Triangular neighbourhood rules

[LaundryPizza03]

Common Rule 150 replicator:

Code: Select all

x = 9, y = 5, rule = B13/SLV
bobo$b3o!

Rich in natural spaceships and wickstretchers:

Code: Select all

x = 0, y = 0, rule = B13/S1LV
o!
[[ RANDOMIZE ]]

Code: Select all

x = 0, y = 0, rule = B135/S1LV
o!
[[ RANDOMIZE ]]

[muzik]

Common Rule 150 replicator:

Code: Select all

x = 9, y = 5, rule = B13/SLV
bobo$b3o!

It even works properly as a unit cell as well:

Code: Select all

x = 60, y = 2, rule = B13/SLV
bobobobo5bobobobo5bobobobobobo9bobo5bobobobo$b3ob3o5b3ob3o5b3ob3ob3o9b
3o5b3ob3o!
[[ AUTOFIT STOP 256 ]]

I believe this is the third Rule 150 replicator that's been found so far in any 2D rule, after the following two.

Code: Select all

x = 1, y = 5, rule = B2a/S1e3eiy5i
o$o2$o$o!
[[ AUTOFIT ]]

Code: Select all

x = 3, y = 1, rule = B02aci6i/S1e5i
3o!
[[ AUTOFIT ]]

If we can find a clean rake or something in this rule, then a "Sierpinski generator" for this replicator must be possible...

[muzik]

Some of the triangular CA examples from Visions of Chaos:

Walls

Code: Select all

x = 20, y = 20, rule = B01237Y/S1234567L
bob4o5b3o3b2o$bobob3o3bo3bobobo$bob3obo7bo$6bo3b2o2b2o2bo$b3o4bo2b3obo
b2o$b2o2bo2bo5b2obo$bo2b4ob2ob2obo3bo$2o2b6ob4obo$o5bo2bob2o2b3o$2ob2o
bob2ob2ob2o2bo$b2o3bo2b2o2bobob2o$o2b2obob3o5bo2bo$2bo4b3o2bo3b2o$2bob
obo2b3o3b2o2bo$bobo2b4ob4ob4o$obo4b2obob2o3bobo$obo3bob2o2bobob3o$obo
2b2ob2o2bo4bobo$obo2b2o4bo2bobo2bo$o2b5o6bo!
[[ RANDOMIZE ]]

Coral

Code: Select all

x = 20, y = 20, rule = B5/S56789L
bob4o5b3o3b2o$bobob3o3bo3bobobo$bob3obo7bo$6bo3b2o2b2o2bo$b3o4bo2b3obo
b2o$b2o2bo2bo5b2obo$bo2b4ob2ob2obo3bo$2o2b6ob4obo$o5bo2bob2o2b3o$2ob2o
bob2ob2ob2o2bo$b2o3bo2b2o2bobob2o$o2b2obob3o5bo2bo$2bo4b3o2bo3b2o$2bob
obo2b3o3b2o2bo$bobo2b4ob4ob4o$obo4b2obob2o3bobo$obo3bob2o2bobob3o$obo
2b2ob2o2bo4bobo$obo2b2o4bo2bobo2bo$o2b5o6bo!
[[ RANDOMIZE ]]

Three-state Life

Code: Select all

x = 20, y = 20, rule = 456X/46/3L
bob4o5b3o3b2o$bobob3o3bo3bobobo$bob3obo7bo$6bo3b2o2b2o2bo$b3o4bo2b3obo
b2o$b2o2bo2bo5b2obo$bo2b4ob2ob2obo3bo$2o2b6ob4obo$o5bo2bob2o2b3o$2ob2o
bob2ob2ob2o2bo$b2o3bo2b2o2bobob2o$o2b2obob3o5bo2bo$2bo4b3o2bo3b2o$2bob
obo2b3o3b2o2bo$bobo2b4ob4ob4o$obo4b2obob2o3bobo$obo3bob2o2bobob3o$obo
2b2ob2o2bo4bobo$obo2b2o4bo2bobo2bo$o2b5o6bo!
[[ RANDOMIZE ]]

Single Centered 01

Code: Select all

x = 20, y = 20, rule = /13/5L
o!

Single Centered 02

Code: Select all

x = 20, y = 20, rule = B13/S2LE
o!

Single Centered 03

Code: Select all

x = 20, y = 20, rule = /1/10LE
o!

[Majestas32]

What exactly *are* the neighborhoods represented by, for example, LV?

