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A271087 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 270", based on the 5-celled von Neumann neighborhood. 4
1, 5, 8, 21, 20, 28, 36, 76, 76, 48, 72, 124, 112, 145, 168, 284, 284, 112, 168, 252, 248, 304, 340, 432, 396, 352, 384, 552, 488, 636, 720, 1144, 1044, 532, 708, 900, 928, 864, 936, 1152, 1048, 1128, 1236, 1448, 1352, 1396, 1608, 1848, 1796, 1676, 1780 (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=270; 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: A340509 A198635 A178675 * A271693 A271281 A246330
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 30 2016
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)