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1D global synchronisation CA

For discussion of other cellular automata.

1D global synchronisation CA

Postby Freywa » November 29th, 2018, 4:01 am

The following rule is incorrectly presented on Wikipedia as a majority problem-solving 1D CA. Rather, from almost all initial configurations on a torus it reaches a final synchronous configuration alternating between all zeros and all ones.

This rule was found by Das, Crutchfield, Mitchell and Hansen in this paper using a genetic algorithm. The rule uses a neighbourhood of 7 cells, which I've emulated here using three cells to a state, hence 9 states including the quiescent one.

@RULE DCMHSync

A globally synchronising 1D cellular automaton by Das, Crutchfield, Mitchell and Hanson:
http://web.cecs.pdx.edu/~mm/EGSCA.pdf
Each pixel holds three bits of data, with state 1 = 000, state 2 = 001, ..., state 8 = 111.
When giving a random seed, the fill density should be set to 100%.

The paper gives the rulestring as FEB1C6EA B8E0C4DA 6484A5AA F410C8A0,
the result of applying the CA to 0000000, 0000001, etc.

@TABLE
n_states:9
neighborhood:Moore
symmetries:none

0,1,1,0,0,0,0,0,1,8
0,1,2,0,0,0,0,0,1,8
0,1,3,0,0,0,0,0,1,8
0,1,4,0,0,0,0,0,1,8
0,1,5,0,0,0,0,0,1,8
0,1,6,0,0,0,0,0,1,8
0,1,7,0,0,0,0,0,1,8
0,1,8,0,0,0,0,0,1,7
0,2,1,0,0,0,0,0,1,8
0,2,2,0,0,0,0,0,1,7
0,2,3,0,0,0,0,0,1,8
0,2,4,0,0,0,0,0,1,8
0,2,5,0,0,0,0,0,1,7
0,2,6,0,0,0,0,0,1,7
0,2,7,0,0,0,0,0,1,5
0,2,8,0,0,0,0,0,1,6
0,3,1,0,0,0,0,0,1,8
0,3,2,0,0,0,0,0,1,8
0,3,3,0,0,0,0,0,1,5
0,3,4,0,0,0,0,0,1,5
0,3,5,0,0,0,0,0,1,7
0,3,6,0,0,0,0,0,1,8
0,3,7,0,0,0,0,0,1,8
0,3,8,0,0,0,0,0,1,7
0,4,1,0,0,0,0,0,1,6
0,4,2,0,0,0,0,0,1,6
0,4,3,0,0,0,0,0,1,6
0,4,4,0,0,0,0,0,1,5
0,4,5,0,0,0,0,0,1,2
0,4,6,0,0,0,0,0,1,1
0,4,7,0,0,0,0,0,1,4
0,4,8,0,0,0,0,0,1,3
0,5,1,0,0,0,0,0,1,8
0,5,2,0,0,0,0,0,1,7
0,5,3,0,0,0,0,0,1,8
0,5,4,0,0,0,0,0,1,8
0,5,5,0,0,0,0,0,1,2
0,5,6,0,0,0,0,0,1,1
0,5,7,0,0,0,0,0,1,1
0,5,8,0,0,0,0,0,1,1
0,6,1,0,0,0,0,0,1,6
0,6,2,0,0,0,0,0,1,6
0,6,3,0,0,0,0,0,1,8
0,6,4,0,0,0,0,0,1,7
0,6,5,0,0,0,0,0,1,7
0,6,6,0,0,0,0,0,1,7
0,6,7,0,0,0,0,0,1,5
0,6,8,0,0,0,0,0,1,5
0,7,1,0,0,0,0,0,1,4
0,7,2,0,0,0,0,0,1,4
0,7,3,0,0,0,0,0,1,3
0,7,4,0,0,0,0,0,1,3
0,7,5,0,0,0,0,0,1,3
0,7,6,0,0,0,0,0,1,4
0,7,7,0,0,0,0,0,1,1
