## B2e3-a/S234ent

For discussion of other cellular automata.

### B2e3-a/S234ent

This is a rule with many interesting natural and semi-natural patterns, which I'll show below.

There are a large amount of small natural spaceships, tagalongs and flotillas; so far, all of them are c/2 orthogonal at various periods. Some of them are shown below, sorted into c/2, 2c/4 and 3c/6 groups:
`x = 59, y = 31, rule = B2e3-a/S234ent3o4b2o5b2o5b2o6bo4b3o6b3o6b3ob3o\$obo3bo2bo3bo2bo3bo2bo4bobo3bobo6bobo6bobobobo\$27bo2bo25bo\$13b2o6b2o33bo\$29b2o3b6o3b6o6b3o\$35b3obo4b4o7bobo7\$3ob3o3b3ob3o3b3ob3o3b3o\$obobobo3bobobobo3bobobobo3bobo\$2bobo7bobo9bo7bob3o\$2bobo7bobo9bo7bobobo\$12bobo19bo\$11b2ob2o18bo7\$3ob3o\$obobobo\$2bobo\$2bobo\$bo2bo\$3b2o\$2bo!`

Here are example oscillators of all of the periods currently known (periods 2, 3, 4, 5, 6 and 8):
`x = 35, y = 17, rule = B2e3-a/S234entbo5bo9bo6bo9bo\$o5bo8b2o8bobo3bobo\$9bo5bo3bo8bobo\$8bo5bo3bo8bo3bo\$17b2o\$16bo7\$2o2bo2b2o7bo\$b7o5b5o\$14bo\$b2o3b2o7b3o\$2bo3bo8b2o!`

Perhaps the most interesting characteristic of this rule, however, is the large variety of infinite growth patterns that can occur naturally. Most of them are based on flotillas of c/2 orthogonal spaceships; some examples are shown below:
`x = 16, y = 16, rule = B2e3-a/S234ento3bo2b2o6bo\$o2bo2bo2b2ob2obo\$bo2bo4b3obobo\$2bob3o2bo3bo\$2ob5o2b2obobo\$2b3o2bo2b2obobo\$2o2bo2b3obo3bo\$o2bobo3bobo2bo\$3obo2bob2ob2obo\$2obob5o4bo\$bo3b3o2bo2b3o\$bob2obob5obo\$3b2obob2o2bobo\$2b2ob2obo2b3obo\$2o3b2o3b4obo\$bo2b3o2bobob2o!`

`x = 16, y = 16, rule = B2e3-a/S234entb2o4bobo3b3o\$3o3b5obob2o\$3ob2o2bo4bobo\$ob4o2b3o4bo\$2o2bobo2bobo2bo\$2ob4o2b2obob2o\$bobobob3obo3bo\$o6bo2b4obo\$o2b3obob2o\$o2b6o3bobo\$ob3ob6o2bo\$2bo2b3ob4o2bo\$o3b2o2bobo2b2o\$o4bobo4b2o\$o2bob2o2bo3bobo\$b3o3b2o2bobo!`

`x = 16, y = 16, rule = B2e3-a/S234entobob2ob2o3b4o\$2bo2bo2b3obob2o\$2b5ob2ob2ob2o\$bobo3b3o3bo\$5obob4ob2o\$4bo7b4o\$4b3ob2ob2o2bo\$obobo2b5o2b2o\$obob2o2b2o2b3o\$ob2obob3o2b4o\$3b3obob2obo\$b4obo2b3o2b2o\$5o5b2o2bo\$3b2o2bob2ob2obo\$3ob3ob2ob2o\$2bobob4o3b3o!`

`x = 16, y = 16, rule = B2e3-a/S234ent2obobo2bobobo2bo\$3o3b2o6bo\$3ob2obo3b3o\$3ob2o2bo2bob3o\$3b5obob2o2bo\$o5b2obo3bobo\$o6b3ob2obo\$o2b4ob2o2b2obo\$ob2o4bob4o\$4b2ob6obo\$2ob2ob3obobo\$4ob2obo2b2obo\$2obo2b2o2bo2b3o\$2obo3b2o3b2obo\$o3b5o2b3obo\$2o3b2o3bo2bobo!`