[muzik]

A neighbourhood consisting of only far vertices (which imo should be supported as one of the usual range-1 neighbourhoods) partitions the grid into three layers:

Code: Select all

x = 5, y = 4, rule = R2,C2,S1,3,B1,3,N@044080L
o!
[[ AUTOFIT GRID ]]

Code: Select all

x = 5, y = 4, rule = R2,C2,S0,2,B1,3,N@044080L
o!
[[ AUTOFIT GRID ]]

[muzik]

This LB neighbourhood rule has long-lasting soups:

Code: Select all

x = 58, y = 31, rule = B3/S245LB
$bob3o4b2o4bob2obo7b2o3bobobo5b3ob2obo5bo$b2ob3obob3ob2o2bobobo3b2obo
bo2b4o2b2o2b2o2bobo2bob2o$b5o3b4o2bo4bob3obobob5ob2o3bobob8ob2o$b5o2b
o5b3o2bo3b4obobo2bobob4o4bob2o4b2o$3b4ob2o3b5o2bobob5o4bo2b2o2b2obo4b
2o3bo$b2obo2b6ob2o2b2o2b2obob2obobob2o8bob2obob5o$b3o2bob2obob4o3b2o4b
2ob9ob4o2b2o2b3o4bo$bo2b9ob2ob3o5bo2b2ob8o2bobobo2bob2obo2b2o$b2obobo
2b2ob3obob2ob2ob3o2b2obobob5ob3obob6o3bo$2bob2obobobobo4bo2b2o2b2obob
2o3b4ob4o4bo2bob3obo$2bobob2o2bobobob2o2b3o2b2obo2b2ob4o8b3ob3ob2o$2b
o4bobobo2b3obobob4ob2ob2obob2ob3o2b6obob2o2b2o$bobobobobo6b2ob5o2bo5b
o8bo2bo2b2obob2o2b2o$b2obobo3b2ob3o3b2o2bobob4o2b3obobo2bob4ob2o2bobo
bo$4b2o3b3obob3ob3o2b2o2b8ob2o2bob5obob2o3bo$3b3obo8b2o2b2obo4b6o2bob
5o4bo9bo$b2o2b2obobo2bo2bob2o4bo5b2o2b2ob3obo4b2obo2b3o$3bob3ob6o2bob
obo6bo3bobo2bo2bo5b2o3b2ob4o$bo4bobo3b2ob2o9bob2obobo4b3o3b2ob3o2b3o$
3b3ob4ob5obob6o4b2o2b2ob2ob2o5bo3b2ob2o$2b2ob3o3bo2bo3b2obo3bo5bobo2b
o3bobo3b4o2bo2bobo$b3obo2bobo3b2o8bob5obo2b5ob5ob3obob2obo$bob2o4b2o2b
2ob3o2b5o2bo2b4o3bob2o3bob2o3bobo2bo$2bo3b2o2bo2b2ob3o3bo3b4o3b2o3bo3b
2obo2bobob2ob2o$bob2obo2bob2o3b2o2bo3b2o2b2o2b6obo2b2ob3o4bo2b3o$2b8o
b2obob3o3b2ob2o2bobobob3o2b5ob2o3b4o$b2o2b2obo3b2o2b2obo2b5o3b2obob9o
b4obo3bob2o$bo8b2o5b5obo3bob2obob2ob2obo2b5o3bo5bo$bo4b3obo3bob3ob4o2b
4o2b3obo3bobob3ob2ob2ob3o$2b2o2b2ob3obobo2b2o3bo2bo2b3ob3o2bobo2b3o7b
3obo!

[muzik]

Some small oscillators, the second having a very strange kinetic symmetry I haven't seen before:

Code: Select all

x = 7, y = 2, rule = B36/S246LB
o5bo$2b3o!

Code: Select all

x = 5, y = 2, rule = B36/S246LB
3b2o$bo2bo!

[bprentice]

Code: Select all

x = 1, y = 1, rule = B1/SLB
o!

Brian Prentice

[muzik]

The following are the replicators for the radiation and biohazard neighbourhoods:

Code: Select all

x = 5, y = 4, rule = B13/S13LR
o!
[[ AUTOFIT GRID ]]

Code: Select all

x = 5, y = 4, rule = B13/S02LR
o!
[[ AUTOFIT GRID ]]

Code: Select all

x = 5, y = 4, rule = B13579/S13579LB
o!
[[ AUTOFIT GRID ]]

Code: Select all

x = 5, y = 4, rule = B13579/S02468LB
o!
[[ AUTOFIT GRID ]]

As mentioned before, Radiation is effectively just an outstretched version of the triangular von Neumann neighbourhood, which ends up emulating the hexagonal range 1 neighbourhood. Biohazard appears to emulate the range 2 asterisk neighbourhood in this case:

Code: Select all

x = 5, y = 4, rule = R2,C2,S0,2,4,6,8,10,12,B1,3,5,7,9,11,NA
o!
[[ AUTOFIT GRID ]]

Code: Select all

x = 5, y = 4, rule = R2,C2,S1,3,5,7,9,11,B1,3,5,7,9,11,NA
o!
[[ AUTOFIT GRID ]]

[muzik]

A bit of investigation reveals that even the full triangular Moore neighbourhood's replicator rule is indeed emulating another hexagonal neighbourhood on even generations, namely the Hexagonal Star neighbourhood:

Code: Select all

x = 30, y = 30, rule = R2,C2,S1,3,5,7,9,11,B1,3,5,7,9,11,N@4799E2H
o!