0,7,8,0,0,0,0,0,1,1
0,8,1,0,0,0,0,0,1,4
0,8,2,0,0,0,0,0,1,4
0,8,3,0,0,0,0,0,1,1
0,8,4,0,0,0,0,0,1,2
0,8,5,0,0,0,0,0,1,8
0,8,6,0,0,0,0,0,1,7
0,8,7,0,0,0,0,0,1,6
0,8,8,0,0,0,0,0,1,5
0,1,1,0,0,0,0,0,2,7
0,1,2,0,0,0,0,0,2,8
0,1,3,0,0,0,0,0,2,6
0,1,4,0,0,0,0,0,2,5
0,1,5,0,0,0,0,0,2,7
0,1,6,0,0,0,0,0,2,8
0,1,7,0,0,0,0,0,2,7
0,1,8,0,0,0,0,0,2,7
0,2,1,0,0,0,0,0,2,4
0,2,2,0,0,0,0,0,2,3
0,2,3,0,0,0,0,0,2,1
0,2,4,0,0,0,0,0,2,1
0,2,5,0,0,0,0,0,2,1
0,2,6,0,0,0,0,0,2,2
0,2,7,0,0,0,0,0,2,1
0,2,8,0,0,0,0,0,2,1
0,3,1,0,0,0,0,0,2,4
0,3,2,0,0,0,0,0,2,3
0,3,3,0,0,0,0,0,2,4
0,3,4,0,0,0,0,0,2,3
0,3,5,0,0,0,0,0,2,7
0,3,6,0,0,0,0,0,2,8
0,3,7,0,0,0,0,0,2,5
0,3,8,0,0,0,0,0,2,6
0,4,1,0,0,0,0,0,2,6
0,4,2,0,0,0,0,0,2,5
0,4,3,0,0,0,0,0,2,6
0,4,4,0,0,0,0,0,2,5
0,4,5,0,0,0,0,0,2,2
0,4,6,0,0,0,0,0,2,1
0,4,7,0,0,0,0,0,2,2
0,4,8,0,0,0,0,0,2,1
0,5,1,0,0,0,0,0,2,8
0,5,2,0,0,0,0,0,2,8
0,5,3,0,0,0,0,0,2,8
0,5,4,0,0,0,0,0,2,8
0,5,5,0,0,0,0,0,2,5
0,5,6,0,0,0,0,0,2,6
0,5,7,0,0,0,0,0,2,5
0,5,8,0,0,0,0,0,2,5
0,6,1,0,0,0,0,0,2,5
0,6,2,0,0,0,0,0,2,5
0,6,3,0,0,0,0,0,2,7
0,6,4,0,0,0,0,0,2,8
0,6,5,0,0,0,0,0,2,1
0,6,6,0,0,0,0,0,2,1
0,6,7,0,0,0,0,0,2,1
0,6,8,0,0,0,0,0,2,1
0,7,1,0,0,0,0,0,2,8
0,7,2,0,0,0,0,0,2,8
0,7,3,0,0,0,0,0,2,7
0,7,4,0,0,0,0,0,2,7
0,7,5,0,0,0,0,0,2,2
0,7,6,0,0,0,0,0,2,1
0,7,7,0,0,0,0,0,2,3
0,7,8,0,0,0,0,0,2,3
0,8,1,0,0,0,0,0,2,8
0,8,2,0,0,0,0,0,2,7
0,8,3,0,0,0,0,0,2,6
0,8,4,0,0,0,0,0,2,5
0,8,5,0,0,0,0,0,2,3
0,8,6,0,0,0,0,0,2,3
0,8,7,0,0,0,0,0,2,1
0,8,8,0,0,0,0,0,2,1
0,1,1,0,0,0,0,0,3,6
0,1,2,0,0,0,0,0,3,6
0,1,3,0,0,0,0,0,3,8
0,1,4,0,0,0,0,0,3,8
0,1,5,0,0,0,0,0,3,4
0,1,6,0,0,0,0,0,3,4
0,1,7,0,0,0,0,0,3,2
0,1,8,0,0,0,0,0,3,1
0,2,1,0,0,0,0,0,3,6
0,2,2,0,0,0,0,0,3,5
0,2,3,0,0,0,0,0,3,8
0,2,4,0,0,0,0,0,3,8
0,2,5,0,0,0,0,0,3,5
0,2,6,0,0,0,0,0,3,5
0,2,7,0,0,0,0,0,3,5
0,2,8,0,0,0,0,0,3,6
0,3,1,0,0,0,0,0,3,8
0,3,2,0,0,0,0,0,3,8
0,3,3,0,0,0,0,0,3,5
0,3,4,0,0,0,0,0,3,5
0,3,5,0,0,0,0,0,3,1
0,3,6,0,0,0,0,0,3,2
0,3,7,0,0,0,0,0,3,2
0,3,8,0,0,0,0,0,3,1
0,4,1,0,0,0,0,0,3,2
0,4,2,0,0,0,0,0,3,2
0,4,3,0,0,0,0,0,3,4
0,4,4,0,0,0,0,0,3,3
0,4,5,0,0,0,0,0,3,2
0,4,6,0,0,0,0,0,3,1
0,4,7,0,0,0,0,0,3,2
0,4,8,0,0,0,0,0,3,1
0,5,1,0,0,0,0,0,3,8
0,5,2,0,0,0,0,0,3,7
0,5,3,0,0,0,0,0,3,6
0,5,4,0,0,0,0,0,3,6
0,5,5,0,0,0,0,0,3,8
0,5,6,0,0,0,0,0,3,7
0,5,7,0,0,0,0,0,3,5
0,5,8,0,0,0,0,0,3,5
0,6,1,0,0,0,0,0,3,6
0,6,2,0,0,0,0,0,3,6
