CA that behave similar to 2x2

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Awesomeness
Posts: 126
Joined: April 5th, 2009, 7:30 am

CA that behave similar to 2x2

Post by Awesomeness » October 17th, 2010, 3:35 pm

I've noticed that many rules, including those that normally explode, emulate a different CA on a 2x2 grid.

An example is B34678/S012458, where normal patterns simply blow up, while on a 2x2 grid it emulates some CA where everything usually dies down...

Code: Select all

x = 298, y = 256, rule = B34678/S012458
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$
296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$71b26o
4b22o173b2o$26b4o41b26o4b22o173b2o$26b4o41b24o2b4o2b20o173b2o$24b2o4b
2o39b24o2b4o2b20o173b2o$24b2o4b2o39b26o2b6o2b16o173b2o$26b2o6b2o35b26o
2b6o2b16o173b2o$26b2o6b2o35b30o4b18o173b2o$30b4o37b30o4b18o173b2o$30b
4o37b16o4b2o2b2o4b4o2b16o173b2o$16b4o2b2o2b4o4b2o35b16o4b2o2b2o4b4o2b
16o173b2o$16b4o2b2o2b4o4b2o35b28o8b16o173b2o$28b8o35b28o8b16o173b2o$
28b8o35b18o4b2o2b2o4b20o173b2o$18b4o2b2o2b4o39b18o4b2o2b2o4b20o173b2o$
18b4o2b2o2b4o39b18o2b10o8b14o173b2o$18b2o10b8o33b18o2b10o8b14o173b2o$
18b2o10b8o33b14o2b2o4b4o4b2o2b4o2b12o173b2o$14b2o2b4o4b4o2b2o4b2o31b
14o2b2o4b4o4b2o2b4o2b12o173b2o$14b2o2b4o4b4o2b2o4b2o31b4o2b2o4b4o2b6o
2b8o4b4o2b8o173b2o$4b2o2b4o4b2o6b2o8b4o4b2o27b4o2b2o4b4o2b6o2b8o4b4o2b
8o173b2o$4b2o2b4o4b2o6b2o8b4o4b2o27b6o2b2o2b2o4b6o2b2o4b6o4b6o2b2o173b
2o$6b2o2b2o2b4o6b2o2b4o6b4o6b2o21b6o2b2o2b2o4b6o2b2o4b6o4b6o2b2o173b2o
$6b2o2b2o2b4o6b2o2b4o6b4o6b2o21b2o2b2o2b2o6b4o2b2o4b2o8b4o2b6o175b2o$
2b2o2b2o2b6o4b2o2b4o2b8o4b2o6b2o19b2o2b2o2b2o6b4o2b2o4b2o8b4o2b6o175b
2o$2b2o2b2o2b6o4b2o2b4o2b8o4b2o6b2o21b6o6b2o2b2o2b8o2b4o8b2o2b2o175b2o
$2o6b6o2b2o2b2o8b2o4b8o2b2o2b2o21b6o6b2o2b2o2b8o2b4o8b2o2b2o175b2o$2o
6b6o2b2o2b2o8b2o4b8o2b2o2b2o21b2o2b2o2b6o2b8o2b4o8b4o2b6o173b2o$2o2b2o
2b2o6b2o8b2o4b8o4b2o27b2o2b2o2b6o2b8o2b4o8b4o2b6o173b2o$2o2b2o2b2o6b2o
8b2o4b8o4b2o25b2o2b8o2b4o10b2o2b4o6b2o2b2o2b2o173b2o$2b2o8b2o4b10o2b2o
4b6o2b2o2b2o21b2o2b8o2b4o10b2o2b4o6b2o2b2o2b2o173b2o$2b2o8b2o4b10o2b2o
4b6o2b2o2b2o21b8o2b20o8b2o2b4o2b4o173b2o$8b2o20b8o2b2o4b2o23b8o2b20o8b
2o2b4o2b4o173b2o$8b2o20b8o2b2o4b2o23b12o2b2o2b2o6b18o2b6o173b2o$12b2o
2b2o2b6o18b2o25b12o2b2o2b2o6b18o2b6o173b2o$12b2o2b2o2b6o18b2o25b8o2b2o
4b4o2b10o8b12o173b2o$8b2o2b4o4b2o10b8o31b8o2b2o4b4o2b10o8b12o173b2o$8b
2o2b4o4b2o10b8o31b8o2b6o8b4o8b4o2b10o173b2o$8b2o6b8o4b8o4b2o29b8o2b6o
8b4o8b4o2b10o173b2o$8b2o6b8o4b8o4b2o29b6o2b2o4b4o2b6o2b8o4b4o2b6o173b
2o$6b2o2b4o4b2o6b2o8b4o4b2o25b6o2b2o4b4o2b6o2b8o4b4o2b6o173b2o$6b2o2b
4o4b2o6b2o8b4o4b2o25b8o2b2o2b2o4b6o2b2o4b6o4b6o175b2o$8b2o2b2o2b4o6b2o
2b4o6b4o6b2o19b8o2b2o2b2o4b6o2b2o4b6o4b6o175b2o$8b2o2b2o2b4o6b2o2b4o6b
4o6b2o19b4o2b2o2b2o6b4o2b2o4b2o2b2o4b4o2b6o173b2o$4b2o2b2o2b6o4b2o2b4o
2b2o2b4o4b2o25b4o2b2o2b2o6b4o2b2o4b2o2b2o4b4o2b6o173b2o$4b2o2b2o2b6o4b
2o2b4o2b2o2b4o4b2o25b2o2b6o6b2o2b2o2b8o2b4o8b2o2b2o173b2o$2b2o6b6o2b2o
2b2o8b2o4b8o2b2o21b2o2b6o6b2o2b2o2b8o2b4o8b2o2b2o173b2o$2b2o6b6o2b2o2b
2o8b2o4b8o2b2o21b2o2b2o2b2o2b6o2b8o4b2o2b2o4b4o2b4o173b2o$2b2o2b2o2b2o
