Rules with Abnormally Common High-Period Patterns

[drc]

p62 Gun:

Code: Select all

x = 26, y = 24, rule = B2cei3acei/S23
5bo$4bobo$4bobo$3bo3bo$4bobo$4bobo$5bo2$2o7b2o$2o7b2o4$21b2o$21bo$15bo
bo5bo$22bo$21bo2bo$14bobobo2b2o2bo$21bo2bo$22bo$15bobo5bo$21bo$21b2o!

There's already a p15 gun:

Code: Select all

x = 7, y = 5, rule = B2cei3acei/S23
3bo$2bobo$2bobo$o2bo2bo$2o3b2o!

[shouldsee]

p40

Code: Select all

x = 5, y = 3, rule = B3568/S13678
2bo$5o$3bo!

[FlameandFury]

p62 Gun:

Code: Select all

x = 26, y = 24, rule = B2cei3acei/S23
5bo$4bobo$4bobo$3bo3bo$4bobo$4bobo$5bo2$2o7b2o$2o7b2o4$21b2o$21bo$15bo
bo5bo$22bo$21bo2bo$14bobobo2b2o2bo$21bo2bo$22bo$15bobo5bo$21bo$21b2o!

Adding that to my oscillator/spaceship collection. Should I post it somewhere?

[BlinkerSpawn]

p62 Gun:

Code: Select all

x = 26, y = 24, rule = B2cei3acei/S23
5bo$4bobo$4bobo$3bo3bo$4bobo$4bobo$5bo2$2o7b2o$2o7b2o4$21b2o$21bo$15bo
bo5bo$22bo$21bo2bo$14bobobo2b2o2bo$21bo2bo$22bo$15bobo5bo$21bo$21b2o!

Adding that to my oscillator/spaceship collection. Should I post it somewhere?

Well, how big is it?

[FlameandFury]

Fairly small, but I guess it will serve as a base for more interesting oscillators and spaceship discoveries.

[drc]

Ignore this post. I'm stupid.

[shouldsee]

4-cell p26

Surprisingly, Eppinstein's page listed NO glider for this rule. Prove him wrong if you can.

Code: Select all

x = 3, y = 3, rule = B0234/S1234
bo$obo$bo!

[Bullet51]

Surprisingly, Eppinstein's page listed NO glider for this rule. Prove him wrong if you can.

Way too easy:

Code: Select all

x = 24, y = 13, rule = B0234/S1234
19bo$11b3o4b2o$11b4ob8o$bobobo5bob3o2bob2o$6o4b2ob9o$7o2b2o2b3ob4o$6o
3b4o2bob4o$7o2b2o2b3ob4o$6o4b2ob9o$bobobo5bob3o2bob2o$11b4ob8o$11b3o4b
2o$19bo!

[_zM]

p100:

Code: Select all

x = 3, y = 3, rule = B2e3-a/S23
bo$o$b2o!

Actually common this time.

[FlameandFury]

i can't seem to make a gun ;-;

[ygh]

p100:

Code: Select all

x = 3, y = 3, rule = B2e3-a/S23
bo$o$b2o!

I discovered that one.

p100 F-Pentomino

Code: Select all

x = 3, y = 3, rule = B2e3-a_S23
b2o$2o$bo!

[_zM]

Then what about this yl64?

Code: Select all

x = 9, y = 25, rule = B2e3-a/S23
5b3o$5bobo$4obo$b2ob2o$5bo2$6bo$4bobo$4bobo2$4bo3$5bobo$4b2o$3bo3bo$3b
2ob2o$3b2ob2o$5bo$4b3o4$7bo$7b2o!

[ygh]

Ooh, nice one! How did you find that?

Edit: by using apgsearch. I'm not good at thinking.

[FlameandFury]

Code: Select all

x = 12, y = 9, rule = B2cei3aei/S23
2$5b3o$3b2o3b2o$2b2o5b2o$2b2o5b2o$2b2o5b2o$3b2o3b2o$5b3o!

Statorless P54 anyone?

[FlameandFury]

p100:

Code: Select all

x = 3, y = 3, rule = B2e3-a/S23
bo$o$b2o!

Actually common this time.

