2ob4o2bobobo2bo
2b2o$97b2ob2ob3o3b3obob3o2b3obobo2b3o3b2o2b2o$99bobobob4o2b2o3bob2o2b
6ob2o2b7o$98b4obo3bob2obobob3obo3b4obobobo5bo$97b2obo3b3obo4bo3b2obob
3o2b3o2bo2bo2b2o$97bo4b3o3bo2bobob3o2bo7bo2bo2bo3bobo$99b2o6b2o2b5o4b
2o3b2o2bobob2o4b2o$99b2o2b2ob2obobob2obobobo3bo6bob3obobo$98b2o2bob3o
4b5obo4b3o4b2o4bob3o$98bo2bob5ob3ob2o5b2o2b2o3b3o4bob2o$99bo2bobobo6b
2obobobo5b3ob4o2b2obo$99bobo2bobo2bo3bo4b3o5b8ob2obo$98bob2obo2b3o4b7o
b3o3b2o2b2ob4o2bo$97b2ob3o2bob2o2bob2obo2bo2b2obo2b2ob2o2bobo$100bob7o
3b4o3b2o2bo4bo3bobobo3bo$97bo5b2o2bo3b3obobo2bo3bob2o2bo4b5o$97bob2ob
obo4b2o2bo2b3ob3ob2o3b2o2bo2bob2o$97bo4bob3obo3bo2bo2b3o2b3o3bobobo2b
3obo$97b2ob2o2b2ob5ob4ob2ob2obob2o2bob2obo$97bobob4obo4bo2b2ob2o4bobo
bobo2b3obo3bo$98b3o2b2o3bob3o2b4ob2o2bo2bo3b2ob2obobo$103bo4bobo2bo3b
o3bo2b2ob2o2b2obo2b2o$o3bo3bo3bo3bo3bo3bo3bo3bo3bo60bo4b4o2b3o3bo2bo2b
4o2bobob3obo3b2o$97bobo4b2o4b3ob3obo2bo2b3obo2b2o2bobobo$98b3o3b2obo2b
2o3b3o3bobob2ob6ob2o2bo$97b2o3bo5bobob2ob2obo4b7o2b4obo2bo$97b5obobob
2o4bobob5o3b3ob3o2bob2o2bo$97b5ob2o3b2obob4obo5b4o3bob3obo2bo$99b2o2b
ob2obob2obo2bobob2o3bo2b2o2bo2b3ob2o$100b4o4b2obo3bobo3b6o3b5o2bo2bo$
98bobo3bo2bob2o2b6ob2o2b3o3b5o3b2o$100bo2b3obo2bo3bo3b2o2bobob2ob3obo
b2obo$99b4obob3obobobo2bob2ob2o4b2obo2bo2bobo$99bob3ob2o2bo2b4ob4o3bo
7b3ob2obo$98b2ob2ob5o5bobob4obo2bo3bob2o3bo2bo$98bob2o5bo4b5o2bo2b3o4b
obob3o4bo$97b3obo2bobob2obo2bo5bobo2b6o3bo$97b2o2bobo3b2obo2b4o4b6o3b
2o2bob2o$97b5ob4ob2o4b5o2bo6b2obo3b2obo$97b3o2b3ob2o2bob3o2b3ob2ob2o2b
4o4b5o$100bob2o3b2obo4b2o2bo4b4obobo4b2obo$97bo4b6o2b2ob3o3b2o5b2o2b2o
2b2o2bo!
[[ THEME Red ]]

Code: Select all

x = 55, y = 45, rule = R10,C2,S3,13-22,B3,20-22,NW100000000010000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000777000000000100000000707000000001000000000777000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000010000000001
52bo$52b3o$53bo10$4b2o$3b4o2$2b6o$3b4o2$2b2o2b2o$2obo2bob2o$3bo2bo3$4b
2o$4b2o12$13b2o2bob2o$12bo2bo2b2o$13bobo$14bo$20bo$18b3o$17bo$18bo$19b
2o!
[[ THEME Red ]]

Code: Select all

x = 72, y = 72, rule = R10,C2,S3,13-22,B3,20-22,NW100000000010000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000777000000000100000000707000000001000000000777000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000010000000001
60b2o$60b2o9$70b2o$70b2o9$40b2o$40b2o9$50b2o$50b2o9$20b2o$20b2o9$30b2o
$30b2o9$2o$2o9$10b2o$o9b2o!
[[ THEME Red ]]

[muzik]

Turns out this has the tendency to be explosive:

Code: Select all

x = 22, y = 2, rule = R10,C0,S3,13-22,B3,20-22,NW100000000010000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000777000000000100000000707000000001000000000777000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000010000000001
2o8b2o8b2o$bo9bo9bo!

Beacons puffing beacons:

Code: Select all

x = 115, y = 110, rule = R10,C0,S3,13-22,B3,20-22,NW100000000010000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000777000000000100000000707000000001000000000777000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000010000000001
23$63b2o$64bo$61bo$61b2o7$13b2o48b2o$14bo49bo$11bo49bo$11b2o48b2o7$13b
2o48b2o$14bo49bo$11bo49bo$11b2o48b2o7$43b2o$44bo$41bo$41b2o7$13b2o$14b
o$11bo$11b2o!

Beaconship:

Code: Select all

x = 41, y = 51, rule = R10,C0,S3,13-22,B3,20-22,NW100000000010000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000777000000000100000000707000000001000000000777000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000010000000001
7$17b2o$17b2o$15b2o$15b2o7$8bo8b2o8b2o$8bo8b2o9bo$15b2o8bo$5b2o8b2o8b
2o7$7bo9b2o$17b2o$5bo9b2o$15b2o!