6b2o8b4o2b2o2b4o4b2o23b2o2b2o2b2o2b6o2b8o4b2o2b2o4b4o2b4o173b2o$2b2o2b
2o2b2o6b2o8b4o2b2o2b4o4b2o23b4o2b8o2b4o6b2o2b10o4b2o2b2o175b2o$4b2o8b
2o4b6o2b2o10b4o2b2o2b2o19b4o2b8o2b4o6b2o2b10o4b2o2b2o175b2o$4b2o8b2o4b
6o2b2o10b4o2b2o2b2o19b10o2b18o2b4o4b2o2b4o2b2o173b2o$10b2o18b2o4b4o2b
2o4b2o21b10o2b18o2b4o4b2o2b4o2b2o173b2o$10b2o18b2o4b4o2b2o4b2o21b14o2b
2o2b4o4b6o2b10o2b4o173b2o$14b2o2b2o4b4o6b2o10b2o23b14o2b2o2b4o4b6o2b
10o2b4o173b2o$14b2o2b2o4b4o6b2o10b2o23b10o2b2o4b16o2b2o4b10o173b2o$10b
2o2b4o16b2o2b4o29b10o2b2o4b16o2b2o4b10o173b2o$10b2o2b4o16b2o2b4o29b10o
2b8o2b8o2b2o2b16o173b2o$10b2o8b2o8b2o2b2o35b10o2b8o2b8o2b2o2b16o173b2o
$10b2o8b2o8b2o2b2o35b40o2b10o173b2o$40b2o29b40o2b10o173b2o$40b2o254b2o
$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o
$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o
$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o
$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o
$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o
$296b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$30b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o236b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o$32b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o234b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$
30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o234b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o$30b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o236b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$32b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o234b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o
$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o236b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o$32b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o234b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$30b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o236b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o
$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o234b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o$30b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o236b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$32b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o234b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o
$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o236b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o$32b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o234b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$30b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o236b2o$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o
$32b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o234b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o236b2o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o236b2o$296b2o$296b2o$296b
2o$296b2o$296b2o$296b2o$296b2o$296b2o$296b2o!
This is the thread for those. I have a few questions to start with:
What rule does the example above emulate?
What other rules (other than 2x2, which is well known) do this too, and what CA do they emulate?

