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A266206 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 315", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 32, 13, 104, 25, 192, 53, 324, 65, 425, 121, 609, 120, 845, 101, 1136, 105, 1365, 232, 1621, 212, 2045, 248, 2297, 380, 2669, 533, 3032, 545, 3533, 573, 3968, 621, 4556, 725, 4940, 805, 5468, 961, 6084, 1101, 6608, 1105, 7360, 1205, 8048, 1269, 8652 (list; graph; refs; listen; history; text; internal format)
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, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=315; 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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A271129 A271152 A271164 * A271397 A264099 A271454
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 02 2016
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)