0,6,3,0,0,0,0,0,3,8
0,6,4,0,0,0,0,0,3,7
0,6,5,0,0,0,0,0,3,1
0,6,6,0,0,0,0,0,3,1
0,6,7,0,0,0,0,0,3,3
0,6,8,0,0,0,0,0,3,3
0,7,1,0,0,0,0,0,3,4
0,7,2,0,0,0,0,0,3,4
0,7,3,0,0,0,0,0,3,1
0,7,4,0,0,0,0,0,3,1
0,7,5,0,0,0,0,0,3,3
0,7,6,0,0,0,0,0,3,4
0,7,7,0,0,0,0,0,3,1
0,7,8,0,0,0,0,0,3,1
0,8,1,0,0,0,0,0,3,4
0,8,2,0,0,0,0,0,3,4
0,8,3,0,0,0,0,0,3,1
0,8,4,0,0,0,0,0,3,2
0,8,5,0,0,0,0,0,3,4
0,8,6,0,0,0,0,0,3,3
0,8,7,0,0,0,0,0,3,2
0,8,8,0,0,0,0,0,3,1
0,1,1,0,0,0,0,0,4,7
0,1,2,0,0,0,0,0,4,8
0,1,3,0,0,0,0,0,4,8
0,1,4,0,0,0,0,0,4,7
0,1,5,0,0,0,0,0,4,7
0,1,6,0,0,0,0,0,4,8
0,1,7,0,0,0,0,0,4,7
0,1,8,0,0,0,0,0,4,7
0,2,1,0,0,0,0,0,4,2
0,2,2,0,0,0,0,0,4,1
0,2,3,0,0,0,0,0,4,3
0,2,4,0,0,0,0,0,4,3
0,2,5,0,0,0,0,0,4,1
0,2,6,0,0,0,0,0,4,2
0,2,7,0,0,0,0,0,4,1
0,2,8,0,0,0,0,0,4,1
0,3,1,0,0,0,0,0,4,2
0,3,2,0,0,0,0,0,4,1
0,3,3,0,0,0,0,0,4,2
0,3,4,0,0,0,0,0,4,1
0,3,5,0,0,0,0,0,4,5
0,3,6,0,0,0,0,0,4,6
0,3,7,0,0,0,0,0,4,7
0,3,8,0,0,0,0,0,4,8
0,4,1,0,0,0,0,0,4,2
0,4,2,0,0,0,0,0,4,1
0,4,3,0,0,0,0,0,4,2
0,4,4,0,0,0,0,0,4,1
0,4,5,0,0,0,0,0,4,2
0,4,6,0,0,0,0,0,4,1
0,4,7,0,0,0,0,0,4,2
0,4,8,0,0,0,0,0,4,1
0,5,1,0,0,0,0,0,4,8
0,5,2,0,0,0,0,0,4,8
0,5,3,0,0,0,0,0,4,8
0,5,4,0,0,0,0,0,4,8
0,5,5,0,0,0,0,0,4,5
0,5,6,0,0,0,0,0,4,6
0,5,7,0,0,0,0,0,4,5
0,5,8,0,0,0,0,0,4,5
0,6,1,0,0,0,0,0,4,3
0,6,2,0,0,0,0,0,4,3
0,6,3,0,0,0,0,0,4,1
0,6,4,0,0,0,0,0,4,2
0,6,5,0,0,0,0,0,4,5
0,6,6,0,0,0,0,0,4,5
0,6,7,0,0,0,0,0,4,5
0,6,8,0,0,0,0,0,4,5
0,7,1,0,0,0,0,0,4,8
0,7,2,0,0,0,0,0,4,8
0,7,3,0,0,0,0,0,4,5
0,7,4,0,0,0,0,0,4,5
0,7,5,0,0,0,0,0,4,4
0,7,6,0,0,0,0,0,4,3
0,7,7,0,0,0,0,0,4,1
0,7,8,0,0,0,0,0,4,1
0,8,1,0,0,0,0,0,4,6
0,8,2,0,0,0,0,0,4,5
0,8,3,0,0,0,0,0,4,6
0,8,4,0,0,0,0,0,4,5
0,8,5,0,0,0,0,0,4,1
0,8,6,0,0,0,0,0,4,1
0,8,7,0,0,0,0,0,4,1
0,8,8,0,0,0,0,0,4,1
0,1,1,0,0,0,0,0,5,4
0,1,2,0,0,0,0,0,5,4
0,1,3,0,0,0,0,0,5,4
0,1,4,0,0,0,0,0,5,4
0,1,5,0,0,0,0,0,5,8
0,1,6,0,0,0,0,0,5,8
0,1,7,0,0,0,0,0,5,8
0,1,8,0,0,0,0,0,5,7
0,2,1,0,0,0,0,0,5,8
0,2,2,0,0,0,0,0,5,7
0,2,3,0,0,0,0,0,5,8
0,2,4,0,0,0,0,0,5,8
0,2,5,0,0,0,0,0,5,3
0,2,6,0,0,0,0,0,5,3
0,2,7,0,0,0,0,0,5,1
0,2,8,0,0,0,0,0,5,2
0,3,1,0,0,0,0,0,5,4
0,3,2,0,0,0,0,0,5,4
0,3,3,0,0,0,0,0,5,1
0,3,4,0,0,0,0,0,5,1
0,3,5,0,0,0,0,0,5,7
0,3,6,0,0,0,0,0,5,8
0,3,7,0,0,0,0,0,5,8
0,3,8,0,0,0,0,0,5,7
0,4,1,0,0,0,0,0,5,2
0,4,2,0,0,0,0,0,5,2
0,4,3,0,0,0,0,0,5,2
0,4,4,0,0,0,0,0,5,1
