Revision History for A270127
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
|
| |
|
| A270127
|
|
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 86", based on the 5-celled von Neumann neighborhood.
(history;
published version)
|
| |
|
|
#9 by Charles R Greathouse IV at Fri Jul 26 21:16:32 EDT 2024
|
|
| NAME
|
Partial sums of the number of active (ON,, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 86", based on the 5-celled von Neumann neighborhood.
|
| |
|
|
Discussion
|
| Fri Jul 26
| 21:16
| OEIS Server: https://oeis.org/edit/global/2997
|
| |
| |
|
|
#8 by Joerg Arndt at Sat Mar 12 11:23:49 EST 2016
| |
| |
| |
|
|
#7 by Michel Marcus at Sat Mar 12 10:52:15 EST 2016
| |
| |
| |
|
|
#6 by Robert Price at Fri Mar 11 21:47:07 EST 2016
| |
| |
| |
|
|
#5 by Robert Price at Fri Mar 11 21:47:04 EST 2016
|
|
| LINKS
|
Robert Price, <a href="/A270127/b270127.txt">Table of n, a(n) for n = 0..128</a>
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#4 by N. J. A. Sloane at Fri Mar 11 21:22:25 EST 2016
| |
| |
| |
|
|
#3 by Robert Price at Fri Mar 11 15:55:15 EST 2016
| |
| |
| |
|
|
#2 by Robert Price at Fri Mar 11 15:55:11 EST 2016
|
|
| NAME
|
allocatedPartial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 86", based on the 5-celled forvon RobertNeumann Priceneighborhood.
|
|
| DATA
|
1, 6, 14, 38, 54, 102, 134, 230, 262, 358, 422, 614, 678, 870, 998, 1382, 1446, 1638, 1766, 2150, 2278, 2662, 2918, 3686, 3814, 4198, 4454, 5222, 5478, 6246, 6758, 8294, 8422, 8806, 9062, 9830, 10086, 10854, 11366, 12902, 13158, 13926, 14438, 15974, 16486
|
|
| OFFSET
|
0,2
|
|
| COMMENTS
|
Initialized with a single black (ON) cell at stage zero.
|
|
| REFERENCES
|
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
|
|
| LINKS
|
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>
|
|
| MATHEMATICA
|
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=86; 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 *)
|
|
| CROSSREFS
|
Cf. A270125.
|
|
| KEYWORD
|
allocated
nonn,easy
|
|
| AUTHOR
|
Robert Price, Mar 11 2016
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#1 by Robert Price at Fri Mar 11 15:55:11 EST 2016
|
|
| NAME
|
allocated for Robert Price
|
|
| KEYWORD
|
allocated
|
|
| STATUS
|
approved
|
| |
| |
|
|