Code: Select all

x = 1, y = 1, rule = B13579Y/S13579YL
o!

Code: Select all

x = 30, y = 30, rule = R2,C2,S0,2,4,6,8,10,12,B1,3,5,7,9,11,N@4799E2H
o!

Code: Select all

x = 1, y = 1, rule = B13579Y/S02468XZL
o!

[bprentice]

Rule definition:

D1.png (90.07 KiB) Viewed 1846 times

D2.png (41.81 KiB) Viewed 1846 times

Brian Prentice

[bprentice]

Guns:

G1.png (179.45 KiB) Viewed 1843 times

G2.png (178.74 KiB) Viewed 1843 times

G3.png (179.85 KiB) Viewed 1843 times

Brian Prentice

[muzik]

Code: Select all

x = 64, y = 64, rule = B3/S245LB
6bo2bob2o4bo4b4o4bobo2bob2o2bob3ob3o2bobo2b4o$o4bob2o2bobo4bobob2obob
o10b5o2bobobo8bob2o$obob4o5b6ob3o2bo2bo2b2o6bo8bobo4bobobo$3bo3bob2ob
obobobob2o4bob2o3b2o2bobob2o2b2obobo2bobobob3obo$b2obobo2bo2bobo2bobo
bob4o5bobo3b3obob6obobo3bo2b2obo$4o4b3obob5o2b4obo4b2obobo2b2ob3ob4o3b
5obo$ob2obo2bo2b2o6bo2b2o2b3obob2ob6obob2obob9o2bo2bo$3o2bobobob4o3b2o
7bo2bobo3b2o2bo3bo4bobo2b4o2bob2o$2bo2b2o3b2obobo2bobo2bobo2b2o2bob2o
bo2bo4b3obo4b2o2bob4o$2obobo3b3o3bo3b2ob3o2b2o2b2ob5o2bobob3ob7o2bobo
bo$b4obo5b2o4bo5b3o5bob5ob3o3b2o6bo2b5o$3bobo8bo2bobo2b2ob2obob4ob3o3b
2ob3ob2obobo2bo3bo2bo$2b4obob2ob10o5b2ob2o3bob3o2bob2o6bo3b4ob3o$5b2o
bo2b3o3bob2o2b3ob2obobob5o2bobo3b3obo2b2o3b2obo$3ob4o2b2obo2bo3b4o2bo
2bo3bo4b2o5bob2obob5o2b2o$bob8ob2o2b5o3bo4bobo4bo2bo2bo2bo3bo2bob3o2b
3o$7b7o3b3ob2o3b2o4b2o4bo2b3obo3bo2bob3obobobo$bob2o2bo4bo5b2ob2ob2ob
2o2b5o2bob6obo2b2obobobobob3o$ob3o9b4obob2obo5b3ob3obobo4b5o3bo2b2ob3o
$bob9obo7b4o3b2o3b6o4b5obobo2b2obo2bo2bo$obob2obo5bobo4bob2ob2obob3o2b
3o2bo2bob3ob3o3bo2bobo$obob2o3b2ob4o3b2ob2o2bob3o2b2obo3b2ob4ob2o4bo3b
o4bo$4obo2bo3bob3obobob3o7b5obo3bo3b4o4bo5bo2bo$2b4ob2obo3b2o2bo4b5o2b
ob2obo2b2o3bo2bobobobo5b4obo$2b2obobobob3obo2b2o2bo3bob3o5bo2b2ob2ob2o
5bo2bobob2o2bo$2b2ob13ob2obo5b2obob2o2bob3o4bob3o6b6o$3obo3bo2b9o2b4o
b10o2b2ob2o2b4ob2obobobo2b3o$2o2b3obo3b2ob2o3b3ob2ob2o3bobob3ob5ob2ob
2o2bobobo3bo$2ob2ob2o2bo4b4o2bobo3bob2obobob3ob2o4b3ob3o2b2obo$b2o4bo
bo3bobo2b6o2bo4b3obo2b4ob4o3b4ob2ob3o2bo$bo2b3o5b6o2b2obobo4bob2ob2o4b
