B4/S3456

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ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

B4/S3456

Post by ebcube » February 27th, 2010, 6:54 pm

Hi! New user here =)

This rule doesn't expand, and stabilizes quickly. However, by drawing a 2 dot wide line and adding something to it, a pattern appears.

You can see some examples here:

Code: Select all

x = 313, y = 69, rule = B4/S3456
3$4b5ob2o17bobo10b3o$3b2obob2obo11b3ob2obobo7b2ob3o11b4o10b2o2b2o15b2o
12b2o2b2o12b2o2b2o9b2o2b2o10b2o2b2o9b4o12b2o14b3o14b5o12b5o12b3o$3bob
2o2bob2o10b2o4bobo7bob3ob2o9b2o2b2o7b8o11b6o10b8o10b8o7b8o8b8o7b4ob2o
10bob2o12b2ob2o13b2obo13b2ob2o11bobobo12b4o14b3o9b2o6b2o$3bobo2b2o2bo
10bo2bobo4bo5b2obob3o8b2o2b2o8b4o2bo12b2o2bo11b4o2bo11b4o2bo8b4o2bo9b
4o2bo7b3o4bo9b5o12b5o13b5o12b2ob2o11b2ob2o11b6o12b2ob2o8b2o6b2o$3b2obo
b2ob2o15b2obobo5bobob4o8b5o10bo4bo14b3o12bo3b2o12bo3b2o9bo3b2o10bo3b2o
7bo3bob2o8b3o2bo12bo2b2o14bob2o13b3o12b2ob2o11b2o2b2o12b2ob2o8b2o2b2o
2b2o$6bo3b2o10b2obo2b4o8b2ob3o10bo3bo9bobo2bo14bobo12bobo2bo12bo4bo9bo
bo2bo10bobo2bo7b5ob2o7b2ob4o12b5o16b2o14b3o11bob3o11b3ob2o12b5o8b2o2b
2o2b2o$4b7ob2o8b2o4bobo13b2o9b2obob2o8b6o14b3o12b6o11b7o8b7o9b7o8bobo
2b2o7bo3b3o13b4o16b2o15b2o12b4o12b5o13b4o7b4o4b4o$4bo2bob2o2bo11bo3b2o
13b2o9bo4b2o7b2o3b2o15b2o11b2o3b2o11b2o3b2o9bo3b2o9b2o3b2o13b2o12b2o
15b2o16b2o15b2o14b2o13b4o15b2o7b2ob6ob2o$4b2o3b2o13b2o2b2o14b2o9bobo2b
2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b
2o12b2o$4bo4b2o13b2o3b3o12b2o9bo4b2o12b2o15b2o16b2o16b2o13b2o14b2o13b
2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o12b2o3bob2o12b2o9b2o3b
2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b
2o12b2o$9b2o10b3obob2o2bo12b2o9bo4b2o12b2o15b2o16b2o16b2o13b2o14b2o13b
2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o10b2o2b3ob3o12b2o14b2o
12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o
12b2o$9b2o10bo4b2ob3o12b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b
2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b
2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b
2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b
2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b
2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b
2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b
2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b
2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b
2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b
2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b
2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b
2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b
2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b
2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b
2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b
2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b
2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b
2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b
2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b
2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b
2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b
2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b
2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b
2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b
2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b
2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b
2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b
2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b
2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b
2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b
2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b
2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b
2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b
2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b
2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b
2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b
2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b
2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b
2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b
2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b
2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b
2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b
2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b
2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b
2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b
2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b
2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b
2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b
2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b
2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b
2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b
2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b
2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b
2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b
2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b
2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b
2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b
2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b
2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b
2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b
2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b
2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b
2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b
2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b
2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b2o15b2o16b2o16b2o13b2o14b
2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b2o$9b2o15b2o16b2o14b2o12b
2o15b2o16b2o16b2o13b2o14b2o13b2o12b2o15b2o16b2o15b2o14b2o15b2o15b2o12b
2o!
Those lines can turn left or right, but the resulting "garbage" from the pattern may (and usually will) vary.

Oscillators of period 6 and 9 appear naturally. I've also managed to create oscillators of period 2 and 3:

Code: Select all

x = 56, y = 20, rule = B4/S3456
2$3b2o3b3o$2b2obob3obobobo$3bob3ob8o$2b2obobobo2bo3bo$3b3obobob5o$2b2o
b3ob3o2bo$bobo2bo2bob5o9b3o$b7o7b2o7b2ob2o8bo12b2o$b2o7b7o8bob2o7b3o
10b4o$2b5obo2bo2bobo8b2obo6b2ob2o8b2ob2o$3bo2b3ob3ob2o7b2obobo5b2o2b2o
7b2o2bo$2b5obobob3o8b2ob3o5b2o2b2o8bo2b2o$bo3bo2bobobob2o7b5o6b2ob2o8b
2ob2o$b8ob3obo9b2o2bo6b3o9b4o$2bobobob3obob2o9b4o7bo11b2o$7b3o3b2o11b
3o!

