Rules with interesting dynamics

[NimbleRogue]

The non c/5 ships in this rule look really weird

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x = 345, y = 30, rule = B2ei3aiy4ar5acijn6ace7c8/S3-anry4aejrwyz5eiky678
b2o13b3ob3o23b3o28b3o32b3o26b3ob3o14b3obobo13b3obobo14bob3o24b3obobo
20b4o28b2o17b2o22b4o$2obo12b7o17bo3bob3obobo22bob3obo24bo3bob3obo24b7o
14b8o10bob8o11bob4o19bo3bob8o20b2obo26b2o16b2ob2o17b4ob2obo$b2obo10b
10o15b3ob10o19bob6obo23b3ob6obo21b11o10b9o9bob9o13b6obo16b3ob9o19b8o
24b4obobo9b8o15b11o$5o8b12o13b15o19b10obo20b13obo19bob10o10b10o9b11o
10b10o14b16o19b6obo21b7obo10b9o13b11obo$bobo9b12o13b16o18b11o19bob14o
20b12o10b9o8b12o11b10o12bob15o18b9obo20b8obo7b12o13b11obo$11b13o12b17o
17b15o16b19o16b13o12b9o7b13o8b11o14b17o17b11o18b11o9b12o10b15o$11b14o
10bob18o15b15o16b19o16b14o9b11o5b15o6bob12o11b19o17b12o16b13o6b14o11b
15o$11b14o10b20o13b17o14b21o14b16o9b11o6b14o7b11o13b19o18b10obo15b13ob
o5b14o8b16obo$12b13o8b22o12b16o16b19o17b15o7b11o8b12o7b12obo10b19o18b
14o13b17o5b15o7b18o$10b13o10b20o15b16o13b22o16b13o11bob3ob3o9b12o6b12o
12b20o18b13o14b15o6b13obo7b18o$11b11o9b23o12b16o14b21o19b10obo12b4o11b
12o6b12o12b20o19b12obo12b15o6b16o9b15obo$10b12o10b20o14b17o14b21o17b
12o14bo13b11obo6b11o11b22o19b9obo15b14o7b15o7b18o$11b9o12b21o11b18o13b
23o18b9o16bo11b13o6b11o13b22o19b5ob3o17b12o7b16o9b17o$11b5ob3o12b21o
12b15o16b23o17b9o30b5ob3o10b8obo10b25o20bobo21b12o8b13o9b19o$13bobo14b
24o11b15o14b23o21bob3o32b5o3bo10b8o13b22o44b13o9b11obo9b19o$31b21o14b
12o16b23o25bo34bo17b5o13b24o45b10o11bob5o3bo11b15obo$29b23o12b14o14b
23o62bo19bobo14b21o46b9obo11b5obo16b12obo$30b20o15b10obo16b23o81bo16b
20obo47b3o3bo17bo16b10ob3o$30b18obo14b11o16b24o99b20o49bobo40b6obo$30b
19o15bob3ob3o19b21o99b20o93bobob3o$28b19o17b3obo3bo19b21o100b19o95bo$
29b18o46b18o100b19o$27b18o46b20o101b18o$28b13o3bo46b17obo102b17o$27b
12obo50b15obo104b15o$28b7o3bo53b14o104b15obo$28b5obo56b13o107b10o3bo$
30bobo60b5ob3obo106b9obo$93bob3o3bo110b3o3bo$212bobo!

[pipsqueek]

This rule forms these cool looking structures

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x = 21, y = 30, rule = B2ce3-i/S1e2ek3eijkr4eijrtwz5cnqry6-en
17bo$18b2o$20bo$20bo$20bo$20bo$20bo$20bo$20bo$20bo$20bo$20bo$3b2o15bo$
5b2o13bo$7b2o11bo$9b2o9bo$11b2o7bo$13b3o4bo$16b3obo$20bo$19bo$19bo$18b
o$18bo$3o7b2o3b3o$3b12o$13bo$13bo$13bo$12b2o!

An explosive variant with a spaceship and a 180 degree reflector

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x = 33, y = 5, rule = B2ce3-ciq4ct6i/S1e2ek3eijkr4eijrtwz5cnqry6-en8
b2o27b2o$bo2bo9bo13bo2bo$2o5bo4b3obo8bo5b2o$bo2bo9bo13bo2bo$b2o27b2o!

[d/dx]

in B3-ky4ct5i/S2-k3-i4awz, the pi heptomino is a 2c/17o ship that moves "backwards".