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

Re: CA that behave similar to 2x2

Post by 137ben » October 17th, 2010, 6:51 pm

In B345/S4567, most soups become low period oscillators. However, random arrangements of 2x2 blocks tend to become very high period oscillators.
For example:

Code: Select all

x = 40, y = 40, rule = B345/S4567
4o6b8o2b2o2b2o4b10o$4o6b8o2b2o2b2o4b10o$4b2o2b6o2b4o2b6o4b4o2b2o$4b2o
2b6o2b4o2b6o4b4o2b2o$2b10o6b2o2b12o$2b10o6b2o2b12o$2b4o2b4o2b2o2b6o4b
4o2b2o$2b4o2b4o2b2o2b6o4b4o2b2o$2o4b2o6b2o2b8o4b2o2b6o$2o4b2o6b2o2b8o
4b2o2b6o$4b2o2b4o2b4o2b4o2b2o4b6o$4b2o2b4o2b4o2b4o2b2o4b6o$2o2b2o6b10o
2b6o4b4o$2o2b2o6b10o2b6o4b4o$4b2o2b4o12b2o2b2o2b2o2b2o$4b2o2b4o12b2o2b
2o2b2o2b2o$8o2b4o10b2o8b4o$8o2b4o10b2o8b4o$6b2o10b4o2b8o2b2o2b2o$6b2o
10b4o2b8o2b2o2b2o$2b8o4b2o4b2o6b2o4b6o$2b8o4b2o4b2o6b2o4b6o$6o2b2o2b2o
2b2o4b6o2b4o4b2o$6o2b2o2b2o2b2o4b6o2b4o4b2o$8b6o4b2o4b6o2b2o4b2o$8b6o
4b2o4b6o2b2o4b2o$2o2b12o4b4o2b4o2b2o$2o2b12o4b4o2b4o2b2o$2b2o6b4o2b2o
2b8o$2b2o6b4o2b2o2b8o$4o4b2o4b4o2b2o6b2o2b4o2b2o$4o4b2o4b4o2b2o6b2o2b
4o2b2o$2o2b4o4b10o10b2o4b2o$2o2b4o4b10o10b2o4b2o$4b2o10b2o6b2o4b2o2b4o
$4b2o10b2o6b2o4b2o2b4o$2b2o8b10o6b4o4b2o$2b2o8b10o6b4o4b2o$6b4o8b4o6b
4o4b2o$6b4o8b4o6b4o4b2o!
Eventually becomes an oscillator of extremely high period. I ran it for over 2 million generations, then ran oscar...which is still going. So far its checked 1,400,000 generations for oscillation and hasn't found anything yet.

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Nathaniel
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Re: CA that behave similar to 2x2

Post by Nathaniel » October 17th, 2010, 8:27 pm

Awesomeness wrote:What other rules (other than 2x2, which is well known) do this too, and what CA do they emulate?
A Life-like cellular automaton emulates a Margolus block cellular automaton (like 2x2) if and only if, in its rulestring, B3 = S5, B4 = S4, B5 = S6 = S7, and B1 = B2 = S3 (where that notation means, for example, that birth occurs for 3 neighbors if and only if survival occurs for 5 neighbors). This can be seen by arranging four 2x2 squares and requiring that the center 2x2 block in the next generation always be made up of the same color.

Anyway, your rule is part of the family of rules B34/S45 - B34678/S012458 that all emulate the same block automaton. 137ben's rule is of the family B345/S4567 - B345678/S1245678.

Awesomeness
Posts: 126
Joined: April 5th, 2009, 7:30 am

Re: CA that behave similar to 2x2

Post by Awesomeness » October 18th, 2010, 4:42 pm

Are there other families? And what automaton do they simulate?

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

Re: CA that behave similar to 2x2

Post by 137ben » October 18th, 2010, 6:46 pm

The 4096 rules which meet the requirements Nathanial gave emulate 64 different blockic CA.

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