0,4,5,0,0,0,0,0,5,2
0,4,6,0,0,0,0,0,5,1
0,4,7,0,0,0,0,0,5,4
0,4,8,0,0,0,0,0,5,3
0,5,1,0,0,0,0,0,5,8
0,5,2,0,0,0,0,0,5,7
0,5,3,0,0,0,0,0,5,8
0,5,4,0,0,0,0,0,5,8
0,5,5,0,0,0,0,0,5,2
0,5,6,0,0,0,0,0,5,1
0,5,7,0,0,0,0,0,5,1
0,5,8,0,0,0,0,0,5,1
0,6,1,0,0,0,0,0,5,2
0,6,2,0,0,0,0,0,5,2
0,6,3,0,0,0,0,0,5,4
0,6,4,0,0,0,0,0,5,3
0,6,5,0,0,0,0,0,5,3
0,6,6,0,0,0,0,0,5,3
0,6,7,0,0,0,0,0,5,1
0,6,8,0,0,0,0,0,5,1
0,7,1,0,0,0,0,0,5,4
0,7,2,0,0,0,0,0,5,4
0,7,3,0,0,0,0,0,5,3
0,7,4,0,0,0,0,0,5,3
0,7,5,0,0,0,0,0,5,7
0,7,6,0,0,0,0,0,5,8
0,7,7,0,0,0,0,0,5,5
0,7,8,0,0,0,0,0,5,5
0,8,1,0,0,0,0,0,5,4
0,8,2,0,0,0,0,0,5,4
0,8,3,0,0,0,0,0,5,1
0,8,4,0,0,0,0,0,5,2
0,8,5,0,0,0,0,0,5,4
0,8,6,0,0,0,0,0,5,3
0,8,7,0,0,0,0,0,5,2
0,8,8,0,0,0,0,0,5,1
0,1,1,0,0,0,0,0,6,7
0,1,2,0,0,0,0,0,6,8
0,1,3,0,0,0,0,0,6,6
0,1,4,0,0,0,0,0,6,5
0,1,5,0,0,0,0,0,6,3
0,1,6,0,0,0,0,0,6,4
0,1,7,0,0,0,0,0,6,3
0,1,8,0,0,0,0,0,6,3
0,2,1,0,0,0,0,0,6,8
0,2,2,0,0,0,0,0,6,7
0,2,3,0,0,0,0,0,6,5
0,2,4,0,0,0,0,0,6,5
0,2,5,0,0,0,0,0,6,1
0,2,6,0,0,0,0,0,6,2
0,2,7,0,0,0,0,0,6,1
0,2,8,0,0,0,0,0,6,1
0,3,1,0,0,0,0,0,6,4
0,3,2,0,0,0,0,0,6,3
0,3,3,0,0,0,0,0,6,4
0,3,4,0,0,0,0,0,6,3
0,3,5,0,0,0,0,0,6,7
0,3,6,0,0,0,0,0,6,8
0,3,7,0,0,0,0,0,6,5
0,3,8,0,0,0,0,0,6,6
0,4,1,0,0,0,0,0,6,2
0,4,2,0,0,0,0,0,6,1
0,4,3,0,0,0,0,0,6,2
0,4,4,0,0,0,0,0,6,1
0,4,5,0,0,0,0,0,6,6
0,4,6,0,0,0,0,0,6,5
0,4,7,0,0,0,0,0,6,6
0,4,8,0,0,0,0,0,6,5
0,5,1,0,0,0,0,0,6,8
0,5,2,0,0,0,0,0,6,8
0,5,3,0,0,0,0,0,6,8
0,5,4,0,0,0,0,0,6,8
0,5,5,0,0,0,0,0,6,1
0,5,6,0,0,0,0,0,6,2
0,5,7,0,0,0,0,0,6,1
0,5,8,0,0,0,0,0,6,1
0,6,1,0,0,0,0,0,6,5
0,6,2,0,0,0,0,0,6,5
0,6,3,0,0,0,0,0,6,7
0,6,4,0,0,0,0,0,6,8
0,6,5,0,0,0,0,0,6,1
0,6,6,0,0,0,0,0,6,1
0,6,7,0,0,0,0,0,6,1
0,6,8,0,0,0,0,0,6,1
0,7,1,0,0,0,0,0,6,8
0,7,2,0,0,0,0,0,6,8
0,7,3,0,0,0,0,0,6,7
0,7,4,0,0,0,0,0,6,7
0,7,5,0,0,0,0,0,6,2
0,7,6,0,0,0,0,0,6,1
0,7,7,0,0,0,0,0,6,3
0,7,8,0,0,0,0,0,6,3
0,8,1,0,0,0,0,0,6,8
0,8,2,0,0,0,0,0,6,7
0,8,3,0,0,0,0,0,6,6
0,8,4,0,0,0,0,0,6,5
0,8,5,0,0,0,0,0,6,3
0,8,6,0,0,0,0,0,6,3
0,8,7,0,0,0,0,0,6,1
0,8,8,0,0,0,0,0,6,1
0,1,1,0,0,0,0,0,7,6
0,1,2,0,0,0,0,0,7,6
0,1,3,0,0,0,0,0,7,8
0,1,4,0,0,0,0,0,7,8
0,1,5,0,0,0,0,0,7,8
0,1,6,0,0,0,0,0,7,8
0,1,7,0,0,0,0,0,7,6
0,1,8,0,0,0,0,0,7,5
0,2,1,0,0,0,0,0,7,6
0,2,2,0,0,0,0,0,7,5
0,2,3,0,0,0,0,0,7,8
0,2,4,0,0,0,0,0,7,8
0,2,5,0,0,0,0,0,7,5
0,2,6,0,0,0,0,0,7,5