[muzik]

Some rather interesting things can be done with a pi ship and two blocks:

Code: Select all

x = 27, y = 43, rule = R6,C0,S4-6,B6,NW1000000000001000000000000000000000000000000000000000000000000000000000222000000000020200000000002220000000000000000000000000000000000000000000000000000000001000000000001
8$2o17b2o$2o17b2o20$9b3o$9bobo$9bobo!

Code: Select all

x = 34, y = 20, rule = R6,C0,S4-6,B6,NW1000000000001000000000000000000000000000000000000000000000000000000000222000000000020200000000002220000000000000000000000000000000000000000000000000000000001000000000001
6$10b2o17b2o$10b2o17b2o$19b3o$19bobo$19bobo!

Code: Select all

x = 36, y = 29, rule = R6,C0,S4-6,B6,NW1000000000001000000000000000000000000000000000000000000000000000000000222000000000020200000000002220000000000000000000000000000000000000000000000000000000001000000000001
6$8b2o17b2o$8b2o17b2o9$17b3o$17bobo$17bobo!

Code: Select all

x = 39, y = 54, rule = R6,C0,S4-6,B6,NW1000000000001000000000000000000000000000000000000000000000000000000000222000000000020200000000002220000000000000000000000000000000000000000000000000000000001000000000001
13$13b2o$13b2o13$4b2o17b2o$4b2o17b2o3$4b2o17b2o$4b2o17b2o3$4b2o17b2o$
4b2o17b2o7$13b3o$13bobo$13bobo!

Nontrivial flotilla:

Code: Select all

x = 17, y = 3, rule = R6,C0,S4-6,B6,NW1000000000001000000000000000000000000000000000000000000000000000000000222000000000020200000000002220000000000000000000000000000000000000000000000000000000001000000000001
3o11b3o$obo11bobo$obo11bobo!

[ZackBuildit777]

found an amazing hexagonal rule using a method studied by me but apparently first discovered by someone else (unsure who it was) for allowing some nontotalistic rules in higher ranges without as complicated of rulestrings. the neighborhood and type of rule used is 1.5 hex and ring totalistic respectively.
the rule that's so of note is this one. (example soup)

Code: Select all

x = 64, y = 64, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
b3o2bob3obobobo4b3obo4b3o2bobob2ob2o2bo2b2ob2obo2b2ob3o$obobo2bo6bo2b
2ob3o3bob2o2b7obobobob2obob3o4bo$2b2obobob2o4b4ob3obobo2b2o2b2ob3ob2o
bo2b2ob2ob2ob2obo$8bo2bo6bo2bobob4o2b2ob3o2b3obo3b3obo2b3ob2ob3o$o2b4o
bob2o3bo2b2obo4b2ob2ob2o2bo5b3o5b2o4bobo$b2o3bo3bob2obo2bo2bobo5bo2b3o
2b6ob3o7bob5obo$bob3o3b3obobo2bo3b3obob3ob3o2b2o8b5o2b2obo4bo$obo2b2o
bobob6obo2bo6bo3b2o2bob2ob2obobo3bo5bo2bo2bo$bob2obob4obob3o2bo2bo2b2o
5b2o2bobob2obob3o7bob6o$2o2b5ob4o2b2o4b6o3bobo4b4obo2bobob2o4bo2b2obo
$3obobob6ob3obobobo2b3o3bobo2bo2b2o2b2o2bo5b2obob3obo$3b4obo9b2obo2bo
3bo3b2o3b2obo3bob2ob9o2b3o$o2b2ob9o4bo3b2ob5o2b2ob2obobobo2b2o4bo2bo2b
2o2b2o$3o4bobo2b2obobo2b5o2b2o2bo3b3o2b2o2b2obo2b2ob4obo4bo$ob2obo7bo
bo5bo2bobob2ob2obo3b2o5b3obo4b3o4bobo$bob3ob2o6bobob3obob5o2b3ob4o2b4o
b3obo2bo2b5obo$b5o4bo3bobo5b4obob2obo3bo3b2o5bob5ob9o$b2ob2ob3obobobo
bob2ob3obobo4bo2b2o2b3o3bob3o2bobob2o4bo$4obob3ob2o3bo3b3obobo2b2obo3b
6o3bo2b2obob2o4b2ob2o$2b5o4bob8ob2o2bo2b3ob3o3b2o5bobo3bo2b5o3bo$3o3b
6ob2obo2bobob2o2bobo2b2o2bobo3b7obobo5b3obo$2b2ob3ob2o3bo2b5obob6o2b3o
bo3b2obob2o3b4obo2b2o$3ob2o6bo2b3obo3bobobo4bo5b4ob4o3b3ob4o3bobo$2bo
4bob3o3b5ob2o3bob2o3bob3ob3o2bo3bobo2b4o3bob2o$2bob5obob2o4bo3bob5o2b
obo2bob2o2bobo2b3o2b2o2b8o$2bobo3b2ob4ob2o3bo2bo2b2o2b2ob2o4b2obo4b6o
bobob2ob2o$4ob3o2bo3b2ob4obo3bob2obobobo3b7o5b3o3bo2bob2o$2obo2b2obob
3o2b2obo2b3ob4o3b3o3b2obobob4obobo3b2obob2o$2bobobo2bo4b4o2bob3obob4o
3b3ob7o3bo3b2o2b4o$4bob3o2b2obobo2bo2b4ob2o2b3o3bob2o2b3obobo4b2o3b4o
$2bo4bob2o2b5o5bo2bo2b2o2bobo2bob4obo3b2o2b2ob2o5bo$3bo2bobob3o3bobob
ob3obobo3b6obobob2ob2o3bob4obobob2o$ob3obo2bo2b2o2b7obob3ob4ob7ob6o5b
2o2bobobo$bo2b2obob2ob3o4bob2o2b3o4b4obo4bo2bo2b3ob2obo3b2o2bo$3bo2b2o
3b2ob2obob2obob2o2b2obobobo4b3ob3o2bobo2b3o$3obo2bo3bob7o5b4ob2ob3o6b
o2b2o2b3o4bo3bobo$obo2bo3bobo4bo5b3o9bob5o5b3o6bo2bob2o$b2o8bo3bob2o3b
o2b3obo3bo2bob4obo2bo2bobob2o2bo4bo$obob9o2b5o2b2o2bo2b2ob2obob3o3bob
4obo2bo4b2o2b2o$ob2ob4o8b2ob2ob2ob2ob2obo3bo2bob2obobo2bobob2o2bobob2o
$3b6o2bob4o2b4ob2o2b2o2b3o3b2ob3o3b2obo2b2o2bob2obo$bo2bo3bob2ob2ob9o
b3ob6o2bo4bo2b2obob2obo5bo2bo$bo2bobob5o3bob4ob2o2b3ob3o4b3obob6ob2o2b
ob3o2b2o$3b3obo2bobobobobo3b7obo4b2obob2o3bo2b5o6bobo$2obo2b5o3bobo6b
2o2bob2o2b2obob2obo3b2ob2o3bo2b2ob2o$obobob3obobob3o3bob4o3bo5bobobo3b
2o2b2obo2bo2b3o3bo$obo4b2o4bo2bob2o9b4ob2obob4o7b2o2bo4b2o$2ob2obob3o
2bobo4bobobo5b6o6bob2obo2bo2bobobo2b2obo$b5ob2ob2o4b2o4bob2obo4b2ob2o
5bo2bo2b4o3b3o3bobo$2o4b2obo2bo2bo2b2obo4bo2bo2bob2obobo5bo2b2obobobo
bo3b2o$4obob2obo2b4ob4o2bo2b4o5b4o2b2ob3o3b2obo4b2obo$6b2obobobobo3b2o
bobo4b3o3bobo3bobob2ob3ob3o2b2o3bo$b3o3bo7bo2b6ob5o6b2obo2b2o5b3ob3o4b
ob2o$3b3o3b4obob2obob3obo2bob7o7b2o3bobob4o3bob2o$3b3obobo2b2ob3obobo
bo3bo3bobo3bob2o5bo3b2o2bobob2o$3o3b2ob4ob3o5bo4bo3b2o2bo2bobo3bob2o2b
ob2o2b2ob5o$5bo2bob2ob4o4b3ob3o3bob4ob3obo4bo5bo5bo$bob2obo4bob4ob2ob
obobo3b6obo3bo2bo3bob2o3b2o2b6o$b2o2bo3bobo12b2obo2b6o3b2o2bo2b3o2bob
obo2b3ob2o$b2obobo2bo2bo3b2o3b2o4bobobo3bo4bo4b2o6b2obob2obo$2o2b3o3b
2ob4o2b2o2bo2bo3b6o2bob9obo2bo4b4o$ob3o4b4o2b2o4bob2obo2bo6bobob5obob
5o2b3ob2ob2o$bob9ob2o4bob2ob4ob2o2bo2bo3bo3bo2bobob2ob3o$bobo3b3obo2b
10o2b2o3bob2o4bob3o3b2o3b4ob2ob2obo!

