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 764 times

D2.png (41.81 KiB) Viewed 764 times

Brian Prentice

[bprentice]

Guns:

G1.png (179.45 KiB) Viewed 761 times

G2.png (178.74 KiB) Viewed 761 times

G3.png (179.85 KiB) Viewed 761 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]

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!

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 ]]

Random soup in same rule:

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!