B2e3-a/S234ent

[77topaz]

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:

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x = 59, y = 31, rule = B2e3-a/S234ent
3o4b2o5b2o5b2o6bo4b3o6b3o6b3ob3o$obo3bo2bo3bo2bo3bo2bo4bobo3bobo6bobo
6bobobobo$27bo2bo25bo$13b2o6b2o33bo$29b2o3b6o3b6o6b3o$35b3obo4b4o7bobo
7$3ob3o3b3ob3o3b3ob3o3b3o$obobobo3bobobobo3bobobobo3bobo$2bobo7bobo9bo
7bob3o$2bobo7bobo9bo7bobobo$12bobo19bo$11b2ob2o18bo7$3ob3o$obobobo$2bo
bo$2bobo$bo2bo$3b2o$2bo!

Here are example oscillators of all of the periods currently known (periods 2, 3, 4, 5, 6 and 8):

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x = 35, y = 17, rule = B2e3-a/S234ent
bo5bo9bo6bo9bo$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:

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x = 16, y = 16, rule = B2e3-a/S234ent
o3bo2b2o6bo$o2bo2bo2b2ob2obo$bo2bo4b3obobo$2bob3o2bo3bo$2ob5o2b2obobo$
2b3o2bo2b2obobo$2o2bo2b3obo3bo$o2bobo3bobo2bo$3obo2bob2ob2obo$2obob5o
4bo$bo3b3o2bo2b3o$bob2obob5obo$3b2obob2o2bobo$2b2ob2obo2b3obo$2o3b2o3b
4obo$bo2b3o2bobob2o!

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x = 16, y = 16, rule = B2e3-a/S234ent
b2o4bobo3b3o$3o3b5obob2o$3ob2o2bo4bobo$ob4o2b3o4bo$2o2bobo2bobo2bo$2ob
4o2b2obob2o$bobobob3obo3bo$o6bo2b4obo$o2b3obob2o$o2b6o3bobo$ob3ob6o2bo
$2bo2b3ob4o2bo$o3b2o2bobo2b2o$o4bobo4b2o$o2bob2o2bo3bobo$b3o3b2o2bobo!

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x = 16, y = 16, rule = B2e3-a/S234ent
obob2ob2o3b4o$2bo2bo2b3obob2o$2b5ob2ob2ob2o$bobo3b3o3bo$5obob4ob2o$4bo
7b4o$4b3ob2ob2o2bo$obobo2b5o2b2o$obob2o2b2o2b3o$ob2obob3o2b4o$3b3obob
2obo$b4obo2b3o2b2o$5o5b2o2bo$3b2o2bob2ob2obo$3ob3ob2ob2o$2bobob4o3b3o!

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x = 16, y = 16, rule = B2e3-a/S234ent
2obobo2bobobo2bo$3o3b2o6bo$3ob2obo3b3o$3ob2o2bo2bob3o$3b5obob2o2bo$o5b
2obo3bobo$o6b3ob2obo$o2b4ob2o2b2obo$ob2o4bob4o$4b2ob6obo$2ob2ob3obobo$
4ob2obo2b2obo$2obo2b2o2bo2b3o$2obo3b2o3b2obo$o3b5o2b3obo$2o3b2o3bo2bob
o!

Code: Select all

x = 16, y = 31, rule = B2e3-a/S234ent
b2o2b3o3bo$2b2ob2obobo2b3o$2bo4bobob4o$o2bo3bo4b2o$bo2bo5b2o3bo$bo2b2o
bo2b4obo$3b2o2bobo3b3o$ob3obo6b3o$2ob4o5b4o$5ob2obobo2bo$b2obob7ob2o$o
b5o4b3obo$2ob5obo5bo$ob2ob4o2bo3bo$3o2bo2bobob3o$2ob2o2b3obobobo$3o2bo
2bobob3o$ob2ob4o2bo3bo$2ob5obo5bo$ob5o4b3obo$b2obob7ob2o$5ob2obobo2bo$
2ob4o5b4o$ob3obo6b3o$3b2o2bobo3b3o$bo2b2obo2b4obo$bo2bo5b2o3bo$o2bo3bo
4b2o$2bo4bobob4o$2b2ob2obobo2b3o$b2o2b3o3bo!

