A374413 - OEIS

%I #12 Aug 04 2024 18:51:20

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

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

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

%N Second center column of elementary triangular automaton rule 210, 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 210 (11010010 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            |1|1|0|1|0|0|1|0|

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

%C Rule 210 is easy to describe: "change the state of cells that have one 1 neighbor".

%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="/A374413/b374413.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/?page=rule-210">Rule 210</a>.

%H Paul Cousin, <a href="https://youtu.be/6jfe_L0YTDc">Rule 210 video</a>.

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

%Y Cf. A372581, A374769.

%K nonn

%O 0

%A _Paul Cousin_, Jul 08 2024