obobobob3o2bobobob2o$bo2bob3obo3b4o3bob2o2b2obo2bo2bob4o2b2o2bo3b2obo
b3o2bo$2bobobo2b6obob2ob5o3bo4b5obobo3bo2bo2b2obo5b2o$2b4o2b2ob2o2b2o
bob3o2bo2b2o2b2o2bo4b4obobobo2b6o3bo$3o5bobobo3bo3bo3bo2b5o2b2ob3ob2o
b2ob2o2bob2o2bob3obo$o4bobobo2b6o3b2o3b2o6b4ob2ob2o2bo2b2obob3ob2ob3o
$3bobobobob3o2b3ob6obob2o2bo7b2ob2ob3o7bobo2bo$b2obobobo2bobob6o2b2o3b
2o2b3o4b2obo8bo2b3o4b3o$bo2b4o2bo4bobob2o2bobob4obobob4ob2o3bo2bob2o2b
o4bo$bo4b2ob2o3bo5bo3bobo8b2obo6bo2b2ob2ob5o2b2o$b2ob2o4b3obo2bo3b3ob
3o2bobobo3bo2bo4bo3bo4bob3obo$ob3obo2bo2bob2o3bobo2bo8b5ob2obo2bo2bob
o4bo2bobo$2o2b2obobobo5bo3b3o2b2obob3obo2bo3bo8b6o4b2o$obo2bob2o4bo2b
o3bob2ob4ob4ob2ob2ob5obo2bo3bobob4obo$b4o2b3o2b3o5b2obobobo5bob2o2b2o
3bob2o4b5o2b3o$bob6obobo2b2o2b2ob2ob4o8b3o2b5o3b3ob2o5bo$2bo5b4o4bo2b
3ob2obo2b2o2bob2ob5o2bob2o3bo2bo5b2o$o4bo2b2ob2o5b4o3b4ob3o3bobo3bobo
b2o2b2o5b2obobo$bo4b2o2bo3b2ob2o2b2o2bobo4b2obo4bobo2b4o2b7o2bob2o$2b
o2bo2bo2b2ob2ob2o2b2obob3ob2o2b2o3bobob2o5b2obo3bobo2b2o$3bo2bo2bobob
obob2obobobo5b2o3bobo3b4ob3obo3b2o2bobo2bo$3ob2o2bo3b2o2b3ob4o2bo3bob
2ob6obobobo2bobob2o2bo3b3o$2bo3b5ob5o2b3o2bo3bobo2b2o3b3o6bob2o2bo2b2o
3bo$2o2b2o2b2o4b2obo5b2o2b2o3bo2b4o5b3obob2ob4o2b2obo$b5o2bob2o5bo2bo
2bob3o2b2o4bo3bo2bo3bo3bobob2obob2obo$6o2bob2o3bo3b3ob2obobob3o3bob2o
3b2o6bo2b2ob7o$5bobob5o3bo2b2obo5b2obobo2bob2o3b6ob3obob3ob2o$b3o3bo2b
ob5ob2ob4o2b2ob3ob4o6bo3bob2o7bo3bo$7o4b2o3b2o2b3ob3ob2o5b2obo8b5obo5b
2obo$2obo2bo4b3obobo3bo2bob2o2b2o2bo3b4obo2b4o2bobo3b3o2bo$2b2o3bobob
2obob2o2b2o2bo2bo2b4obo2b2obob4ob2ob6ob3o2bo$2bob2o2b2o2b3ob4ob2o2bob
obobo2bobobo2b3ob3obobo2b3obo$b2o3bo3bo2b2ob3o2bo2b4ob3ob2o5b2obobo3b
obob2ob2ob5o$2ob4obo3b3o7bobo5b2o4b3o2bo2b4o3b3obob4o!
[[ RANDOMIZE RANDCHANCE FIXED ZOOM 4 AUTOSTART SHOWGENSTATS SHOWTIMING EXTENDEDTIMING ]]

[muzik]

Code: Select all

x = 4, y = 2, rule = R4,C2,S,B6,NL
b3o$b3o!

[confocaloid]

Several oscillators in B367/S24679LB:

Code: Select all

x = 30, y = 7, rule = B367/S24679LB
2b5o8bo9b2ob2o$b3ob3o7b3o7b2ob2o$2b5o9b2o$3bobo2$10bo13b3o$10bobo11b3o!
#C [[ GRID ZOOM 12 GPS 5 ]]

A soup in the same CA:

Code: Select all

#C [[ RANDWIDTH 64 RANDHEIGHT 32 RANDOMIZE ]]
#C [[ GRID ZOOM 4 ]]
x = 33, y = 17, rule = B367/S24679LB
$bobo3bob2obob2ob4obob3o2b4o$bob3o2bo2bo3bob2o3b4o3bobo$4bobobo3bo5bo
4b2o2bobob2o$bo2bobobobo2b4ob3ob3obo2bobo$3bob2obobo3b2ob6o9bo$3b2obo
3b9o3bo3bo2b2o$b3o4b2o4bo2bobobo2bobobobobo$5bo2b2o4bo3bob2o4bob2o$bo
b3obobob2o2b2o2bobo2b2obo2bobo$bo2b2ob4o3b2ob4o2bo2bob5o$2bo2bobo4bo6b
ob3o3bobob2o$b3ob2obo2bobo2b2ob3o2bob3obo$5bo2b4o5b3obob7o2bo$bo3bob2o
bo3bobo3b5o2bo2bo$4b6o3b4ob4o2bo3b2ob2o$bob3obo4b2ob3o13b2o!

[confocaloid]

Several objects on the triangular tiling (two-state CA, isotropic rules, weighted neighbourhood):

Code: Select all

#C [[ THEME MCell ]]
x = 70, y = 35, rule = R2,C0,S6,9,28,33-34,36-37,40,57,60-61,64,74,84,88,101,104,B2-3,7,10-11,13-17,20,28,34,37-41,61-65,85-92,NW000000000001041C0401041C001C0400040104000000000000L
4bo$2b3o2$58b3o$56b3o2bo$57b2ob2o$55b3o$57bo7$bo2$o4$65b3o$46b3o14b3o
2b2o$45bo2bo14b2o2b2o$45b3o17bo7$23bobo27b3o$20bobo4b2o2b2o20b3o$22b2o
3b2o2b2o24bo$25bo28b2ob2o$54b2ob2o!

A p444 gun that doesn't work in B39/S278xyzL:

Code: Select all

#C [[ THEME Caterer ZOOM 4 ]]
x = 78, y = 13, rule = R2,C0,S2,5,8,11,15,19,22-26,29,32,43,46-47,49-50,52-53,55-56,67,70-71,73-74,76-77,79-80,82-83,91,94-95,97-98,100-101,103-104,106-107,109-111,B3,6,9,12,27,30,33,36,51,54,57,60,75,78,81,84,99,102,105,108,NW000000000001041C0401041C001C0400040104000000000000L
64bob2o$61bo7bo$68bo$10b2obo$8bo7bo55bo$9bo51bo3b3o5b2o$65bo$5bo54bo3b
o11bo$3b2o5b3o3bo43b2o14bo$12bo64bo$bo11bo3bo$bo14b2o$o!

[...] The following example should show a way of working with a large subspace of "two-state isotropic CA with range-1 neighbourhood on the triangular tiling". The three side-by-side adjacent neighbours, the three distant neighbours, and the six intermediate neighbours are counted separately. Combined with two possible states of the middle cell, this yields (2 x 4 x 7 x 4 = 224) distinguishable fully-specified cell conditions. For each of those 224 conditions the rules can prescribe either "the cell will live in the next generation" or "the cell will be dead in the next generation", which means this weighted neighbourhood allows to specify any of 2^224 different isotropic cellular automata. It's a subset, but it's a large subset.
search.php?keywords=NW000000000001041C0 ... 000000000L

Code: Select all

#C [[ THEME MCell GRID STARTFROM 1 ]]
x = 10, y = 1, rule = R2,C0,S0,B1,4,28,NW000000000001041C0401041C001C0400040104000000000000L
o8bo!

Code: Select all

#C [[ THEME Caterer GRID STARTFROM 1 ]]
x = 10, y = 1, rule = R2,C0,S0,B1,4,NW000000000001041C0401041C001C0400040104000000000000L
o8bo!

Code: Select all

#C [[ THEME Caterer GRID STARTFROM 1 ]]
x = 10, y = 1, rule = R2,C0,S0,B1,28,NW000000000001041C0401041C001C0400040104000000000000L
o8bo!

Code: Select all

#C [[ THEME Caterer GRID STARTFROM 1 ]]
x = 10, y = 1, rule = R2,C0,S0,B4,28,NW000000000001041C0401041C001C0400040104000000000000L
o8bo!

[R2INT]

Here is a Triangular Biohazard INT notation proposal (that can also be applied to Triangular Vertecies INT):