0,2,7,0,0,0,0,0,7,5
0,2,8,0,0,0,0,0,7,6
0,3,1,0,0,0,0,0,7,4
0,3,2,0,0,0,0,0,7,4
0,3,3,0,0,0,0,0,7,1
0,3,4,0,0,0,0,0,7,1
0,3,5,0,0,0,0,0,7,5
0,3,6,0,0,0,0,0,7,6
0,3,7,0,0,0,0,0,7,6
0,3,8,0,0,0,0,0,7,5
0,4,1,0,0,0,0,0,7,2
0,4,2,0,0,0,0,0,7,2
0,4,3,0,0,0,0,0,7,4
0,4,4,0,0,0,0,0,7,3
0,4,5,0,0,0,0,0,7,2
0,4,6,0,0,0,0,0,7,1
0,4,7,0,0,0,0,0,7,2
0,4,8,0,0,0,0,0,7,1
0,5,1,0,0,0,0,0,7,4
0,5,2,0,0,0,0,0,7,3
0,5,3,0,0,0,0,0,7,2
0,5,4,0,0,0,0,0,7,2
0,5,5,0,0,0,0,0,7,4
0,5,6,0,0,0,0,0,7,3
0,5,7,0,0,0,0,0,7,1
0,5,8,0,0,0,0,0,7,1
0,6,1,0,0,0,0,0,7,2
0,6,2,0,0,0,0,0,7,2
0,6,3,0,0,0,0,0,7,4
0,6,4,0,0,0,0,0,7,3
0,6,5,0,0,0,0,0,7,5
0,6,6,0,0,0,0,0,7,5
0,6,7,0,0,0,0,0,7,7
0,6,8,0,0,0,0,0,7,7
0,7,1,0,0,0,0,0,7,4
0,7,2,0,0,0,0,0,7,4
0,7,3,0,0,0,0,0,7,1
0,7,4,0,0,0,0,0,7,1
0,7,5,0,0,0,0,0,7,3
0,7,6,0,0,0,0,0,7,4
0,7,7,0,0,0,0,0,7,1
0,7,8,0,0,0,0,0,7,1
0,8,1,0,0,0,0,0,7,4
0,8,2,0,0,0,0,0,7,4
0,8,3,0,0,0,0,0,7,1
0,8,4,0,0,0,0,0,7,2
0,8,5,0,0,0,0,0,7,4
0,8,6,0,0,0,0,0,7,3
0,8,7,0,0,0,0,0,7,2
0,8,8,0,0,0,0,0,7,1
0,1,1,0,0,0,0,0,8,7
0,1,2,0,0,0,0,0,8,8
0,1,3,0,0,0,0,0,8,8
0,1,4,0,0,0,0,0,8,7
0,1,5,0,0,0,0,0,8,7
0,1,6,0,0,0,0,0,8,8
0,1,7,0,0,0,0,0,8,7
0,1,8,0,0,0,0,0,8,7
0,2,1,0,0,0,0,0,8,2
0,2,2,0,0,0,0,0,8,1
0,2,3,0,0,0,0,0,8,3
0,2,4,0,0,0,0,0,8,3
0,2,5,0,0,0,0,0,8,1
0,2,6,0,0,0,0,0,8,2
0,2,7,0,0,0,0,0,8,1
0,2,8,0,0,0,0,0,8,1
0,3,1,0,0,0,0,0,8,6
0,3,2,0,0,0,0,0,8,5
0,3,3,0,0,0,0,0,8,6
0,3,4,0,0,0,0,0,8,5
0,3,5,0,0,0,0,0,8,1
0,3,6,0,0,0,0,0,8,2
0,3,7,0,0,0,0,0,8,3
0,3,8,0,0,0,0,0,8,4
0,4,1,0,0,0,0,0,8,2
0,4,2,0,0,0,0,0,8,1
0,4,3,0,0,0,0,0,8,2
0,4,4,0,0,0,0,0,8,1
0,4,5,0,0,0,0,0,8,2
0,4,6,0,0,0,0,0,8,1
0,4,7,0,0,0,0,0,8,2
0,4,8,0,0,0,0,0,8,1
0,5,1,0,0,0,0,0,8,8
0,5,2,0,0,0,0,0,8,8
0,5,3,0,0,0,0,0,8,8
0,5,4,0,0,0,0,0,8,8
0,5,5,0,0,0,0,0,8,1
0,5,6,0,0,0,0,0,8,2
0,5,7,0,0,0,0,0,8,1
0,5,8,0,0,0,0,0,8,1
0,6,1,0,0,0,0,0,8,7
0,6,2,0,0,0,0,0,8,7
0,6,3,0,0,0,0,0,8,5
0,6,4,0,0,0,0,0,8,6
0,6,5,0,0,0,0,0,8,1
0,6,6,0,0,0,0,0,8,1
0,6,7,0,0,0,0,0,8,1
0,6,8,0,0,0,0,0,8,1
0,7,1,0,0,0,0,0,8,4
0,7,2,0,0,0,0,0,8,4
0,7,3,0,0,0,0,0,8,1
0,7,4,0,0,0,0,0,8,1
0,7,5,0,0,0,0,0,8,4
0,7,6,0,0,0,0,0,8,3
0,7,7,0,0,0,0,0,8,1
0,7,8,0,0,0,0,0,8,1
0,8,1,0,0,0,0,0,8,2
0,8,2,0,0,0,0,0,8,1
0,8,3,0,0,0,0,0,8,2
0,8,4,0,0,0,0,0,8,1
0,8,5,0,0,0,0,0,8,1
0,8,6,0,0,0,0,0,8,1
0,8,7,0,0,0,0,0,8,1
0,8,8,0,0,0,0,0,8,1