Sokwe
Moderator
Posts: 1480
Joined: July 9th, 2009, 2:44 pm

Re: B4/S3456

Post by Sokwe » February 28th, 2010, 12:23 am

Here are oscillators of periods 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, and 18:

Code: Select all

x = 231, y = 28, rule = B4/S3456
151b3o6b3o$150b3obob2obob3o$149b2obob6obob2o$148b3ob2obo2bob2ob3o22b2o
$148b2obob8obob2o21b4o$146b4obobo2b2o2bobob4o18b2o2b2o$145b4ob2ob2o4b
2ob2ob4o18b3ob2o$144b3o2b2obo8bob2o2b3o17bob4o29bo4b2o$86b2o41b2o12b2o
2b3o2bo8bo2b3o2b2o9b2o3b2ob2o31b2o4b3o$65b2o18bob2o13b2o7b2o15b4o11b4o
3b4o6b4o3b4o8b3o4b2ob2o29b2obo2b2ob2o$48b2o14b4o13bo3b3obo11bob2o5b2ob
o15bob2o10bo2b4o2bo8bo2b4o2bo7b2obob3obob2o29b4o3b2o$48b2ob2o10bobob2o
11b2o2b2obob2o10b2o2b5o2b2o16bo13b2obobo14bobob2o7b2ob7ob3obo16b4o9bob
3o$17b2o30bob2o9b2o3b3o9bo5bobo12bob4obob4obo14b2o5bo8b3o18b3o8b2obobo
2b5ob2o2bo7b2obob3ob2o10bobo$2o2b2ob2o8b2o15b5o10bobo9b4o2bo2bo7b7ob2o
11b3o3b2ob2o3b3o10bo2b2ob2ob3o6b2ob2o16b2ob2o8b4ob2obobob2ob4o6b2ob3ob
ob2o10b3obo$2ob6o9bo13bo2bob2o9b3o9b2o7b3o6bobo2bo3bobo9bobo4bobo4bobo
9b2o3b5ob2o6b2ob2o16b2ob2o9bo2b2ob5o2bobob2o6b4o14b2o3b4o$b3o2bo10b2o
13b2o13b3o10b3o7b2o7b4o5b4o7bobo4bobo4bobo8b2ob5o3b2o8b3o18b3o13bob3ob
7ob2o22b2ob2o2bob2o$2o4b2o10bo12b2o13bobo12bo2bo2b4o10bobo3bo2bobo6b3o
3b2ob2o3b3o8b3ob2ob2o2bo8b2obobo14bobob2o14b2obob3obob2o24b3o4b2o$2o5b
2o7bo9b2obo2bo12b2obo13b3o3b2o13b2ob7o7bob4obob4obo10bo5b2o10bo2b4o2bo
8bo2b4o2bo13b2ob2o4b3o26b2o4bo$b2o4b2o7b2o8b5o14b2ob2o13b2obobo14bobo
5bo9b2o2b5o2b2o17bo11b4o3b4o6b4o3b4o14b2ob2o3b2o$2bo2b3o8bo31b2o14b4o
12b2obob2o2b2o10bob2o5b2obo15b2obo10b2o2b3o2bo8bo2b3o2b2o11b4obo$6ob2o
7b2o47b2o14bob3o3bo12b2o7b2o17b4o10b3o2b2obo8bob2o2b3o12b2ob3o$2ob2o2b
2o7b2o64b2obo45b2o12b4ob2ob2o4b2ob2ob4o14b2o2b2o$83b2o61b4obobo2b2o2bo
bob4o16b4o$148b2obob8obob2o19b2o$148b3ob2obo2bob2ob3o$149b2obob6obob2o
$150b3obob2obob3o$151b3o6b3o!
-Matthias Merzenich

User avatar
Lewis
Posts: 320
Joined: March 17th, 2009, 5:26 pm
Location: UK
Contact:

Re: B4/S3456

Post by Lewis » February 28th, 2010, 6:37 am

A while ago I found a variation of this rule (B456/S3456) which has similar oscillators to this rule. Some of them may even work in both rules.