it's comparable to CGOL, though with more spaceships and less diverse still lifes. the name for the rule is currently Amazo (please give suggestions for other names), and the definition for the rule is "a cell is born if out has 1 cell and inner has 2, or if outer has 3 cells and inner has 1, 3, or 4 cells. a cell survives if inner has 2 or 3 cells" with inner referring to the six closest cells, and outer referring to the next six after them.

known (natural) spaceships:

Code: Select all

x = 7, y = 53, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
o$2o2$bo19$bo$3o$2o$b2o19$2bo$2b2o$3bobo$2bo2b2o$5bo$o4b2o$bo$b2o$2bo16$
b2o$b2o$o$obo$2b2o!

listed in order of frequency.
names and speeds:
1) glider, c/4d
2) odder, 3c/16o
3) wider, 4c/10o
4) queener, (3,8)c/23 (how the heck is there a natural oblique this is awesome)

there's also a common weakly sparky p22 oscillator, the bumbler

Code: Select all

x = 4, y = 4, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
b2o$ob2o$2o$bo!

KNOWN TECH STUFF

odder>glider using a hex:

Code: Select all

x = 12, y = 11, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
9b2o$9bobo$10b2o5$bo$3o$2o$b2o!

odder eat:

Code: Select all

x = 18, y = 8, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
15b2o$15bobo$16b2o2$bo$3o$2o$b2o!

wider eat:

Code: Select all

x = 19, y = 13, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
16b2o$16bobo$17b2o2$2bo$2b2o$3bobo$2bo2b2o$5bo$o4b2o$bo$b2o$2bo!

oblique odder rake based on the queener (stabilized):

Code: Select all

x = 134, y = 81, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
9b2o$9b2o$8bo$8bobo$10b2o44$b2o$b2o$o$obo$2b2o5$129b2o$129b2o$128bo$128b
obo$130b2o5$130bo$128b2o$129bo2bo$130bob2o$131b2o$131b3o$131b3o4$110b
2o$110b2o$109bo$109bobo$111b2o!

edit 1:

2g bumbler synthesis:

Code: Select all

x = 12, y = 6, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
9bo$9b2o$o$2o9bo2$bo!

edit 2:

glider deletion in passing:

Code: Select all

x = 12, y = 7, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
9bobo$9b2o4$obo$2b2o!

