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A278870 Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 99", based on the 5-celled von Neumann neighborhood. 4

%I #7 Nov 29 2016 22:43:55

%S 1,1,1,1111,100,110111,0,11110111,0,1111111101,10001,111111111111,

%T 1010000,11111101010111,1010000,1111111111011111,100000100,

%U 111111110101111111,100010100,11111111110101010111,101010000,1111111111110101010101,101010101

%N Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 99", based on the 5-celled von Neumann neighborhood.

%C Initialized with a single black (ON) cell at stage zero.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

%H Robert Price, <a href="/A278870/b278870.txt">Table of n, a(n) for n = 0..126</a>

%H Robert Price, <a href="/A278870/a278870.tmp.txt">Diagrams of first 20 stages</a>

%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015

%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_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>

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

%t CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];

%t code=99; stages=128;

%t rule=IntegerDigits[code,2,10];

%t g=2*stages+1; (* Maximum size of grid *)

%t a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)

%t ca=a;

%t ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];

%t PrependTo[ca,a];

%t (* Trim full grid to reflect growth by one cell at each stage *)

%t k=(Length[ca[[1]]]+1)/2;

%t ca=Table[Table[Part[ca[[n]][[j]],Range[k+1-n,k-1+n]],{j,k+1-n,k-1+n}],{n,1,k}];

%t Table[FromDigits[Part[ca[[i]][[i]],Range[1,i]],10], {i,1,stages-1}]

%Y Cf. A278871, A278872, A278873.

%K nonn,easy

%O 0,4

%A _Robert Price_, Nov 29 2016

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)