Code: Select all

x = 137, y = 93, rule = 3456/456
89bobobo$98bo$89bo3bo3b3o$obobo28bobobobobo55bo2bo$15b2o16bob
obobobo47bobobo3b2obo5b6o$4bo10b3o13b3o7b3o54bobo4b2ob5o$8b2o
5bob2o7bo62bo3bo4b3o5b5ob2o$obobo2b2obo4b2o2bo4b3o4b2o9b2o55b
o7b2o2b2o$8bob2o4bo2b2o4b3o61bobobo$o8b2o6b2ob2o3bo5b2o9b2o$18b
4o$obobo26b3o7b3o$33bobobobobo47bobobo$33bobobobobo56b4o$89bo
3bo3b2ob2o6b4ob2o$obobo92b2ob3o4b2ob2ob3o$26bo62bobobo3b7o3b2o
b2ob2o$4bo4bo6b2o7b3o70b2ob4o3b4o$8b3o4b3o6b5o64bo5b3ob2o$obo
bo3b4o4b4o3b7o70b4o$10b3o5b3o3b5o60bobobo$4bo5b2o6b2o5b3o$26b
o$obobo$120b5o5b5o$86bo2bobobo8bo16b3ob2o5b2ob3o$101b3o14b2ob
ob2o5b2obob2o$o3bo81bo2bo3bo6b4o8b2o4b19o$9b3o29b2o2b2o13bo6b
o31b5o5b3ob2o3bo2bo2bo2bo2bo2bo2bo$o3bo3b2ob2o4bo5bo10bo5b8o11b
3o4b3o4bo12bo2bo3bo4b5o5b2o2b2o4b19o$8b5o3b3o3b3o8b3o5b2o2b2o
4b3o4b5o2b2obo3b3o23bob3o4b2o2b2o5b2obob2o5b2obob2o$obobo3b5o
2b2obo3bo2bo6b4o14b2o2bo2b6o2b2obo2bo2bo11bo2bo3bo4bob2o4b2ob
3o7b3ob2o5b2ob3o$8b2ob2o2bo2bo4bo2bo4b5o14bo2b2o2bo2b3o2b2obo
2bo2bo23b3o6b2o11b5o5b5o$4bo4b3o3b3o6bob2o4b3o6b2ob2o5b3o3b2o
2bo3bob2o2b2obo11bo2bobobo5bo$16bo8b2o6bo6b7o11b3o4b3o4b3o$4b
o36b2ob2o13bo6bo6bo3$10b4o19b4o53bo2bo5b2o$9b2ob3o6b6o5b2o2b2o
60b2ob3o$8b5ob2o4b3obob2o3b8o51bo2bo4bo4b2o$7b2ob2ob4o3bob2ob
3o2b4o2b4o58bo5bo$7b3o3b2obo3b2o3bobo2bobo4bobo50bo2bo3bo5bo$
7bob2o3b3o3bobo3b2o2bobo4bobo57b2o4bo$7b4ob2ob2o3b3ob2obo2b4o
2b4o50bo2bo4b3ob2o$8b2ob5o4b2obob3o3b8o62b2o$9b3ob2o6b6o5b2o2b
2o52bo2bo$10b4o19b4o2$obobo2$o10bo$10b3o$obobo4b2ob2o$8b2o3b2o
71bobobo2bobobo$4bo4b5o89b5o$90bo6bo4bo4b2o$obobo96b2o2b3o$86b
obobo2bobobo2b2ob3o$101b2o$86bo6bo$obobo$86bobobo2bobobo$o$8b
4o$obobo2b2o3bo$7bo3b2o$o3bo3b4o2$obobo80bobobo2bobobo7b3o$103b
6o$89bo2bo3bo5b3ob4o$102b2o4b3o$85bobobo2bobobo4b3o5b2o$101b2o
5b3o$85bo6bo3bo4b3o4b2o$102b4ob3o$85bobobo2bobobo6b6o$105b3o5$
85bobobo2bobobo9b2o$106b2o$89bo2bo3bo9b2o$101b7o$85bobobo2bo3b
o4b7o$104b7o$89bo2bo3bo7b7o$104b2o$85bobobo2bobobo7b2o$104b2o
!

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

Re: B4/S3456

Post by ebcube » March 1st, 2010, 3:51 pm

I'm trying to understand how the "line travellers" work. I came across some interesting ones:

This one creates a line traveler with a symmetric garbage pattern, then sends more line travellers that destroy the garbage pattern from the first ones.

Code: Select all

x = 18, y = 140, rule = B4/S3456
2$8b2o$3b2obob2obob2o$4b2ob7o$3b4ob2obob2o$5bo2b2o3bo$3bobo2b2o2b2o$2b
o5b2o2b4o$2b2obo2b2ob2o2bo$4b2o2b2ob2ob4o$3b2obob2o2b2o3bo$5b2ob2o3b4o
$3b2o3b2o4bobo$b4o3b2o3b2obo$bo6b2o$obo5b2o$o2bo4b2o$2b2o4b2o$b2o5b2o$
2b2o4b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$
8b2o$8b2o$8b2o$8b2o$8b2o$8b2o$8b2o!

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