`x = 16, y = 31, rule = B2e3-a/S234entb2o2b3o3bo\$2b2ob2obobo2b3o\$2bo4bobob4o\$o2bo3bo4b2o\$bo2bo5b2o3bo\$bo2b2obo2b4obo\$3b2o2bobo3b3o\$ob3obo6b3o\$2ob4o5b4o\$5ob2obobo2bo\$b2obob7ob2o\$ob5o4b3obo\$2ob5obo5bo\$ob2ob4o2bo3bo\$3o2bo2bobob3o\$2ob2o2b3obobobo\$3o2bo2bobob3o\$ob2ob4o2bo3bo\$2ob5obo5bo\$ob5o4b3obo\$b2obob7ob2o\$5ob2obobo2bo\$2ob4o5b4o\$ob3obo6b3o\$3b2o2bobo3b3o\$bo2b2obo2b4obo\$bo2bo5b2o3bo\$o2bo3bo4b2o\$2bo4bobob4o\$2b2ob2obobo2b3o\$b2o2b3o3bo!`

There is one backrake that can form a wickstretcher:
`x = 16, y = 32, rule = B2e3-a/S234ent4o2bob2obo3bo\$3obob2ob5o\$b2obo4b3ob2o\$5ob2o2b3obo\$o2bob4o2bobo\$2ob4o4b4o\$3bobobo2b2ob3o\$3obob2ob2ob2obo\$ob3ob2ob2ob3o\$o3bo2b2obo4bo\$7obo4bo\$obo4b3ob3o\$2ob5ob2o3b2o\$3b2ob2o2b2ob3o\$bo3b2obob2o3bo\$bo2bob3obob2obo\$bo2bob3obob2obo\$bo3b2obob2o3bo\$3b2ob2o2b2ob3o\$2ob5ob2o3b2o\$obo4b3ob3o\$7obo4bo\$o3bo2b2obo4bo\$ob3ob2ob2ob3o\$3obob2ob2ob2obo\$3bobobo2b2ob3o\$2ob4o4b4o\$o2bob4o2bobo\$5ob2o2b3obo\$b2obo4b3ob2o\$3obob2ob5o\$4o2bob2obo3bo!`

And even a growing spaceship, with a back end formed by a crystal that moves at 2c/12 (c/6):
`x = 16, y = 32, rule = B2e3-a/S234entbo2bob4o2bob2o\$o2b2o8b2o\$o2bo2b3obo2b2o\$3b2ob5o2bobo\$b2o2bob2obobob2o\$2b4o3bob3o\$b3o2bo2bo3b2o\$2bobo7bo2bo\$b3ob3ob2o2bo\$2b2o3b3o2bob2o\$6obobob4o\$b8obo3b2o\$b2ob2obobob2ob2o\$obo2b2o2bob2ob2o\$3ob8obo\$3obobobo4bo\$3obobobo4bo\$3ob8obo\$obo2b2o2bob2ob2o\$b2ob2obobob2ob2o\$b8obo3b2o\$6obobob4o\$2b2o3b3o2bob2o\$b3ob3ob2o2bo\$2bobo7bo2bo\$b3o2bo2bo3b2o\$2b4o3bob3o\$b2o2bob2obobob2o\$3b2ob5o2bobo\$o2bo2b3obo2b2o\$o2b2o8b2o\$bo2bob4o2bob2o!`

There also exist backrakes that move at 3c/30 orthogonal (c/10); they are so far the only moving patterns at a speed other than c/2. I wonder if they can be stabilised into spaceships?
`x = 16, y = 31, rule = B2e3-a/S234entbo4b3ob5o\$bobo2b3ob3o2bo\$2ob4obo3bobo\$3bo2bobobo\$ob5o\$2obobob2obob4o\$o2b2o4bobo3bo\$4b5o6bo\$bo3bo2bobo2b3o\$o2b2o3bo2bo2b2o\$o5bo4b3o\$2o2b2o3b2o4bo\$bo2bo3bob2o2b2o\$6bob2ob2o2bo\$2o2b5obob2obo\$2b5o3b4obo\$2o2b5obob2obo\$6bob2ob2o2bo\$bo2bo3bob2o2b2o\$2o2b2o3b2o4bo\$o5bo4b3o\$o2b2o3bo2bo2b2o\$bo3bo2bobo2b3o\$4b5o6bo\$o2b2o4bobo3bo\$2obobob2obob4o\$ob5o\$3bo2bobobo\$2ob4obo3bobo\$bobo2b3ob3o2bo\$bo4b3ob5o!`