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 COLOR DEAD 0 0 96 ]]
x = 136, y = 157, rule = 0123456789xyz//5L
17.7C7.5C5.7C3.7C7.C5.C7.7C7.9C3.7C5.9C3.7C$16.2C5.2C9.2C4.2C4.2C8.2C
6.2C4.2C6.2C12.2C16.2C4.2C6.2C2.2C4.2C$15.2C7.2C7.2C10.2C8.2C6.8C6.8C
6.2C16.2C4.2C6.2C3.7C$15.2C7.2C6.2C4.8C5.6C11.2C12.2C6.9C9.2C4.10C8.2C
$16.2C5.2C6.2C4.2C17.2C9.2C12.2C6.2C6.2C8.2C4.2C6.2C8.2C$17.7C3.7C3.7C
7.7C9.C7.7C7.9C8.2C5.9C8.2C2$126.5B$17.5B103.2BDBD2B$16.2B.B.2B101.2B
2DA2D2B$15.2B2.A2.2B100.3B3D3B$15.3B3.3B101.7B$16.7B2$11.5C13.5B7.5B7.
5B7.5B7.5B7.5B7.5B7.5B$10.2C3.2C11.2B.B.2B5.2B.B.2B5.2B.B.2B5.2B.B.2B
5.2BDBD2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$9.8C10.2B2.A2.2B3.2B.DA2.2B3.2B.
DAD.2B3.2B.DAD.2B3.2BD.A.D2B3.2BD.A.D2B3.2BD.A2D2B3.2B2DA2D2B$9.2C16.
3B.D.3B3.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B3.3BD.D3B3.3BD.D3B
$10.7C11.7B5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$11.5C13.5B7.5B7.5B7.5B7.5B7.
5B7.5B7.5B$10.2C3.2C11.2B.B.2B5.2B.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2B
DB.2B5.2BDBD2B5.2BDBD2B$10.2C3.2C10.2B2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.
2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DA2D2B$11.5C11.3BD2.3B
3.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B3.3B.2D3B$28.7B
5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$11.5C25.5B7.5B7.5B7.5B7.5B7.5B$15.2C23.
2B.B.2B5.2B.B.2B5.2B.BD2B5.2BDB.2B5.2BDBD2B5.2BDBD2B$9.8C22.2B2.A2.2B
3.2BD.A2.2B3.2B2.AD.2B3.2B2DA.D2B3.2B.DA2D2B3.2B2DA2D2B$8.2C4.2C23.3B
.2D3B3.3B2D.3B3.3B2D.3B3.3B2.D3B3.3B2.D3B3.3BD2.3B$8.7C25.7B5.7B5.7B5.
7B5.7B5.7B2$13.C27.5B7.5B7.5B7.5B7.5B7.5B$40.2B.BD2B5.2B.B.2B5.2B.B.2B
5.2BDBD2B5.2BDBD2B5.2BDB.2B$11.2C26.2B2.A2.2B3.2B2.A2.2B3.2B2.A2D2B3.
2B2DA2.2B3.2B2DA2D2B3.2B2DA2D2B$10.2C27.3B.D.3B3.3B3D3B3.3B.2D3B3.3BD
2.3B3.3B3.3B3.3BD.D3B$9.2C29.7B5.7B5.7B5.7B5.7B5.7B2$11.2C28.5B7.5B7.
5B7.5B7.5B7.5B$10.2C28.2B.B.2B5.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.BD2B5.2B
DBD2B$9.2C2.2C24.2B2.A.D2B3.2B2.AD.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA.D2B
3.2B2DAD.2B$8.4C27.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B3.3BD.D
3B$7.2C2.2C27.7B5.7B5.7B5.7B5.7B5.7B2$9.5C27.5B7.5B7.5B7.5B7.5B7.5B$8.
2C2.2C26.2B.B.2B5.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$7.2C2.2C
26.2B2.A2.2B3.2B2.A2D2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA2.2B3.2B2DA2D2B$6.
2C2.2C27.3BD.D3B3.3B.D.3B3.3B3D3B3.3B3.3B3.3BD.D3B3.3B.D.3B$5.2C2.2C29.
7B5.7B5.7B5.7B5.7B5.7B2$7.9C25.5B7.5B7.5B7.5B7.5B7.5B$6.2C2.2C2.2C24.
2B.BD2B5.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B$5.2C2.2C2.2C24.2B
2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DA2D2B$4.2C2.
2C2.2C25.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B$4.C6.2C
27.7B5.7B5.7B5.7B5.7B5.7B2$9.5C27.5B7.5B7.5B7.5B7.5B7.5B$8.2C2.2C26.2B
DB.2B5.2B.BD2B5.2BDBD2B5.2B.B.2B5.2BDB.2B5.2B.BD2B$7.6C26.2B2.A2.2B3.
2BD.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DA2D2B3.2B2DA2D2B$6.2C31.3B2.D3B3.
3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B$6.C33.7B5.7B5.7B5.7B5.7B5.
7B$12.2C$11.2C2.C37.5B7.5B7.5B7.5B$10.3C.2C36.2B.BD2B5.2B.BD2B5.2BDB.
2B5.2BDB.2B$9.2C.3C36.2B2.AD.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA.D2B$8.2C
2.2C37.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B$7.2C2.2C39.7B5.7B5.7B5.7B2$
13.2C38.5B7.5B7.5B7.5B$12.2C38.2B.BD2B5.2B.B.2B5.2BDBD2B5.2BDB.2B$11.
2C38.2B2.A2.2B3.2BD.A.D2B3.2B.DAD.2B3.2B2DA2D2B$11.2C38.3BD.D3B3.3BD.
D3B3.3B.D.3B3.3B.D.3B$11.3C38.7B5.7B5.7B5.7B2$13.C39.5B7.5B7.5B7.5B$52.
2B.B.2B5.2B.BD2B5.2BDB.2B5.2BDBD2B$11.2C38.2B2.A.D2B3.2B2.A.D2B3.2B2D
AD.2B3.2B2DAD.2B$10.2C39.3B2D.3B3.3B2D.3B3.3B2.D3B3.3B2.D3B$7.4C41.7B
5.7B5.7B5.7B2$7.5C41.5B7.5B7.5B7.5B$6.2C2.2C40.2B.BD2B5.2B.BD2B5.2BDB
.2B5.2BDB.2B$6.5C40.2B2.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B2DA2D2B$8.2C2.
C38.3B2D.3B3.3B3D3B3.3B3.3B3.3B2.D3B$8.5C39.7B5.7B5.7B5.7B2$9.C43.5B7.
5B7.5B7.5B$8.5C39.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.BD2B$7.2C3.C38.2B2.A2.
2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DA2D2B$6.2C43.3B2D.3B3.3B3D3B3.3B3.3B3.3B
2.D3B$5.2C45.7B5.7B5.7B5.7B2$11.2C40.5B7.5B7.5B7.5B$8.6C38.2BDB.2B5.2B
DBD2B5.2B.B.2B5.2B.BD2B$9.2C40.2B2.A.D2B3.2B2.A2.2B3.2B2DA2D2B3.2B2DA
D.2B$8.2C41.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B$7.2C43.7B5.7B5.7B5.7B2$
9.2C2.2C38.5B7.5B7.5B7.5B$8.2C2.2C38.2B.BD2B5.2BDBD2B5.2B.B.2B5.2BDB.
2B$7.2C2.2C38.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B$6.6C39.3B.D.
3B3.3B.D.3B3.3BD.D3B3.3BD.D3B$52.7B5.7B5.7B5.7B2$6.2C3.2C40.5B7.5B7.5B
7.5B$7.2C.2C40.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B$8.3C40.2BD.A.D2B3.2B
D.A.D2B3.2B.DAD.2B3.2B.DAD.2B$9.C41.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B
$52.7B5.7B5.7B5.7B$6.2C2.C$6.2C.2C42.5B7.5B7.5B7.5B$7.3C42.2BDBD2B5.2B
DB.2B5.2B.BD2B5.2B.B.2B$3.C3.2C42.2B2.A2.2B3.2B2.A.D2B3.2B2DAD.2B3.2B
2DA2D2B$3.5C43.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B$52.7B5.7B5.7B5.7B2$
7.4C54.5B7.5B$6.2C56.2BDB.2B5.2B.BD2B$5.2C56.2B.DA.D2B3.2B2DA.D2B$5.4C
54.3B.D.3B3.3B2.D3B$64.7B5.7B2$11.C53.5B7.5B$10.2C52.2B.BD2B5.2BDB.2B
$5.6C52.2BD.A.D2B3.2B.DAD.2B$4.2C2.2C53.3B.D.3B3.3BD.D3B$4.5C55.7B5.7B
2$7.5C53.5B7.5B$6.2C2.2C52.2BDB.2B5.2B.BD2B$5.3C55.2BD.A2.2B3.2B.DA2D
2B$4.2C.2C54.3B2D.3B3.3B2.D3B$4.C59.7B5.7B2$7.5C53.5B7.5B$6.2C2.2C52.
2B.B.2B5.2BDBD2B$6.5C52.2BD.AD.2B3.2B.DA.D2B$8.2C53.3B2D.3B3.3B2.D3B$
4.5C55.7B5.7B2$3.C3.C3.C53.5B7.5B$2.2C2.2C2.2C52.2B.BD2B5.2BDB.2B$.2C
2.2C2.2C52.2BD.A2.2B3.2B.DA2D2B$.9C53.3B2D.3B3.3B2.D3B$64.7B5.7B$4.C5.
C$4.2C3.2C54.5B7.5B$5.5C54.2BDB.2B5.2B.BD2B$5.2C.2C53.2BD.AD.2B3.2B.D
A.D2B$4.2C3.2C52.3B.D.3B3.3BD.D3B$64.7B5.7B$3.6C$7.2C56.5B7.5B$6.2C56.
2B.B.2B5.2BDBD2B$5.2C56.2BD.AD.2B3.2B.DA.D2B$5.6C52.3B.2D3B3.3BD2.3B$
64.7B5.7B!