I guess this'll be my first term project then: Finding a proof of universal computation. I know it's going to be hard, but it's going to be easier than actually making one, and I'm collecting useful slow salvos. I'm pretty sure I just need the proper PUSH, PULL, and FIRE reactions as well as a method to create more gliders, or am I wrong?

[Rich Holmes]

I'm surprised drc hasn't (at least in this thread) mentioned B3/S14567, which he appears to have been the first to investigate with apgsearch. Huge number of oscillator periods up through this p1189:

Code: Select all

x = 7, y = 12, rule = B3/S14567
2bo4b$2bo4b$b3o3b$b3o3b$2b3o2b$b5ob$2obob2o$7o$bobobob$b4o2b$3bo3b$3bo3b!

There are two rotors, one on each side, with periods 29 and 41, sharing a stator.

[dvgrn]

I guess this'll be my first term project then: Finding a proof of universal computation. I know it's going to be hard, but it's going to be easier than actually making one, and I'm collecting useful slow salvos. I'm pretty sure I just need the proper PUSH, PULL, and FIRE reactions as well as a method to create more gliders, or am I wrong?

It sounds more like you're describing a universal constructor than a universal computer. You can easily have the second without the first. For example, in many rules you could build circuitry out of structures that it's impossible to either create or destroy.

However, as long as there are mechanisms available that can perform simple logic operations, even if they're Gardens of Eden that had to be there at T=0, most likely those mechanisms could still be arranged into a structure that can perform universal computations to make something programmable, equivalent to a Turing machine.

So if you do want a universal computer, you have a somewhat harder job than just finding PUSH, PULL, and FIRE mechanisms -- and you don't even really need those at all. Instead, you have to find some basic logic mechanisms and workable ways of stringing them together.

Conversely, if you want a universal constructor, you also have a somewhat harder job if you're working with a new rule. To show that a constructor is "universal", you have to somehow show that it's capable of constructing anything constructible.

-- Or at least you have to show that the constructor is capable of constructing a wide enough variety of objects that it could construct itself, with the proper programming, or an unlimited number of other configurations. Theoretically there might be weird not-quite-Garden-of-Eden patterns that are provably not constructible using the universal constructor, but _can_ be constructed by some other means -- crashing spaceships together that are themselves Gardens of Eden, perhaps.

That seems as if it would usually be a really strange degenerate case, however, and concrete examples are very hard to find.

So if the constructor can provably construct "almost everything", or even can just provably construct all the components that make up the constructor, many people consider that to be a demonstration of "universality" -- even if there does turn out to be some weird class of technically constructible things that it can't actually construct (!).

[BlinkerSpawn]

I'm surprised drc hasn't (at least in this thread) mentioned B3/S14567, which he appears to have been the first to investigate with apgsearch. Huge number of oscillator periods up through this p1189:

Code: Select all

x = 7, y = 12, rule = B3/S14567
2bo4b$2bo4b$b3o3b$b3o3b$2b3o2b$b5ob$2obob2o$7o$bobobob$b4o2b$3bo3b$3bo3b!

There are two rotors, one on each side, with periods 29 and 41, sharing a stator.

The first and fourth PATHOLOGICAL in that rule are both this p1326 (= 34 * 39):

Code: Select all

x = 13, y = 6, rule = B3/S14567
3bo3b2o$2b2ob5o$7obobo$2b2ob8o$3bo5b2o$10bo!

The second is a p1462 (= 2 * 17 * 43):

Code: Select all

x = 17, y = 6, rule = B3/S14567
2b3ob4o3b2o$8obo2b3o$2bob2ob10o$3b6obobobo$3b3ob7o$4bo4bob2o!

The third is a p1820 (= 5 * 13 * 28):

Code: Select all

x = 20, y = 10, rule = B3/S14567
4b2o3b2o$2b11o$2bobob3ob6o$7ob2o3b4o$2b2ob5o3bobobo$5bob5o2b4o$9b2ob3o
b4o$8b8obo$10b2o2b3o$15bo!

[shouldsee]

I'm surprised drc hasn't (at least in this thread) mentioned B3/S14567, which he appears to have been the first to investigate with apgsearch. Huge number of oscillator periods up through this p1189:

Code: Select all

x = 7, y = 12, rule = B3/S14567
2bo4b$2bo4b$b3o3b$b3o3b$2b3o2b$b5ob$2obob2o$7o$bobobob$b4o2b$3bo3b$3bo3b!

