Revision History for A278466
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| A278466
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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 49", based on the 5-celled von Neumann neighborhood.
(history;
published version)
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#7 by Bruno Berselli at Wed Nov 23 02:51:21 EST 2016
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#6 by Robert Price at Tue Nov 22 21:37:26 EST 2016
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#5 by Robert Price at Tue Nov 22 21:37:21 EST 2016
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#4 by Robert Price at Tue Nov 22 21:32:39 EST 2016
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| LINKS
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Robert Price, <a href="/A278466/a278466.tmp.txt">Diagrams of first 20 stages</a>
Robert Price, <a href="/A278466/a278466.tmp.txt">Diagrams of first 20 stages</a>
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#3 by Robert Price at Tue Nov 22 21:32:23 EST 2016
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| LINKS
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Robert Price, <a href="/A278466/b278466.txt">Table of n, a(n) for n = 0..126</a>
Robert Price, <a href="/A278466/a278466.tmp.txt">Diagrams of first 20 stages</a>
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#2 by Robert Price at Tue Nov 22 21:31:51 EST 2016
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| NAME
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allocatedBinary 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 49", based on the 5-celled forvon RobertNeumann Priceneighborhood.
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| DATA
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1, 0, 1, 1100, 1, 111100, 1, 11111100, 1001, 1111100000, 1111, 111111100000, 1111, 11111111100100, 1, 1111111111111100, 11001001, 111111111000000000, 11111111, 11111111111001001100, 1, 1111111111111111111100, 1101011001, 111111111111100010000000, 1010111111
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| OFFSET
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0,4
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| COMMENTS
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Initialized with a single black (ON) cell at stage zero.
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| REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
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| LINKS
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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
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
<a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
<a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
<a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
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| MATHEMATICA
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CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=49; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]][[i]], Range[1, i]], 10], {i, 1, stages-1}]
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| KEYWORD
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allocated
nonn,easy
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| AUTHOR
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Robert Price, Nov 22 2016
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| STATUS
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approved
editing
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#1 by Robert Price at Tue Nov 22 21:31:51 EST 2016
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| NAME
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allocated for Robert Price
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| KEYWORD
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allocated
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| STATUS
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approved
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