It is a minor variant of a previous proposal, with a few transitions swapped in an attempt to make it more 'intuitive'. However, I do not expect to make many changes to it in the future.
Using this notation, here are some examples of rules supporting spaceships in this rulespace:

Code: Select all

#C Hexagonally-restricted spaceship
x = 6, y = 6, rule = B2o/S2m34LB
$2bo$bo3bo$4bo$bobo$o!

Code: Select all

#C p2 spaceship
x = 12, y = 5, rule = B3ai5ru/S2a3nLB
$2bo$bo2bo5b2o$b3o4b3o$10bo!

It is possible to emulate all hexagonal rules using this rulespace, thus guaranteeing that it is at least as interesting as the hexagonal rulespace.

[confocaloid]

Here is a Triangular Biohazard INT notation proposal (that can also be applied to Triangular Vertecies INT):
[...][...]
It is a minor variant of a previous proposal, with a few transitions swapped in an attempt to make it more 'intuitive'. However, I do not expect to make many changes to it in the future.
[...]
It is possible to emulate all hexagonal rules using this rulespace, thus guaranteeing that it is at least as interesting as the hexagonal rulespace.

I don't see 'interestingness' in terms of ability to emulate. Out of two ways to solve the same problem, the simpler way is more 'interesting', I think.
I would say that directly considering cellular automata on the hexagonal tiling is more 'interesting', because it is simpler, compared to inserting an intermediate encoding/representation.
(Similarly, I would say that directly considering reactions in "plain two-state CGoL" is more 'interesting', compared to considering the same reactions as a subset of what is possible in a three-state CA where patterns entirely consisting out of state-0 and state-1 cells follow CGoL.)

That means a family of CA on the triangular tiling becomes interesting, only if/when there is something interesting and unique to that family (rather than "borrowed from a simpler CA family").


Speaking of 'intuitive', I think you would need to either write down explicit definitions of the jargon used in your post, or (probably better) replace jargon with plain-English explanations likely to be understood intuitively and correctly without checking any "local" definitions.

• The pattern you posted apparently shows some single-generation ("static") configurations of live and dead triangular cells. However, your post fails to mention that in any way. Is it a relevant observation? Can the relevance of those configurations of cells with different current states be made clearer to a reader by editing the post?
• The post mentions "previous proposal", but doesn't link to it, nor otherwise explains the intended meaning. Again, there seems to be no way for a reader to understand what is meant here.

Referring to common usage doesn't answer the question, because "common usage" is highly inconsistent/self-contradictory on many issues that can potentially be considered as relevant here, and also because "common" doesn't imply either "correct" or "simple to understand intuitively" in any way.

[muzik]

Code: Select all

#C https://discord.com/channels/357922255553953794/370571046971244545/1410381422631588034
x = 18, y = 24, rule = B39/S23L
$7bobobo$6b2obob2o$6b2o3b2o$8bobo$8bobo$6b2o3b2o$6b2obob2o$7bobobo$9b
o$5b4ob4o$5b2o5b2o3$5b2o5b2o$5b4ob4o$7bo3bo3$4bo9bo$3bob3o3b3obo$bo3b
3o3b3o3bo$b4o9b4o$b3o11b3o!
[[ AUTOSTART GPS 30 ZOOM 4 TRACK 0 12/-21 ]]

[muzik]

Code: Select all

# presumably C2_4 static, D4_x4 kinetic, if I'm reading things right
x = 6, y = 2, rule = B3/S23L
b3obo$bob3o!

I wonder if we have any more interesting high period oscillators with time symmetries. We can cheat by emulating hexagonal rules using Tri6outer, but the purity of the symmetry is reduced since the triangles can only be of one alignment, so for a flipping oscillator like this the triangular version technically doesn't become its vertical mirror image:

Code: Select all

x = 7, y = 4, rule = B2/S34H
o5bo2$3bobo$3b4o!

Code: Select all

x = 14, y = 4, rule = B2/S34LO
bo11bo2$5bo3bo$4bobobobo!
[[ ZOOM 17 ]]

...which is a shame, as this would get us a mod 1/3 centered gutteroid if it worked:

Code: Select all

x = 4, y = 3, rule = B2/S34H
2o$3bo$3o!

Code: Select all

x = 9, y = 3, rule = B2/S34LO
3bobo$8bo$bobobo!
[[ ZOOM 17 ]]

[TheWayOfTheCon]

An explosive rule that creates cool maze-like structures. Other than that it's probably useless.

Code: Select all

x = 7, y = 3, rule = B3/S123LV
!
#C [[ RANDOMIZE2 SQUARECELLS ]]