There are two rotors, one on each side, with periods 29 and 41, sharing a stator.

Speaking of this, there is a surface replicator in a rule closely-related.

replicator-based p62

Code: Select all

x = 17, y = 26, rule = B47/S14567
$4b8o$3b10o$3b2obobobob2o$4b11o$3b2obob2o2b4o$3b7o2bob2o$3b2obo2b7o$2b
6obobob3o$2b2obob5o2b3o$3b5obob5o$4b2ob5obobo$5b4o2b5o$6b4obo2b2o$7b6o
b2o$8b3ob5o$9b7o$10b3obo$12b4o$11b5o$10b3ob2o$10b5o$11b3o!

Similarly, with a second dimension, we have:

Code: Select all

x = 47, y = 39, rule = B012367/S0345
4$8b11o$9b10ob3o$8b15ob6o$7b23ob3o$4bob29o$4b35o$4b34obo$4b35o$4b36o$
5b36o$5b37obo$5b39o$5b39o$5b39o$5b39o$5b39o$5b39o$5b39o$5bob37o$8b35o$
9b34o$10b33o$9b33o$12b30o$15b27o$16b3ob20obo$20b3ob15o$24b2ob11o$27b
10o$28b10o!

[shouldsee]

p40 c/4 glider in an explosive rule

Code: Select all

x = 4, y = 4, rule = B01358/S3
b2o$bo$obo$3bo!

[shouldsee]

p202 oscillator

Code: Select all

x = 18, y = 17, rule = B3457/S567
7bo2$5b2ob2o2$4b8o$2bobo$2bobob5ob2o$o3bo$2bob3o2b7o$2bobo$6b12o2$8b2o
4b3o2$10b5o2$12bo!

EDIT:
p2014

Code: Select all

x = 8, y = 33, rule = B3457/S567
3bo$4b2o$b3o$4bob2o$4o$4b4o$b3o$4b4o$b3o$4b3o$2obo$4bo$b3o$4b3o$b3o$4b
4o$2obo$4b4o$o2bo$4b3o$o2bo$4bo$4o$4b3o$4o$4b4o$o2bo$4b4o$o2bo$4bob2o$
b3o$4b2o$3bo!

[Rhombic]

Common, naturally occurring xp44_166y0oo:

Code: Select all

x = 9, y = 5, rule = B2in35c/S23-j
o$b2o$b2o$7b2o$7b2o!

[toroidalet]

Life has a p96 switch engine, which commonly appears as a p288 or p384 puffer, but we already know that. B37e/S23 has a fairly common p52 puffer.http://catagolue.appspot.com/object/yl5 ... 4/b37-cs23. here is a soup which produces 2:

Code: Select all

x = 16, y = 16, rule = B37e/S23
2obob2o2b6o$3bob2obob3ob2o$o4bo2bo3b3o$3bo2b2o2b3ob2o$8bo2bob2o$bo2bo
5b3o2bo$2bob2o3bo4bo$ob2o2b7obo$o2b2o2bobob2o2bo$2obo2b3ob2o2bo$4obob
3o3bo$bo2b4obob5o$3o3bo2b3obo$6ob2o3b3o$o4bo3bo2b2obo$5bob2ob2o3bo!

[Rich Holmes]

Same engine plus a boat produces a p52 spaceship.

Code: Select all

x = 11, y = 14, rule = B37-c/S23
3b3o5b$3bobo5b$2bo2bo5b$bo3bob2o2b$3o2bob2o2b$o5bo4b$3bo2bo4b$2bo3bo4b$
2bo3bo4b$2bo8b$bo7bob$8bobo$8bobo$9bob!

[ygh]

Code: Select all

x = 9, y = 5, rule = B2ce3aiy/S12aei3r
6bo$5bobo3$obo!

Don't know the period, but it's pretty high.

EDIT:

Code: Select all

x = 4, y = 11, rule = B2ce3aiy/S12aei3r
2bo$bobo6$obo2$obo$bo!

This is my favorite rule!