Rules with Abnormally Common High-Period Patterns

[Bullet51]

Yes. When you are counting you have to take account into the current state of the central cell. This would attribute a neighborhood index to each cell. And by monitoring covariance between counts of different index values, we can identify the strength of tangling between neighorhoods.

It turns out that chaotic rules have weak tangling, and complex rules have moderate tangling.Maybe we are going off-topic...

[BlinkerSpawn]

Maybe instead of looking at variance between neighbor counts, look at variance between neighborhoods within neighbor counts?
For instance, a relatively orderly B2 rule would likely experience a lot more B2a or B2e than other B2 transitions.

[shouldsee]

Maybe instead of looking at variance between neighbor counts, look at variance between neighborhoods within neighbor counts?
For instance, a relatively orderly B2 rule would likely experience a lot more B2a or B2e than other B2 transitions.

Yes I tried to include orientation into account but it multiplies the number of variable by 45, and consider this is a O(n^2) complexity..... It's not clear how much symmetry we should impose on this scheme. The less symmetry in the prior, the harder the computation. So I guess we have to impose some symmetry to reduce the computation power required.

It turns out that chaotic rules have weak tangling, and complex rules have moderate tangling.Maybe we are going off-topic...

If we just use the crude estimation, rules with glider usually has an average tangling around 0.25-0.20.

Yes it's quite off topic I guess we should switch to the "smoothness" post.If we just use the crude estimation,

[Bullet51]

36c/72 Puffer:

Code: Select all

x = 3, y = 4, rule = B34kjrn_S2-i3
o$2o$b2o$2o!

[BlinkerSpawn]

36c/72 Puffer:

Code: Select all

x = 3, y = 4, rule = B34kjrn_S2-i3
o$2o$b2o$2o!

Really simple quadratic:

Code: Select all

x = 3, y = 14, rule = B34jknr/S2-i3
o$2o$b2o$2o7$2o$b2o$2o$o!

[shouldsee]

36c/72 Puffer:

Code: Select all

x = 3, y = 4, rule = B34kjrn_S2-i3
o$2o$b2o$2o!

Really simple quadratic:

Code: Select all

x = 3, y = 14, rule = B34jknr/S2-i3
o$2o$b2o$2o7$2o$b2o$2o$o!

You guys sure this is high-period pattern ?

[Bullet51]

36c/72 Puffer:

Code: Select all

x = 3, y = 4, rule = B34kjrn_S2-i3
o$2o$b2o$2o!

Really simple quadratic:

Code: Select all

x = 3, y = 14, rule = B34jknr/S2-i3
o$2o$b2o$2o7$2o$b2o$2o$o!

You guys sure this is high-period pattern ?

Puffers have their own definition of "period", which is different from oscillators.

[shouldsee]

Puffers have their own definition of "period", which is different from oscillators.

True

[drc]

Have some:

Code: Select all

x = 45, y = 65, rule = B34c5y/S236c
obobo15b2o5b2o$obobo15bo6bo$ob3o$o3bo$o3bo$21bo6bo$20bobo4bobo2$20b3o
4b3o$21bo6bo3$20b2o6b2o$20b2o6b2o7$2b3o15bo5bo13b3o$obo17b2o3b2o14bo$o
b3o15bo5bo$obobo$ob3o$43bo$42b3o14$3obobo14bo$o3bobo13b2o$3ob3o14bo$2b
o3bo$3o3bo$21bo$20b2o$21bo13$3ob3o13b3o$o3bobo14b2o2bo$3ob3o18b2o$2bob
obo19b2o$3ob3o18b2o!

[shouldsee]

p78

Code: Select all

x = 4, y = 4, rule = B368/S3467
obo$4o$3o$b3o!

[shouldsee]

p48

Code: Select all

x = 5, y = 5, rule = B01234567/S346
o3bo$b3o$5o$b3o$bobo!

[shouldsee]

4-cell p126

Code: Select all

x = 2, y = 2, rule = B01356/S0123
2o$2o!