They can interact with each other in interesting ways:
`x = 31, y = 31, rule = B2e3-a/S234ent3obob2o2b3o2bo2b3o2b2obob3o\$obo2b2o2bo3b5o3bo2b2o2bobo\$2o2b2ob2ob11ob2ob2o2b2o\$3bob3o2bob3ob3obo2b3obo\$obo3b3o2b4ob4o2b3o3bobo\$b3obo3b2obob3obob2o3bob3o\$2ob2o2bobob4ob4obobo2b2ob2o\$ob3obobob3ob3ob3obobob3obo\$2bobo2b2ob4obob4ob2o2bobo\$bo3b2o3b2o3bo3b2o3b2o3bo\$ob2obob7o3b7obob2obo\$obobob5ob2o3b2ob5obobobo\$ob7ob2obo3bob2ob7obo\$b4obobob5ob5obobob4o\$b7o5b5o5b7o\$3o2bob3o4bobo4b3obo2b3o\$b7o5b5o5b7o\$b4obobob5ob5obobob4o\$ob7ob2obo3bob2ob7obo\$obobob5ob2o3b2ob5obobobo\$ob2obob7o3b7obob2obo\$bo3b2o3b2o3bo3b2o3b2o3bo\$2bobo2b2ob4obob4ob2o2bobo\$ob3obobob3ob3ob3obobob3obo\$2ob2o2bobob4ob4obobo2b2ob2o\$b3obo3b2obob3obob2o3bob3o\$obo3b3o2b4ob4o2b3o3bobo\$3bob3o2bob3ob3obo2b3obo\$2o2b2ob2ob11ob2ob2o2b2o\$obo2b2o2bo3b5o3bo2b2o2bobo\$3obob2o2b3o2bo2b3o2b2obob3o!`

This interaction eventually (after 2000 gens) ends up shooting out a different type of spaceship at 90 degrees to the other streams:
`x = 32, y = 31, rule = B2e3-a/S234ent2b3o2b2o4b6o4b2o2b3o\$bo3bo2b2o3bob2obo3b2o2bo3bo\$b2obo4bo2bo2b2o2bo2bo4bob2o\$o3b2obo4bob4obo4bob2o3bo\$o3bo2b4o2bo4bo2b4o2bo3bo\$b2ob2obob4ob4ob4obob2ob2o\$obo5b3o10b3o5bobo\$b3ob2o3bobob4obobo3b2ob3o\$7bob3obob2obob3obo\$obo3bob3o10b3obo3bobo\$2bob3ob3obob4obob3ob3obo\$2o2b2ob7ob2ob7ob2o2b2o\$4o2b2o2bob2ob2ob2obo2b2o2b4o\$o4b3ob4o2b2o2b4ob3o4bo\$bob2obobo2b2o2b2o2b2o2bobob2obo\$3ob2obo3bo8bo3bob2ob3o\$bob2obobo2b2o2b2o2b2o2bobob2obo\$o4b3ob4o2b2o2b4ob3o4bo\$4o2b2o2bob2ob2ob2obo2b2o2b4o\$2o2b2ob7ob2ob7ob2o2b2o\$2bob3ob3obob4obob3ob3obo\$obo3bob3o10b3obo3bobo\$7bob3obob2obob3obo\$b3ob2o3bobob4obobo3b2ob3o\$obo5b3o10b3o5bobo\$b2ob2obob4ob4ob4obob2ob2o\$o3bo2b4o2bo4bo2b4o2bo3bo\$o3b2obo4bob4obo4bob2o3bo\$b2obo4bo2bo2b2o2bo2bo4bob2o\$bo3bo2b2o3bob2obo3b2o2bo3bo\$2b3o2b2o4b6o4b2o2b3o!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: B2e3-a/S234ent

Nice find!
excited to see more
Failed Replicator!
`x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8bo\$obo\$bobo\$2bo!`

(That I wish was not failed D:)

jimmyChen2013

Posts: 133
Joined: December 11th, 2017, 3:28 am

### Re: B2e3-a/S234ent

A new natural, high-period puffer:
`x = 16, y = 16, rule = B2e3-a/S234ent2bo3b2obobo2bo\$ob2obob2o2b2obo\$2b2o2bo2b4o\$o5b2obo2b2obo\$4bob3ob5o\$ob4ob3o4bo\$3ob5ob6o\$3b2o5b6o\$obob2obob3o\$7obo2b2obo\$obo2bo2b2obo3bo\$6bob4ob3o\$3o5b8o\$2bo2b4o2b5o\$ob2o2bob2obobo\$b2ob5o2bo2b2o!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: B2e3-a/S234ent

Some more small, natural spaceships (buried in the xp2 census amongst numerous improperly-separated flotillas):
`x = 16, y = 6, rule = B2e3-a/S234entb2o10b3o\$o2bo8b2obo\$11bobo\$10bo2bo\$6o\$b4o7b2o!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: B2e3-a/S234ent

Some related rules that also show interesting behaviour:

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm