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A266068 Binary representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell. 2

%I

%S 1,100,10,1111001,100,11111110011,1000,111111111100111,10000,

%T 1111111111111001111,100000,11111111111111110011111,1000000,

%U 111111111111111111100111111,10000000,1111111111111111111111001111111,100000000,11111111111111111111111110011111111

%N Binary representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

%C Rule 35 also generates this sequence.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A266068/b266068.txt">Table of n, a(n) for n = 0..999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F Empirical g.f.: (1+100*x-10001*x^2+109901*x^3+10000*x^4-120000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)). - _Colin Barker_, Dec 21 2015

%e From _Michael De Vlieger_, Dec 21 2015: (Start)

%e First 8 rows, replacing leading zeros with ".", the row converted to its binary equivalent at right:

%e 1 = 1

%e 1 0 0 = 100

%e . . . 1 0 = 10

%e 1 1 1 1 0 0 1 = 1111001

%e . . . . . . 1 0 0 = 100

%e 1 1 1 1 1 1 1 0 0 1 1 = 11111110011

%e . . . . . . . . . 1 0 0 0 = 1000

%e 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 = 111111111100111

%e (End)

%t rule = 3; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]]], {k,1,rows}]

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 20 2015

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Last modified September 22 11:29 EDT 2020. Contains 337289 sequences. (Running on oeis4.)