[Rhombic]

p20

Code: Select all

x = 5, y = 4, rule = B2n34qz/S2-i34q
ob3o$4bo$4o$2bo!

p30

Code: Select all

x = 10, y = 10, rule = B2n34qz/S2-i34q
o$4bo2bo$4b3obo$3bobobo$b2o3b2o$2b2o3b2o$2bobobo$bob3o$2bo2bo$9bo!

p156

Code: Select all

x = 22, y = 12, rule = B2n34qz/S2-i34q5a
$12b2o$12bobob2o$8b3o2bob2o2b2o$9b3ob5o2b2o$10bob5o2b2o$19bo$3bo$2b3o$
bo3bo$2b2obo$3b2o!

(1,1)c/68 spaceship!!

Code: Select all

x = 4, y = 5, rule = B2n34qz/S2-i34q6e
bo$obo$o$2b2o$3bo!

[Bullet51]

9c/23, along the lines:

Code: Select all

x = 37, y = 20, rule = B2n34qz7e_S2-i34q
8$23b3o$22bo3bo$22b2ob2o!

Adding B7c gives a little surprise:

Code: Select all

x = 4, y = 3, rule = B2n34qz7_S2-i34q
2bo$b3o$2obo!

(The surprise is on gen 2117.)

[Rhombic]

p76

Code: Select all

x = 7, y = 8, rule = B2-a3-n/S2-a3aik4ijz5cr6n
2$3bo$2b3o$b3o$2bo!

(1,1)c/12

Code: Select all

x = 6, y = 6, rule = B2en35cek6ci/S123cek4ci5cek6ci8
5bo$5bo$2bobo2$2bo$2o!

[AbhpzTa]

p70 oscillator in B2en3/S25678, bounding box = 9*9

Code: Select all

x = 4, y = 4, rule = B2en3/S25678
o$b3o$b2o$bo!

[FlameandFury]

P80:

Code: Select all

x = 10, y = 27, rule = B34qtw6/S245
2$3b4o$3b4o3$b8o$b8o$2b6o$2b2o2b2o$3bo2bo$4b2o$4b2o$4b2o$4b2o3$4b2o$4b
2o3$2o6b2o3$4b2o$4b2o!

P70 in related rule:

Code: Select all

x = 6, y = 9, rule = B34qt6/S2456c
2b2o$2b2o4$2b2o$b4o$b4o!

[Rocknlol]

Here's an 8-cell c/144 ship:

Code: Select all

# [[ Z 16 STEP 5 TRACK 1/144 0 ]]
x = 3, y = 7, rule = B2i3-e4ijnrwyz5akqy6ac/S23-jqr4c5n8
bo$3o$bo2$2bo$2bo$2bo!

[Rhombic]

16c/38

Code: Select all

x = 14, y = 3, rule = B3/S23-r6c
bobo7bo$2o2bo5b2obo$bobo7bo!

Most common spaceship in another rule is 4c/18:

Code: Select all

x = 4, y = 4, rule = B2-a3i/S23-cnq
bo$o2bo$bobo$2bo!

p20:

Code: Select all

x = 6, y = 8, rule = B2-a3i/S23-cnq
bo$2o2$2b2o$3bo2$4b2o$4bo!

[BlinkerSpawn]

16c/38

Code: Select all

x = 14, y = 3, rule = B3/S23-r6c
bobo7bo$2o2bo5b2obo$bobo7bo!

Rake:

Code: Select all

x = 15, y = 20, rule = B3/S23-r6c
bobo7bo$2o2bo5b2obo$bobo7bo15$2bobo7bo$b2o2bo5b2obo$2bobo7bo!

[FlameandFury]

2/25c diagonal spaceship:

Code: Select all

x = 4, y = 4, rule = B2-ac3aceik/S24-a56-c8
2b2o$3bo$obo$2o!

[Rhombic]

6c/33

Code: Select all

x = 3, y = 3, rule = B2-a35n7c/S1c2a7e
obo$3o$bo!

[_zM]

Not that common, but still a very small p24.

Code: Select all

x = 5, y = 5, rule = B2c3-i/S1c23
b2o$o2bo$b2obo$bo2bo$3bo!

Note that the rotor only contains 7 cells

[FlameandFury]

This monstrosity I found by hand 0.o

Code: Select all

x = 8, y = 13, rule = B2cei3acei/S23
$b2o$b2o3$2b2o3bo$bo2bo2bo$2b2o3bo3$b2o$b2o!

[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!