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x = 8, y = 7, rule = B3-ky4ct5i/S2-k3-i4awz
$3b3o$3bobo$3bobo!

[confocaloid]

in B3-ky4ct5i/S2-k3-i4awz, the pi heptomino is a 2c/17o ship that moves "backwards".

Code: Select all

x = 8, y = 7, rule = B3-ky4ct5i/S2-k3-i4awz
$3b3o$3bobo$3bobo!

Statorless p28 oscillator in the same CA

Code: Select all

x = 5, y = 5, rule = B3-ky4ct5i/S2-k3-i4awz
2ob2o$bobo$bobo$bobo$2ob2o!

[d/dx]

Statorless p28 oscillator in the same CA

Code: Select all

x = 5, y = 5, rule = B3-ky4ct5i/S2-k3-i4awz
2ob2o$bobo$bobo$bobo$2ob2o!

Found it first, sorry.

[confocaloid]

Statorless p28 oscillator in the same CA

Code: Select all

x = 5, y = 5, rule = B3-ky4ct5i/S2-k3-i4awz
2ob2o$bobo$bobo$bobo$2ob2o!

Found it first, sorry.

I don't know whether the oscillator was found earlier (possibly much earlier) in some other CA where it evolves the same way.
I found that p28 on 2024-05-04 by apgsearching the C1 census: /census/b3-ky4ct5is2-k3-i4awz/C1

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apgluxe v5.41-ll2.5.7: Rule b3-ky4ct5is2-k3-i4awz is correctly configured.
apgluxe v5.41-ll2.5.7: Symmetry C1 is correctly configured.

Greetings, this is apgluxe v5.41-ll2.5.7, configured for b3-ky4ct5is2-k3-i4awz/C1.

Lifelib version: ll2.5.7
Compiler version: 11.4.0
Python version: '3.10.12 (main, Nov 20 2023, 15:14:05) [GCC 11.4.0]'

Peer-reviewing hauls:

No more hauls to verify.

Peer-review complete; proceeding search.

Using seed k_hkqPGxUyaqv3
Instruction set SSE4.2 detected
Running 19683 soups per haul:
b3-ky4ct5is2-k3-i4awz/C1: 711 soups completed (70.838 soups/second current, 70.838 overall).
b3-ky4ct5is2-k3-i4awz/C1: 1393 soups completed (67.962 soups/second current, 69.397 overall).
b3-ky4ct5is2-k3-i4awz/C1: 2059 soups completed (66.600 soups/second current, 68.467 overall).
b3-ky4ct5is2-k3-i4awz/C1: 2708 soups completed (64.881 soups/second current, 67.570 overall).
b3-ky4ct5is2-k3-i4awz/C1: 3527 soups completed (81.826 soups/second current, 70.417 overall).
b3-ky4ct5is2-k3-i4awz/C1: 4352 soups completed (81.894 soups/second current, 72.339 overall).
b3-ky4ct5is2-k3-i4awz/C1: 5024 soups completed (67.006 soups/second current, 71.577 overall).
b3-ky4ct5is2-k3-i4awz/C1: 5825 soups completed (79.972 soups/second current, 72.625 overall).
b3-ky4ct5is2-k3-i4awz/C1: 6583 soups completed (75.800 soups/second current, 72.977 overall).
b3-ky4ct5is2-k3-i4awz/C1: 7333 soups completed (74.918 soups/second current, 73.170 overall).
b3-ky4ct5is2-k3-i4awz/C1: 8031 soups completed (69.557 soups/second current, 72.841 overall).
b3-ky4ct5is2-k3-i4awz/C1: 8804 soups completed (77.285 soups/second current, 73.210 overall).
b3-ky4ct5is2-k3-i4awz/C1: 9561 soups completed (75.159 soups/second current, 73.360 overall).
b3-ky4ct5is2-k3-i4awz/C1: 10388 soups completed (82.289 soups/second current, 73.999 overall).
b3-ky4ct5is2-k3-i4awz/C1: 11174 soups completed (78.420 soups/second current, 74.294 overall).
b3-ky4ct5is2-k3-i4awz/C1: 11959 soups completed (78.328 soups/second current, 74.545 overall).
b3-ky4ct5is2-k3-i4awz/C1: 12699 soups completed (73.941 soups/second current, 74.509 overall).
b3-ky4ct5is2-k3-i4awz/C1: 13522 soups completed (82.111 soups/second current, 74.932 overall).
b3-ky4ct5is2-k3-i4awz/C1: 14243 soups completed (71.942 soups/second current, 74.774 overall).
b3-ky4ct5is2-k3-i4awz/C1: 15071 soups completed (82.701 soups/second current, 75.170 overall).
b3-ky4ct5is2-k3-i4awz/C1: 15860 soups completed (78.900 soups/second current, 75.347 overall).
b3-ky4ct5is2-k3-i4awz/C1: 16597 soups completed (73.700 soups/second current, 75.272 overall).
b3-ky4ct5is2-k3-i4awz/C1: 17337 soups completed (73.948 soups/second current, 75.214 overall).
b3-ky4ct5is2-k3-i4awz/C1: 17982 soups completed (64.500 soups/second current, 74.769 overall).
b3-ky4ct5is2-k3-i4awz/C1: 18699 soups completed (71.686 soups/second current, 74.646 overall).
b3-ky4ct5is2-k3-i4awz/C1: 19478 soups completed (77.861 soups/second current, 74.769 overall).
b3-ky4ct5is2-k3-i4awz/C1: 19683 soups completed (63.783 soups/second current, 74.635 overall).
----------------------------------------------------------------------
19683 soups completed.
953446752 tiles processed.
Attempting to contact Catagolue...
Saving results to log.1714841193.k_hkqPGxUyaqv3.txt
Payosha256 authentication succeeded.
***********************************************