@COLORS
0  30  30  30
1  48  48  48
2  72  72  72
3  72  72  72
4  96  96  96
5  72  72  72
6  96  96  96
7  96  96  96
8 120 120 120

@ICONS

XPM
"7 56 4 1"
". c #313030"
"A c #787878"
"B c #606060"
"C c #484848"
"......."
"......."
"......."
"......."
"......."
"......."
"......."

"....CAA"
"....CAA"
"....CAA"
"....CAA"
"....CAA"
"....CAA"
"....CAA"

"..BAB.."
"..BAB.."
"..BAB.."
"..BAB.."
"..BAB.."
"..BAB.."
"..BAB.."

"..BAAAA"
"..BAAAA"
"..BAAAA"
"..BAAAA"
"..BAAAA"
"..BAAAA"
"..BAAAA"

"AAC...."
"AAC...."
"AAC...."
"AAC...."
"AAC...."
"AAC...."
"AAC...."

"AAC.CAA"
"AAC.CAA"
"AAC.CAA"
"AAC.CAA"
"AAC.CAA"
"AAC.CAA"
"AAC.CAA"

"AAAAB.."
"AAAAB.."
"AAAAB.."
"AAAAB.."
"AAAAB.."
"AAAAB.."
"AAAAB.."

"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"
"AAAAAAA"

XPM
"15 120 2 1"
". c #313030"
"A c #787878"
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."
"..............."

"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"
"..........AAAAA"

".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."
".....AAAAA....."

".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"

"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."

"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"

"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."

"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"


Here is a configuration which does not reach global synchronisation:
x = 200, y = 1, rule = DCMHSync:T200,0
EBG2CD2GDAGCEFGFEBGBHFCACDAHEGBEBH2A2FAFGCGDG3E2FDFCAHEGEAGBFCD2EGA2D
FAGH2EH2CAH4GFCHCHED2FDGCACDADFDB2FAGCD2EGCGBFEG2CECA2EAEGABGB2HDCDCB
4G2BA3BDBEBAFAFG4C2EDBEBFAH2GA2EF2C2GCFAEF2BABEDECEFHE!
Princess of Science, Parcly Taxel
User avatar
Freywa
 
Posts: 343
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

Re: 1D global synchronisation CA

Postby Freywa » November 29th, 2018, 6:05 am

And this is an actual majority rule – the Gacs–Kurdyumov–Levin rule, which correctly finds the majority in around 80% of cases.

