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Second center column of elementary triangular automaton rule 45, from a lone 1 cell.
2

%I #8 Aug 04 2024 18:51:27

%S 0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,

%T 0,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,1,

%U 0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0

%N Second center column of elementary triangular automaton rule 45, from a lone 1 cell.

%C An Elementary Triangular Automaton (ETA) is a cellular automaton in the triangular grid where cells hold binary states and rules are local to the first neighborhood. There are 256 possible ETA rules.

%C Rule 45 (101101 in binary):

%C -----------------------------------------------

%C |state of the cell |1|1|1|1|0|0|0|0|

%C |sum of the neighbors' states |3|2|1|0|3|2|1|0|

%C |cell's next state |0|0|1|0|1|1|0|1|

%C -----------------------------------------------

%C The second center column is the sequence of states of the direct neighbors of the initial 1 cell.

%D Paul Cousin, "Triangular Automata: The 256 Elementary Cellular Automata of the 2D Plane", Complex Systems, 33(2), 2024.

%H Paul Cousin, <a href="/A374769/b374769.txt">Table of n, a(n) for n = 0..4096</a>

%H Paul Cousin, <a href="https://arxiv.org/abs/2309.15795">Triangular Automata: The 256 Elementary Cellular Automata of the 2D Plane</a>, arXiv:2309.15795 [nlin.CG], 2023.

%H Paul Cousin, <a href="https://paulcousin.github.io/triangular-automata">Triangular Automata</a>

%H Paul Cousin, <a href="https://paulcousin.github.io/triangular-automata/rules.html?rule=45">Rule 45</a>

%H Paul Cousin, <a href="https://paulcousin.github.io/triangular-automata-mathematica/">Triangular Automata Mathematica Package</a>

%Y Cf. A374413.

%K nonn

%O 0

%A _Paul Cousin_, Jul 18 2024