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A271258 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 324", based on the 5-celled von Neumann neighborhood. 1
3, 1, 7, -4, 16, 1, 15, -7, 11, -4, 48, -11, 23, 21, 55, -39, 27, -23, 63, 13, 71, 21, 75, -31, 51, -3, 107, 5, 51, 37, 123, -23, -29, 57, 95, 25, 115, 17, 187, -39, -5, -11, 155, 73, 83, 73, 147, -19, 39, -11, 203, 13, 147, 21, 219, -35, 95, 13, 219, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
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=324; 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[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A246316.
Sequence in context: A328461 A341494 A210198 * A100584 A185877 A135858
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 02 2016
STATUS
approved

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)