@RULE GKLMajority

Gacs, Kurdyumov and Levin's 1D majority rule. Successfully finds the majority in ~80% of cases.
Each pixel holds three bits of data, with state 0 = 000, state 1 = 001, ..., state 7 = 111.

@TABLE
n_states:8
neighborhood:Moore
symmetries:none

0,0,1,0,0,0,0,0,0,0
0,0,2,0,0,0,0,0,0,0
0,0,3,0,0,0,0,0,0,0
0,0,4,0,0,0,0,0,0,0
0,0,5,0,0,0,0,0,0,0
0,0,6,0,0,0,0,0,0,0
0,0,7,0,0,0,0,0,0,0
0,1,0,0,0,0,0,0,0,0
0,1,1,0,0,0,0,0,0,1
0,1,2,0,0,0,0,0,0,0
0,1,3,0,0,0,0,0,0,1
0,1,4,0,0,0,0,0,0,1
0,1,5,0,0,0,0,0,0,1
0,1,6,0,0,0,0,0,0,1
0,1,7,0,0,0,0,0,0,1
0,2,0,0,0,0,0,0,0,0
0,2,1,0,0,0,0,0,0,0
0,2,2,0,0,0,0,0,0,2
0,2,3,0,0,0,0,0,0,2
0,2,4,0,0,0,0,0,0,0
0,2,5,0,0,0,0,0,0,0
0,2,6,0,0,0,0,0,0,2
0,2,7,0,0,0,0,0,0,2
0,3,0,0,0,0,0,0,0,2
0,3,1,0,0,0,0,0,0,3
0,3,2,0,0,0,0,0,0,2
0,3,3,0,0,0,0,0,0,3
0,3,4,0,0,0,0,0,0,3
0,3,5,0,0,0,0,0,0,3
0,3,6,0,0,0,0,0,0,3
0,3,7,0,0,0,0,0,0,3
0,4,0,0,0,0,0,0,0,0
0,4,1,0,0,0,0,0,0,0
0,4,2,0,0,0,0,0,0,0
0,4,3,0,0,0,0,0,0,0
0,4,4,0,0,0,0,0,0,4
0,4,5,0,0,0,0,0,0,4
0,4,6,0,0,0,0,0,0,4
0,4,7,0,0,0,0,0,0,4
0,5,0,0,0,0,0,0,0,0
0,5,1,0,0,0,0,0,0,1
0,5,2,0,0,0,0,0,0,0
0,5,3,0,0,0,0,0,0,1
0,5,4,0,0,0,0,0,0,5
0,5,5,0,0,0,0,0,0,5
0,5,6,0,0,0,0,0,0,5
0,5,7,0,0,0,0,0,0,5
0,6,0,0,0,0,0,0,0,4
0,6,1,0,0,0,0,0,0,4
0,6,2,0,0,0,0,0,0,6
0,6,3,0,0,0,0,0,0,6
0,6,4,0,0,0,0,0,0,4
0,6,5,0,0,0,0,0,0,4
0,6,6,0,0,0,0,0,0,6
0,6,7,0,0,0,0,0,0,6
0,7,0,0,0,0,0,0,0,6
0,7,1,0,0,0,0,0,0,7
0,7,2,0,0,0,0,0,0,6
0,7,3,0,0,0,0,0,0,7
0,7,4,0,0,0,0,0,0,7
0,7,5,0,0,0,0,0,0,7
0,7,6,0,0,0,0,0,0,7
0,7,7,0,0,0,0,0,0,7
0,0,0,0,0,0,0,0,1,0
0,0,1,0,0,0,0,0,1,0
0,0,2,0,0,0,0,0,1,0
0,0,3,0,0,0,0,0,1,0
0,0,4,0,0,0,0,0,1,0
0,0,5,0,0,0,0,0,1,0
0,0,6,0,0,0,0,0,1,0
0,0,7,0,0,0,0,0,1,0
0,1,0,0,0,0,0,0,1,0
0,1,1,0,0,0,0,0,1,1
0,1,2,0,0,0,0,0,1,0
0,1,3,0,0,0,0,0,1,1
0,1,4,0,0,0,0,0,1,1
0,1,5,0,0,0,0,0,1,1
0,1,6,0,0,0,0,0,1,1
0,1,7,0,0,0,0,0,1,1
0,2,0,0,0,0,0,0,1,1
0,2,1,0,0,0,0,0,1,1
0,2,2,0,0,0,0,0,1,3
0,2,3,0,0,0,0,0,1,3
0,2,4,0,0,0,0,0,1,1
0,2,5,0,0,0,0,0,1,1
0,2,6,0,0,0,0,0,1,3
0,2,7,0,0,0,0,0,1,3
0,3,0,0,0,0,0,0,1,2
0,3,1,0,0,0,0,0,1,3
0,3,2,0,0,0,0,0,1,2
0,3,3,0,0,0,0,0,1,3
0,3,4,0,0,0,0,0,1,3
0,3,5,0,0,0,0,0,1,3
0,3,6,0,0,0,0,0,1,3
0,3,7,0,0,0,0,0,1,3
0,4,0,0,0,0,0,0,1,0
0,4,1,0,0,0,0,0,1,0
0,4,2,0,0,0,0,0,1,0
0,4,3,0,0,0,0,0,1,0
0,4,4,0,0,0,0,0,1,4
0,4,5,0,0,0,0,0,1,4
0,4,6,0,0,0,0,0,1,4
0,4,7,0,0,0,0,0,1,4
0,5,0,0,0,0,0,0,1,0
0,5,1,0,0,0,0,0,1,1
0,5,2,0,0,0,0,0,1,0
0,5,3,0,0,0,0,0,1,1
0,5,4,0,0,0,0,0,1,5
0,5,5,0,0,0,0,0,1,5
0,5,6,0,0,0,0,0,1,5
0,5,7,0,0,0,0,0,1,5
0,6,0,0,0,0,0,0,1,5
0,6,1,0,0,0,0,0,1,5
0,6,2,0,0,0,0,0,1,7
0,6,3,0,0,0,0,0,1,7
0,6,4,0,0,0,0,0,1,5
0,6,5,0,0,0,0,0,1,5
0,6,6,0,0,0,0,0,1,7
0,6,7,0,0,0,0,0,1,7
0,7,0,0,0,0,0,0,1,6
0,7,1,0,0,0,0,0,1,7
0,7,2,0,0,0,0,0,1,6
0,7,3,0,0,0,0,0,1,7
0,7,4,0,0,0,0,0,1,7
0,7,5,0,0,0,0,0,1,7
0,7,6,0,0,0,0,0,1,7
0,7,7,0,0,0,0,0,1,7
0,0,0,0,0,0,0,0,2,0
0,0,1,0,0,0,0,0,2,0
0,0,2,0,0,0,0,0,2,0
0,0,3,0,0,0,0,0,2,0
0,0,4,0,0,0,0,0,2,0
0,0,5,0,0,0,0,0,2,0
0,0,6,0,0,0,0,0,2,0
0,0,7,0,0,0,0,0,2,0
0,1,0,0,0,0,0,0,2,0
0,1,1,0,0,0,0,0,2,1
0,1,2,0,0,0,0,0,2,0
0,1,3,0,0,0,0,0,2,1
0,1,4,0,0,0,0,0,2,1
0,1,5,0,0,0,0,0,2,1
0,1,6,0,0,0,0,0,2,1
0,1,7,0,0,0,0,0,2,1
0,2,0,0,0,0,0,0,2,0
0,2,1,0,0,0,0,0,2,0
0,2,2,0,0,0,0,0,2,2
0,2,3,0,0,0,0,0,2,2
0,2,4,0,0,0,0,0,2,0
0,2,5,0,0,0,0,0,2,0
0,2,6,0,0,0,0,0,2,2
0,2,7,0,0,0,0,0,2,2
0,3,0,0,0,0,0,0,2,2
0,3,1,0,0,0,0,0,2,3
0,3,2,0,0,0,0,0,2,2
0,3,3,0,0,0,0,0,2,3
0,3,4,0,0,0,0,0,2,3
0,3,5,0,0,0,0,0,2,3
0,3,6,0,0,0,0,0,2,3
0,3,7,0,0,0,0,0,2,3
0,4,0,0,0,0,0,0,2,2
0,4,1,0,0,0,0,0,2,2
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1  72  72  72
2  72  72  72
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4  72  72  72
5  96  96  96
6  96  96  96
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".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"
".....AAAAAAAAAA"

