Revision History for A271014
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| A271014
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Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 249", based on the 5-celled von Neumann neighborhood.
(history;
published version)
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#9 by Charles R Greathouse IV at Fri Jul 26 21:16:35 EDT 2024
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Partial sums of the number of active (ON,, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 249", based on the 5-celled von Neumann neighborhood.
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Discussion
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| Fri Jul 26
| 21:16
| OEIS Server: https://oeis.org/edit/global/2997
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#8 by Joerg Arndt at Tue Mar 29 13:19:41 EDT 2016
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#7 by Robert Price at Tue Mar 29 13:13:27 EDT 2016
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#6 by Robert Price at Tue Mar 29 13:13:23 EDT 2016
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| LINKS
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Robert Price, <a href="/A271014/b271014.txt">Table of n, a(n) for n = 0..128</a>
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approved
editing
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#5 by Joerg Arndt at Tue Mar 29 03:13:04 EDT 2016
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#4 by Michel Marcus at Tue Mar 29 03:02:39 EDT 2016
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#3 by Robert Price at Mon Mar 28 12:27:14 EDT 2016
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#2 by Robert Price at Mon Mar 28 12:27:10 EDT 2016
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allocatedPartial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 249", based on the 5-celled forvon RobertNeumann Priceneighborhood.
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| DATA
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1, 5, 18, 58, 83, 171, 252, 428, 489, 805, 929, 1353, 1570, 2130, 2427, 3255, 3479, 4543, 4920, 6168, 6653, 8221, 8877, 10765, 11402, 13586, 14491, 17071, 18067, 20988, 22332, 25585, 26737, 30589, 31881, 36062, 37682, 42299, 44007, 49332, 51252, 56972, 59288
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| OFFSET
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0,2
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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=249; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
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| CROSSREFS
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Cf. A271012.
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| KEYWORD
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allocated
nonn,easy
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| AUTHOR
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Robert Price, Mar 28 2016
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| STATUS
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approved
editing
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#1 by Robert Price at Mon Mar 28 12:27:10 EDT 2016
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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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