by the way, the system for copying patterns with HROT rules on hexagonal grids is broken. trying to copy or save the pattern and then load it gives an error of an incorrect rule length. if this is causing anyone interested in this rule issues, the square grid version is R2,C2,S20-36,B13,21,33,43,NW001000000010a0a0100000a000a0000010a0a010000000100

edit 3:

glider kickback

Code: Select all

x = 14, y = 3, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
b2o$3o8bobo$2bo8b2o!

edit 4:

glider eat using bihex, also a bihex > 2 hex reaction

Code: Select all

x = 21, y = 18, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
2b2o$2bob2o$3b2obo$5b2o5$obo$2b2o3$16b2o$16bob2o$17b2obo$19b2o$4bobo$
6b2o!

later I'll make terminology for some of the still lifes and p2 stuff in the rule

edit 5:

final step for a (slightly) dirty synthesis of the queener:

Code: Select all

x = 21, y = 13, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
2o$2o$b3o$3bo6$16b2o$16bob2o$17b2obo$19b2o!

also, does anyone want to try to find a glider gun in this rule? the bumbler (p22) looks like it would work maybe, but i haven't found anything using it to make a glider without destroying at least one support

edit 6:

wider based puffer, can be turned into a glider siderake:

Code: Select all

x = 24, y = 57, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
o$2o$bo$bo4b2o$7bo$5bo2b2o$7bobo$7b2o$8bo4$10bo$10b2o$11bobo$10bo2b2o
$13bo$8bo4b2o$9bo$9b2o$10bo11$9bo$9b2o$10bo$10bo4b2o$16bo$14bo2b2o$16b
obo$16b2o$17bo4$19bo$19b2o$20bobo$19bo2b2o$22bo$3o14bo4b2o$3o15bo$2b4o
12b2o$3b3o13bo$4bo$o3b2o$o4bo$2o$3o!

edit 7:

queener eat:

Code: Select all

x = 25, y = 16, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
b2o$b2o$o$obo$2b2o9$22b2o$22bobo$23b2o!

edit 8:

Q>g:

Code: Select all

x = 57, y = 16, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
b2o$b2o$o$obo$2b2o9$54b2o$54bobo$55b2o!

edit 9:

p3, this kind of stuff should allow omniperiodicity:

Code: Select all

x = 13, y = 8, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
$10b2o$7bob2obo$7b3ob2o$6b2o2b2o$6bobo$7b2o!

[muzik]

Can a rule preserve a gutter more than one cell wide? I tried this for 3, but it only persists for one generation:

Code: Select all

x = 13, y = 6, rule = R2,C0,S,B1,3,5,7,9
2b3o3b3o$b2o7b2o$b2o7b2o$bo9bo$2o9b2o$o11bo!

[confocaloid]

found an amazing hexagonal rule using a method studied by me but apparently first discovered by someone else (unsure who it was) for allowing some nontotalistic rules in higher ranges without as complicated of rulestrings. the neighborhood and type of rule used is 1.5 hex and ring totalistic respectively.
[...]
it's comparable to CGOL, though with more spaceships and less diverse still lifes. the name for the rule is currently Amazo (please give suggestions for other names), and the definition for the rule is "a cell is born if out has 1 cell and inner has 2, or if outer has 3 cells and inner has 1, 3, or 4 cells. a cell survives if inner has 2 or 3 cells" with inner referring to the six closest cells, and outer referring to the next six after them.

known (natural) spaceships:

Code: Select all

x = 7, y = 53, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
o$2o2$bo19$bo$3o$2o$b2o19$2bo$2b2o$3bobo$2bo2b2o$5bo$o4b2o$bo$b2o$2bo16$
b2o$b2o$o$obo$2b2o!

listed in order of frequency.
names and speeds:
1) glider, c/4d
2) odder, 3c/16o
3) wider, 4c/10o
4) queener, (3,8)c/23 (how the heck is there a natural oblique this is awesome)
[...]

A 2c/66 orthogonal in a variant of the rule:

Code: Select all

x = 12, y = 5, rule = R2,C0,S3,20-36,B13,21,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
2bo$2b2o2bo2bo$2obo2b5o$b2o3bo3b2o$2bo7bo!

This variant also supports the small objects and reactions:

Code: Select all

#C optional birth: 6-9, 15-19, 27-29, 36-39, 46-49, 56-59, 62, 65-66
#C optional survival: 5-9, 15-19, 25-29, 35, 37-39, 46-49, 55-60, 63-66
#C fixed birth: 0-5, 10-14, 20-26, 30-35, 40-45, 50-55, 60-61, 63-64
#C fixed survival: 0-4, 10-14, 20-24, 30-34, 36, 40-45, 50-54, 61-62
x = 78, y = 73, rule = R2,C0,S3,20-36,B13,21,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
71bo$71b2o2$72bo9$16b2o$16bobo$17b2o5$8bo$7b3o$7b2o$8b2o62bo$71b3o$71b
2o$72b2o3$45b2o$44bob2o$44b2o$45bo$16b2o$16bobo$17b2o2$2bo$b3o$b2o$2b
2o5$73bo$73b2o$74bobo$73bo2b2o$76bo$71bo4b2o$42bo29bo$42b2o2bo2bo22b2o
$16b2o22b2obo2b5o22bo$16bobo22b2o3bo3b2o$17b2o23bo7bo2$2bo$2b2o$3bobo$
2bo2b2o$5bo$o4b2o$bo$b2o$2bo4$72b2o$72b2o$71bo$71bobo$73b2o!