"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."
"AAAAA.........."

"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"
"AAAAA.....AAAAA"

"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."
"AAAAAAAAAA....."

"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"
"AAAAAAAAAAAAAAA"


To automatically generate starting patterns of a certain density, use the following Python script:

#!/usr/bin/env python3.7
from random import SystemRandom
rng = SystemRandom()

def gen3randombits(p): return (rng.random() < p) * 4 + (rng.random() < p) * 2 + (rng.random() < p)
transtable = ".ABCDEFG"
n, p = 200, 0.52 # width of Golly torus (number of bits / 3), probability that bit is 1

header = f"x = {n}, y = 1, rule = GKLMajority:T{n},0\n"
data = []
for q in range(n): data.append(transtable[gen3randombits(p)])
print(header + "".join(data) + '!')


Try it out on the following initial configuration:
x = 200, y = 1, rule = GKLMajority:T200,0
C.F.G3EF2GF.2EA.2FEGCBE2A2.2E3D.G.CGF.EA3CD.BD3AD2EDEB2CE.CABEBEBAG.C
.BG3BGCABEFCABA2.FCBECG.E2FCFGFEABFC2EFBG2F.CA2FEAB.FA2EADB2ECF2E.DA.
E2AE.2D2G2ADCGADAGC2E.DECFGBCAGCECDCGCBCAGFEB2GCE2DBFA.EB!
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