There is one backrake that can form a wickstretcher:

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x = 16, y = 32, rule = B2e3-a/S234ent
4o2bob2obo3bo$3obob2ob5o$b2obo4b3ob2o$5ob2o2b3obo$o2bob4o2bobo$2ob4o4b
4o$3bobobo2b2ob3o$3obob2ob2ob2obo$ob3ob2ob2ob3o$o3bo2b2obo4bo$7obo4bo$
obo4b3ob3o$2ob5ob2o3b2o$3b2ob2o2b2ob3o$bo3b2obob2o3bo$bo2bob3obob2obo$
bo2bob3obob2obo$bo3b2obob2o3bo$3b2ob2o2b2ob3o$2ob5ob2o3b2o$obo4b3ob3o$
7obo4bo$o3bo2b2obo4bo$ob3ob2ob2ob3o$3obob2ob2ob2obo$3bobobo2b2ob3o$2ob
4o4b4o$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):

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x = 16, y = 32, rule = B2e3-a/S234ent
bo2bob4o2bob2o$o2b2o8b2o$o2bo2b3obo2b2o$3b2ob5o2bobo$b2o2bob2obobob2o$
2b4o3bob3o$b3o2bo2bo3b2o$2bobo7bo2bo$b3ob3ob2o2bo$2b2o3b3o2bob2o$6obob
ob4o$b8obo3b2o$b2ob2obobob2ob2o$obo2b2o2bob2ob2o$3ob8obo$3obobobo4bo$
3obobobo4bo$3ob8obo$obo2b2o2bob2ob2o$b2ob2obobob2ob2o$b8obo3b2o$6obobo
b4o$2b2o3b3o2bob2o$b3ob3ob2o2bo$2bobo7bo2bo$b3o2bo2bo3b2o$2b4o3bob3o$b
2o2bob2obobob2o$3b2ob5o2bobo$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?

Code: Select all

x = 16, y = 31, rule = B2e3-a/S234ent
bo4b3ob5o$bobo2b3ob3o2bo$2ob4obo3bobo$3bo2bobobo$ob5o$2obobob2obob4o$o
2b2o4bobo3bo$4b5o6bo$bo3bo2bobo2b3o$o2b2o3bo2bo2b2o$o5bo4b3o$2o2b2o3b
2o4bo$bo2bo3bob2o2b2o$6bob2ob2o2bo$2o2b5obob2obo$2b5o3b4obo$2o2b5obob
2obo$6bob2ob2o2bo$bo2bo3bob2o2b2o$2o2b2o3b2o4bo$o5bo4b3o$o2b2o3bo2bo2b
2o$bo3bo2bobo2b3o$4b5o6bo$o2b2o4bobo3bo$2obobob2obob4o$ob5o$3bo2bobobo
$2ob4obo3bobo$bobo2b3ob3o2bo$bo4b3ob5o!

They can interact with each other in interesting ways:

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x = 31, y = 31, rule = B2e3-a/S234ent
3obob2o2b3o2bo2b3o2b2obob3o$obo2b2o2bo3b5o3bo2b2o2bobo$2o2b2ob2ob11ob
2ob2o2b2o$3bob3o2bob3ob3obo2b3obo$obo3b3o2b4ob4o2b3o3bobo$b3obo3b2obob
3obob2o3bob3o$2ob2o2bobob4ob4obobo2b2ob2o$ob3obobob3ob3ob3obobob3obo$
2bobo2b2ob4obob4ob2o2bobo$bo3b2o3b2o3bo3b2o3b2o3bo$ob2obob7o3b7obob2ob
o$obobob5ob2o3b2ob5obobobo$ob7ob2obo3bob2ob7obo$b4obobob5ob5obobob4o$b
7o5b5o5b7o$3o2bob3o4bobo4b3obo2b3o$b7o5b5o5b7o$b4obobob5ob5obobob4o$ob
7ob2obo3bob2ob7obo$obobob5ob2o3b2ob5obobobo$ob2obob7o3b7obob2obo$bo3b
2o3b2o3bo3b2o3b2o3bo$2bobo2b2ob4obob4ob2o2bobo$ob3obobob3ob3ob3obobob
3obo$2ob2o2bobob4ob4obobo2b2ob2o$b3obo3b2obob3obob2o3bob3o$obo3b3o2b4o
b4o2b3o3bobo$3bob3o2bob3ob3obo2b3obo$2o2b2ob2ob11ob2ob2o2b2o$obo2b2o2b
o3b5o3bo2b2o2bobo$3obob2o2b3o2bo2b3o2b2obob3o!

This interaction eventually (after 2000 gens) ends up shooting out a different type of spaceship at 90 degrees to the other streams:

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x = 32, y = 31, rule = B2e3-a/S234ent
2b3o2b2o4b6o4b2o2b3o$bo3bo2b2o3bob2obo3b2o2bo3bo$b2obo4bo2bo2b2o2bo2bo
4bob2o$o3b2obo4bob4obo4bob2o3bo$o3bo2b4o2bo4bo2b4o2bo3bo$b2ob2obob4ob
4ob4obob2ob2o$obo5b3o10b3o5bobo$b3ob2o3bobob4obobo3b2ob3o$7bob3obob2ob
ob3obo$obo3bob3o10b3obo3bobo$2bob3ob3obob4obob3ob3obo$2o2b2ob7ob2ob7ob
2o2b2o$4o2b2o2bob2ob2ob2obo2b2o2b4o$o4b3ob4o2b2o2b4ob3o4bo$bob2obobo2b
2o2b2o2b2o2bobob2obo$3ob2obo3bo8bo3bob2ob3o$bob2obobo2b2o2b2o2b2o2bobo
b2obo$o4b3ob4o2b2o2b4ob3o4bo$4o2b2o2bob2ob2ob2obo2b2o2b4o$2o2b2ob7ob2o
b7ob2o2b2o$2bob3ob3obob4obob3ob3obo$obo3bob3o10b3obo3bobo$7bob3obob2ob
ob3obo$b3ob2o3bobob4obobo3b2ob3o$obo5b3o10b3o5bobo$b2ob2obob4ob4ob4obo
b2ob2o$o3bo2b4o2bo4bo2b4o2bo3bo$o3b2obo4bob4obo4bob2o3bo$b2obo4bo2bo2b
2o2bo2bo4bob2o$bo3bo2b2o3bob2obo3b2o2bo3bo$2b3o2b2o4b6o4b2o2b3o!

[jimmyChen2013]

Nice find!
excited to see more

[77topaz]

A new natural, high-period puffer:

Code: Select all

x = 16, y = 16, rule = B2e3-a/S234ent
2bo3b2obobo2bo$ob2obob2o2b2obo$2b2o2bo2b4o$o5b2obo2b2obo$4bob3ob5o$ob
4ob3o4bo$3ob5ob6o$3b2o5b6o$obob2obob3o$7obo2b2obo$obo2bo2b2obo3bo$6bob
4ob3o$3o5b8o$2bo2b4o2b5o$ob2o2bob2obobo$b2ob5o2bo2b2o!

[77topaz]

Some more small, natural spaceships (buried in the xp2 census amongst numerous improperly-separated flotillas):

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x = 16, y = 6, rule = B2e3-a/S234ent
b2o10b3o$o2bo8b2obo$11bobo$10bo2bo$6o$b4o7b2o!

[77topaz]

Some related rules that also show interesting behaviour:

• B2e3-a/S234j
• B2e3-any/S234wz