Edit: here is a variant with a p216 oscillator and a glider gun

Code: Select all

#C optional birth (6): 6, 15-16, 56, 65-66
#C optional survival (12): 5-6, 16, 26, 46, 55-56, 60, 63-66
#C [[ THEME LifeHistory MAXGRIDSIZE 9 ]]
x = 166, y = 83, rule = R2,C0,S3,20-36,B13,21,26,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
46b2o$45b3o$47bo4$4bo$4b2o$4b2o3bo$9b3o$159bo$11b2o146b2o2$8b3o149bo$
9b2o$10bo7$104b2o$32b2o70bobo$32bobo70b2o$33b2o2$2b2o3bobo$ob2obo$o3b
2o90bo$bo2bo90b3o$2o93b2o$bo94b2o62bo$159b3o$159b2o$160b2o7$44bo59b2o$
44b2o58bobo$44b2o59b2o$48bo$46bo43bo$47bobo39b3o$89b2o$47bo42b2o$46b2o
b2o$46b4o$47b2o$48bo$161bo$161b2o$162bobo$161bo2b2o$164bo$159bo4b2o$
130bo29bo$130b2o2bo2bo22b2o$104b2o22b2obo2b5o22bo$104bobo22b2o3bo3b2o$
105b2o23bo7bo2$90bo$90b2o$91bobo$90bo2b2o$93bo$88bo4b2o$89bo$89b2o$90b
o4$160b2o$160b2o$159bo$159bobo$161b2o!

[ZackBuildit777]

found an amazing hexagonal rule using a method studied by me but apparently first discovered by someone else (unsure who it was) for allowing some nontotalistic rules in higher ranges without as complicated of rulestrings. the neighborhood and type of rule used is 1.5 hex and ring totalistic respectively.
[...]
it's comparable to CGOL, though with more spaceships and less diverse still lifes. the name for the rule is currently Amazo (please give suggestions for other names), and the definition for the rule is "a cell is born if out has 1 cell and inner has 2, or if outer has 3 cells and inner has 1, 3, or 4 cells. a cell survives if inner has 2 or 3 cells" with inner referring to the six closest cells, and outer referring to the next six after them.

known (natural) spaceships:

Code: Select all

x = 7, y = 53, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
o$2o2$bo19$bo$3o$2o$b2o19$2bo$2b2o$3bobo$2bo2b2o$5bo$o4b2o$bo$b2o$2bo16$
b2o$b2o$o$obo$2b2o!

listed in order of frequency.
names and speeds:
1) glider, c/4d
2) odder, 3c/16o
3) wider, 4c/10o
4) queener, (3,8)c/23 (how the heck is there a natural oblique this is awesome)
[...]

A 2c/66 orthogonal in a variant of the rule:

Code: Select all

x = 12, y = 5, rule = R2,C0,S3,20-36,B13,21,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
2bo$2b2o2bo2bo$2obo2b5o$b2o3bo3b2o$2bo7bo!

This variant also supports the small objects and reactions:

Code: Select all

#C optional birth: 6-9, 15-19, 27-29, 36-39, 46-49, 56-59, 62, 65-66
#C optional survival: 5-9, 15-19, 25-29, 35, 37-39, 46-49, 55-60, 63-66
#C fixed birth: 0-5, 10-14, 20-26, 30-35, 40-45, 50-55, 60-61, 63-64
#C fixed survival: 0-4, 10-14, 20-24, 30-34, 36, 40-45, 50-54, 61-62
x = 78, y = 73, rule = R2,C0,S3,20-36,B13,21,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
71bo$71b2o2$72bo9$16b2o$16bobo$17b2o5$8bo$7b3o$7b2o$8b2o62bo$71b3o$71b
2o$72b2o3$45b2o$44bob2o$44b2o$45bo$16b2o$16bobo$17b2o2$2bo$b3o$b2o$2b
2o5$73bo$73b2o$74bobo$73bo2b2o$76bo$71bo4b2o$42bo29bo$42b2o2bo2bo22b2o
$16b2o22b2obo2b5o22bo$16bobo22b2o3bo3b2o$17b2o23bo7bo2$2bo$2b2o$3bobo$
2bo2b2o$5bo$o4b2o$bo$b2o$2bo4$72b2o$72b2o$71bo$71bobo$73b2o!

Edit: here is a variant with a p216 oscillator and a glider gun

Code: Select all

#C optional birth (6): 6, 15-16, 56, 65-66
#C optional survival (12): 5-6, 16, 26, 46, 55-56, 60, 63-66
#C [[ THEME LifeHistory MAXGRIDSIZE 9 ]]
x = 166, y = 83, rule = R2,C0,S3,20-36,B13,21,26,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
46b2o$45b3o$47bo4$4bo$4b2o$4b2o3bo$9b3o$159bo$11b2o146b2o2$8b3o149bo$
9b2o$10bo7$104b2o$32b2o70bobo$32bobo70b2o$33b2o2$2b2o3bobo$ob2obo$o3b
2o90bo$bo2bo90b3o$2o93b2o$bo94b2o62bo$159b3o$159b2o$160b2o7$44bo59b2o$
44b2o58bobo$44b2o59b2o$48bo$46bo43bo$47bobo39b3o$89b2o$47bo42b2o$46b2o
b2o$46b4o$47b2o$48bo$161bo$161b2o$162bobo$161bo2b2o$164bo$159bo4b2o$
130bo29bo$130b2o2bo2bo22b2o$104b2o22b2obo2b5o22bo$104bobo22b2o3bo3b2o$
105b2o23bo7bo2$90bo$90b2o$91bobo$90bo2b2o$93bo$88bo4b2o$89bo$89b2o$90b
o4$160b2o$160b2o$159bo$159bobo$161b2o!

THAT IS REMARKABLY IMPRESSIVE! And also I believe it marks the first hexagonal rule with a neighborhood size less than range 3 to have a spaceship gun?

[confocaloid]

long nested quote

THAT IS REMARKABLY IMPRESSIVE! And also I believe it marks the first hexagonal rule with a neighborhood size less than range 3 to have a spaceship gun?

It is not the first hexagonal rule to have a gun. There were certainly earlier spaceship guns, see for example Hex rule B2o/S2m34: 1997 write-up with viewable patterns (range-1 isotropic neighbourhood):

[...]
Larger constructions: A Glider Gun

Three of the period-42 oscillators can be combined to make a glider gun. I found this by first pairing up oscillators and testing the results. This didn't yield a glider gun, but it yielded a pair with a larger spark, to which I added the third:

Code: Select all

x = 10, y = 10, rule = B2o/S2m34H
12b2ob$12bob$12bo4b2ob$2bo9bo5b2obob$b2obo10bo2bob2ob$2ob3o13b2ob2ob$
2bobobo13bobob$2b2ob4o3b2o6bob2ob$2bob2obo5b3o4b3obob$13bobo6bob$12b4ob$
12bo3bob$13b5ob$15bob$15bob!

[...]

Edit: links to some other rules
B2/S2opH viewtopic.php?p=11334#p11334
B2o3m56/S2om4oH viewtopic.php?p=29296#p29296
2/23/7H viewtopic.php?p=144141#p144141
B2o3-o4-m56/S2m3o4-o56H viewtopic.php?p=174548#p174548

[pcallahan]

It is not the first hexagonal rule to have a gun.

Correct. The hex rule I explored in 1997 has many oscillators, reflectors, and guns. It gives the appearance of stabilizing fast on random patterns, but if you enumerate small seeds, all kinds of things show up. I probably used a modification of gencols to find the glider guns, but I don't remember now. I was in Aberystwyth, Wales at the time with Nick Gotts, looking for the bound on infinite growth patterns in CGOL and somehow had time to work on this as well.

[lemon41625]

Can a rule preserve a gutter more than one cell wide? I tried this for 3, but it only persists for one generation:

Code: Select all

x = 13, y = 6, rule = R2,C0,S,B1,3,5,7,9
2b3o3b3o$b2o7b2o$b2o7b2o$bo9bo$2o9b2o$o11bo!

Ok so I thought about this for a bit. For the case of non-weighted isotropic HROT, I'm pretty sure its impossible unless the rule is unable to escape its own bounding box. If it can't escape its bounding box, however, it is possible.

In addition, for weighted rules, it may be possible that with the right combination of weights, there might be one birth condition that slips through the gaps and enables this symmetry to hold.

Proof:
Let w_ij be the weights of the rule in the ith column and the jth row and they can either be 0 or 1 (the 0th row/column is the centre one). We will assume that the neighbourhood weights are D8 symmetric. We also let R denote the range of the rule and w_i denote the sum of all weights in the ith column.

For the rule to preserve width-3 gutter symmetry & escape its bounding box, there are 3 conditions:

1. we need birth on any number smaller than or equal to w_1 + ... + w_R. (to escape bounding box)
2. we need no births on any even number smaller than 2(w_2 + ... + w_R). (preserve central column)
3. there must be no births in the set { sum(S): S ∈ { 𝒫({w_ij : i > (R - 2)} ∪ {w_ij + w_(i+2)j : (R - 2) ≥ i ≥ 1 }) } }. (preserve column one cell to the left of the central column)

Any forbidden condition in set (3) can be split into 2 parts X and Y. X originates from the first set and since w_ij = 0 or 1, we know X can be any number from 0 to w_(R-1) + w_R. Now, since X can be any number, not just odd / even, set (3) will cover all conditions smaller than or equal to max(X + Y). Thus, the only way to ensure that the rule can fulfil (1) is for max(X + Y) < (w_1 + ... + w_R).

As it turns out, max(Y) = (w_1 + ... + w_(R-2)) + (w_3 + ... + w_R).

Thus,
(w_1 + ... + w_(R-2)) + (w_3 + ... + w_R) + w_(R-1) + w_R < (w_1 + ... + w_R)
(w_2 + ... + w_(R-2)) + w_(R-1) + w_R < w_2

This is impossible. Therefore, a rule preserving width-3 gutters cannot escape its own bounding box.

[confocaloid]

3. there must be no births in the set { sum(S): S ∈ { 𝒫({w_ij : i ≥ 2} ∪ {w_ij + w_(i+2)j : 1 ≥ i ≥ R - 2 }) } }. (preserve column one cell to the left of the central column)

I don't yet follow this part. At least the inequality 1 ≥ i ≥ R - 2 must be incorrect (e.g. if R = 4, it becomes 1 ≥ i ≥ 2 which is impossible).

In addition, I'm not sure if I understand how the columns/rows in the (2R+1)-by-(2R+1) neighbourhood should be numbered. Would the following be correct for range 3? (With w_ij = w_ji due to symmetry.)

Code: Select all

--------------------------- +
w33 w23 w13 w03 w13 w23 w33 | w3
w32 w22 w12 w02 w12 w22 w32 | w2
w31 w21 w11 w01 w11 w21 w31 | w1
w30 w20 w10 w00 w10 w20 w30 | w0
w31 w21 w11 w01 w11 w21 w31 | w1
w32 w22 w12 w02 w12 w22 w32 | w2
w33 w23 w13 w03 w13 w23 w33 | w3
--------------------------- +
 w3  w2  w1  w0  w1  w2  w3

Edit: if I'm not wrong, the part "3." should be like this instead:

To preserve empty column to the left of the central column, no birth condition is allowed to be the sum of elements of a subset of

{ w_ij : i > R-2 } ∪ { w_ij + w_(i+2)j : 1 <= i <= R-2 }

(In the numbering above, suppose the columns "w0 w1 w2" in the right half are empty and the pattern is symmetric w.r.t. the right column "w1". Then the first of two sets in the union is for pattern cells in several leftmost columns that are in the neighbourhood but the corresponding mirror-symmetric cells are not, and second set is for pattern cells that are in the neighbourhood and their corresponding mirror-symmetric cells are also in the neighbourhood.)

[lemon41625]

3. there must be no births in the set { sum(S): S ∈ { 𝒫({w_ij : i ≥ 2} ∪ {w_ij + w_(i+2)j : 1 ≥ i ≥ R - 2 }) } }. (preserve column one cell to the left of the central column)

I don't yet follow this part. At least the inequality 1 ≥ i ≥ R - 2 must be incorrect (e.g. if R = 4, it becomes 1 ≥ i ≥ 2 which is impossible).

oh yes, my mistake the inequality should be (R - 2) ≥ i ≥ 1. I'll edit the post to correct that.

In addition, I'm not sure if I understand how the columns/rows in the (2R+1)-by-(2R+1) neighbourhood should be numbered. Would the following be correct for range 3? (With w_ij = w_ji due to symmetry.)

Code: Select all

--------------------------- +
w33 w23 w13 w03 w13 w23 w33 | w3
w32 w22 w12 w02 w12 w22 w32 | w2
w31 w21 w11 w01 w11 w21 w31 | w1
w30 w20 w10 w00 w10 w20 w30 | w0
w31 w21 w11 w01 w11 w21 w31 | w1
w32 w22 w12 w02 w12 w22 w32 | w2
w33 w23 w13 w03 w13 w23 w33 | w3
--------------------------- +
 w3  w2  w1  w0  w1  w2  w3

yes, that should be correct. the 0th column / row is the centre one. I'll clarify that in the original post as well.

EDIT:

Edit: if I'm not wrong, the part "3." should be like this instead:

To preserve empty column to the left of the central column, no birth condition is allowed to be the sum of elements of a subset of

{ w_ij : i > R-2 } ∪ { w_ij + w_(i+2)j : 1 <= i <= R-2 }

(In the numbering above, suppose the columns "w0 w1 w2" in the right half are empty and the pattern is symmetric w.r.t. the right column "w1". Then the first of two sets in the union is for pattern cells in several leftmost columns that are in the neighbourhood but the corresponding mirror-symmetric cells are not, and second set is for pattern cells that are in the neighbourhood and their corresponding mirror-symmetric cells are also in the neighbourhood.)

oops yeah my bad, I realised the condition i > 2 was wrong while writing down the proof but forgot to change it in the conditions listed. it is corrected now. thanks for looking through the proof

[iddi01]

One thing you can do with weighted neighborhood is creating a rule almost identical to a range-1 outer-totalistic rule but with the dynamics slightly tilted to your favor, like Life with "nine neighbors".

I made three such rules based on Seeds, which are (almost) non-explosive.

1. This one is explosive on the large scale due to rakes being way too common:

Code: Select all

R2,C0,S,B12,14-16,NW1111116761170711676111111

2. This one has a common, diagonal spaceship, quite stable, except for the block, which causes explosive growth:

Code: Select all

R2,C0,S,B12,14-17,NW1010106760170710676010101

3. This one differs the most from Seeds, but is also the most interesting, and dots spaced in a correct way emulates B3/S23:

Code: Select all

x = 118, y = 184, rule = R3,C0,S2-3,B3,14,16-20,NW1001001000000000777001070701007770000000001001001
8$11bo$10bo71$9bo2bo$10b2o15$10bo67bo$11bo66bo$75bo$75bo4$9bo$8bo19$
10b2o68bo2bo2$9bo2bo$83bo2bo3$83bo50$110b2o$109bo2bo!

The census turned out to be pretty good: https://catagolue.hatsya.com/census/xps ... th-life/C1

[b-engine]

c/3 and extensible c/4:

Code: Select all

x = 33, y = 14, rule = R1,C2,S4,6,B6,NW222202223
3bo$2b2o2$b2o$3o2$23bo7bo$23b2o6b2o$4bo8bo7bobo5bobo$4b2o7b2o6b2o6b2o
$2bobo6bobo5bobo5bobo$2b2o7b2o6b2o6b2o$obo6bobo5bobo5bobo$bo8bo7bo7bo
!

[hotcrystal0]

Rules like this one are fun:

Code: Select all

x = 40, y = 25, rule = R3,C2,S2-3,14-18,21-22,B3,21-27,NW1001001000000000777001070701007770000000001001001
o2bo3$o2bo15$24bo2bo2bo6b3o$37bo$38bo$24bo3$27bo!

Edit: This rule allows for cursed flotillae like this one:

Code: Select all

x = 8, y = 14, rule = R4,C2,S2-3,14-22,27,B3,21-27,NW100010001000000000000000000000777000100707001000777000000000000000000000100010001
5b2o$2b3ob2o$2b5o$3b3o7$b3o$5o$3ob2o$3b2o!

Edit 2: Two meta-blinkers:

Code: Select all

x = 22, y = 3, rule = R4,C2,S2-3,14-22,27,B3,21-27,NW100010001000000000000000000000777000100707001000777000000000000000000000100010001
17bo$o2b3o2bo4bo3bo3bo$17bo!

[hotcrystal0]

Edit: This rule allows for cursed flotillae like this one:

Code: Select all

x = 8, y = 14, rule = R4,C2,S2-3,14-22,27,B3,21-27,NW100010001000000000000000000000777000100707001000777000000000000000000000100010001
5b2o$2b3ob2o$2b5o$3b3o7$b3o$5o$3ob2o$3b2o!

3 cursed queen bee shuttle stabilizations (from top to bottom, P36, P30, P26):

Code: Select all

x = 46, y = 77, rule = R4,C2,S2-3,14-22,27,B3,21-27,NW100010001000000000000000000000777000100707001000777000000000000000000000100010001
25$28bo$28bobo$14bo14bobo$14bo14bo2bo3b3o$14bo14bobo$28bobo$28bo11$37b
o$15b3o19bo$37bo$28bo$28bobo$29bobo$29bo2bo$29bobo$28bobo$28bo10$28bo
$28bobo$17bo11bobo$17bo11bo2bo2b3o$17bo11bobo$28bobo$28bo!

[lemon41625]

Found these photons in Minibugs with factoriosrc

Code: Select all

x = 90, y = 20, rule = R2,C2,S6-9,B7-8,NM
11b8o25b10o24b3o9b$7b3ob3o2b3ob3o19b3ob2o2b2ob3o20b7o7b$6b4o2b2o2b2o2b4o14b3ob2o2b2o2b2o2b2ob3o12b3ob2o3b2ob3o3b$5b2o2bo10bo2b2o12b4o2bo10bo2b4o10b4o2bo3bo2b4o2b$5b2o2bo2b2o2b2o2bo2b2o11b2o2bo2bo4b2o4bo2bo2b2o8b2o2bo2bo3bo2bo2b2ob$5bo3bo10bo3bo11b2o2bo16bo2b2o8b2o2bo9bo2b2ob$4b3o2b2o8b2o2b3o10bo4bo14bo4bo8bo4bo7bo4bob$9b2o8b2o14b3o22b3o6b3o15b3o$9b2o8b2o69b$7bob2o8b2obo67b$10bo8bo27b3o21b2o13b2o2b$5bobo2b2o6b2o2bobo20b7o20b3o9b3o3b$3b3obo14bob3o14b3ob2o3b2ob3o14b2o2b3o5b3o2b2ob$2b3o2b2o12b2o2b3o12b4o2bo3bo2b4o13b2o2b2ob5ob2o2b2ob$2bobo2b2o12b2o2bobo11b2o2bo2bo3bo2bo2b2o16bo2b2ob2o2bo5b$bo2bo2bo14bo2bo2bo10b2o2bo9bo2b2o16bo2bo3bo2bo5b$2o2bo20bo2b2o9bo4bo7bo4bo15bo11bo4b$2o2bo20bo2b2o8b3o15b3o16bobo3bobo6b$bo2b3o16b3o2bo47bobobobo7b$3bo22bo!

I believe this brings the number of speeds in this rule up to 6 speeds (not including multiples of the same speed)

EDIT:

Some results from cfind

2c/3o partial

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,B7-8,NM
5b3ob2ob3o$3b3ob2o2b2ob3o$2b2o4bo2bo4b2o$7b2o2b2o$2b4ob2o2b2ob4o$3b4ob
4ob4o$4b2o2bo2bo2b2o$8bo2bo$6bo6bo$6b3o2b3o$4b2o2bo2bo2b2o$3b3o8b3o$3b
2o10b2o$6bo6bo$2bob2o8b2obo$ob2ob4o2b4ob2obo!

3c/4o partial

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,B7-8,NM
4bo8bo$3b3o6b3o$b3ob3o2b3ob3o$b2o3b2o2b2o3b2o$3bo2b2o2b2o2bo$4b4o2b4o$4b
2o2b2o2b2o$3bo4b2o4bo$2b3o2bo2bo2b3o$2o14b2o$2o5bo2bo5b2o$b3o2bob2obo2b3o
$b3o10b3o$2bo2b2o4b2o2bo$2b14o$2bo5b2o5bo$3o5b2o5b3o!

[iddi01]

Two varants of Factorio (made them because i like some of its dynamics but hate the way that everything vanishes quickly into nothingness)

Pseudo-Factorio (similar birth and survival conditions but using ultimium weighted neighborhood):

Code: Select all

x = 63, y = 23, rule = R2,C0,S2,4,B3,NW0010000200120210020000100
3$52bo2$51bo$50bo$48bo$58b2o2$58b2o4$6bo55bo$34bo$3bo2b2o53bo$34b2o$
59bo$33bo$60bo!

"SlowFactorio" (Made the same way as SlowLifeB0 but based on Factorio):

Code: Select all

x = 105, y = 51, rule = R3,C0,S4,6,9,B0-7,10,N+
26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$
26b79o$26b79o$26b79o$26b79o$26b79o$bo2b3o19b15ob2o3b58o$26b79o$26b79o$
26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$
26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$
26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$26b79o$
26b79o$26b79o$26b79o!

[confocaloid]

p20 diagonal 1c/1 spaceship in a hexagonal rule

Code: Select all

x = 24, y = 11, rule = R3,C0,S,B2,20,200,NW00010A00000000640A64016400000A0100000A01000064000000640000010A0000010A00006401640A64000000000A0100H
bobo13bo$20bo$o5bo$22bo3$o22bo4$23bo!

[muzik]

Is it at all possible to construct a range-2 rule that behaves identically to range-1 Life, except cells are also born with this range-2 transition?

Code: Select all

x = 5, y = 5, rule = B3/S23
5o$5o$2ob2o$5o$5o!

[b-engine]

Is it at all possible to construct a range-2 rule that behaves identically to range-1 Life, except cells are also born with this range-2 transition?

Code: Select all

x = 5, y = 5, rule = B3/S23
5o$5o$2ob2o$5o$5o!

There's seems a bug here:

Code: Select all

x = 0, y = 0, rule = R2,C2,S2-3,B3,136,NW8888881118810188111888888
5o$5o$2ob2o$5o$5o!

There're 136 neighbors in the weighted neighborhood, but LifeViewer says the maximum neighbors a cell can have is 8.