Connection was successful.
New seed: k_kG4maD3kzvKg; iterations = 1; quitByUser = 0
Terminating...

edit (2024-05-05): p119 orthogonal 2c/17 spaceship

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#C https://catagolue.hatsya.com/object/xq119_elrzggxccy0ok8zda/b3-ky4ct5is2-k3-i4awz
x = 14, y = 14, rule = B3-ky4ct5i/S2-k3-i4awz
b2o$obo$2o$obo$b2o3$5b2o5bo$5b2o4bobo$2o9b2o$o$bo$o$2o!

edit 2 (2024-05-06): another statorless p28 oscillator!

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x = 6, y = 5, rule = B3-ky4ct5i/S2-k3-i4awz
2o2b2o$2o2b2o2$6o$o4bo!

[d/dx]

I think it's safe to say we found it on the same day so we can both be credited for the find.

By the way, the pi ship is called "wishbone".

[hotcrystal0]

the new rule:
r2,c2,s9-24,b3

when random circles appear!
circles appear.png

The way the circles behave seem to be like how the anti-tubs behave in the Anti-Tub Rule.
Compare:

Code: Select all

x = 13, y = 6, rule = R2,C2,S9-24,B3
9b2o$8b4o$b2o5b5o$4o5b4o$4o6b2o$b2o!

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x = 11, y = 8, rule = B36-c7c8/S134cijkrw5-aej6-a7
7b3o$6b2ob2o$6bobobo$b7ob2o$2ob2o2b3o$obobo$2ob2o$b3o!

[tommyaweosme]

the new rule:
r2,c2,s9-24,b3

when random circles appear!
circles appear.png

The way the circles behave seem to be like how the anti-tubs behave in the Anti-Tub Rule.
Compare:

Code: Select all

x = 13, y = 6, rule = R2,C2,S9-24,B3
9b2o$8b4o$b2o5b5o$4o5b4o$4o6b2o$b2o!

Code: Select all

x = 11, y = 8, rule = B36-c7c8/S134cijkrw5-aej6-a7
7b3o$6b2ob2o$6bobobo$b7ob2o$2ob2o2b3o$obobo$2ob2o$b3o!

i made it because r2,c2,s,b1 emulates b1/s, so i tried to make a life emulator. i failed and got this. the three cell line is a spaceship!

[hotcrystal0]

R2,C2,S4,B4 seems to be interesting. There’s a 4-cell predecessor of 4 very smoky ships and some smaller spaceships:

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x = 4, y = 2, rule = R2,C2,S4,B4
o2bo$o2bo!

Edit: Other than the variety of simplified 3c/2 spaceships, the only other natural objects are a few still lives, a P2, and a P8 that looks like a block in one phase and a phase of Cross in another:

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x = 17, y = 19, rule = R2,C2,S4,B4
2o5b2o4bobo$bo4bo7bo$2o4bobo4bobo12$15b2o$bo13b2o$o$2b2o$2bo!

[H. H. P. M. P. Cole]

R2,C2,S4,B4 seems to be interesting.

https://www.sciencedirect.com/science/a ... 8907004022
viewtopic.php?f=11&t=4942&p=115740#p115740

Also read K. M. Evans' thesis on LtL, if you haven't already. Chapter 11 mentions this rule, calling it the LtL rule with the most intriguing dynamics.